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## ScienceDirect A behavioral study of "noise" in coordination games-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

### Citations

2372 |
Conditional Logit Analysis of Qualitative Choice Behavior
- McFadden
- 1974
(Show Context)
Citation Context ...tions, inertia, or trial-and-error experiments. Evolutionary game theory demonstrates that the exact nature of such individual-level deviations can crucially influence equilibrium selection (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). To study deviations, it is fundamental to justify the behavioral model relative to which a decision is considered a deviation. Most evolutionary game theory models focus on variants on myopic best-response (MBR) behavior, which assumes that agents maximize their individual payoffs in the current p... |

1324 |
Non-cooperative games,” The
- Nash
- 1951
(Show Context)
Citation Context ... study deviations, it is fundamental to justify the behavioral model relative to which a decision is considered a deviation. Most evolutionary game theory models focus on variants on myopic best-response (MBR) behavior, which assumes that agents maximize their individual payoffs in the current period by best-responding to others’ actions as previously sampled. The concept of myopic best response dates back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1995; Erev and Roth, 1998) make virtually identical predictions in our experiment. Hence, while we cannot be certain as to which precise underlying decision rule the s... |

1025 | Evolutionary Game Theory
- Weibull
- 1995
(Show Context)
Citation Context ...increase when players enter an experimental state of mind, which may be due to payoff losses or recent action changes (Young, 2009; Pradelski and Young, 2012). Related trial-and-error dynamics (Thuijsman et al., 1995; Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria (Pradelski and Young, 2012).3 Although the empirical literature on the three deviation assumptions is very limited, there are related strands of literature. There is empirical research on evolutionary dynamics related to replicator dynamics (Taylor and Jonker, 1978; Weibull, 1995). Examples include the evolutionary interpretation by Crawford (1991) of the seminal study by Van Huyck et al. (1990), as well as more recent experiments by Friedman and Ostrov (2013), Xu et al. (2013), Cason et al. (2014), Hoffman et al. (2015). These studies show that replication makes macro-predictions that correspond to observed system behavior such as cyclical patterns in rock-paper-scissor games. However, in contrast to our study, these studies test macro-predictions that follow from competing deviation assumptions and were not designed to directly test the behavioral assumptions about m... |

724 | A General Theory of Equilibrium Selection in Games
- Harsanyi, Selten
- 1988
(Show Context)
Citation Context ...onary dynamics. 2. Competing deviation assumptions We tested three competing deviation assumptions as used in theoretical models. First, we tested the assumption that deviations occur with constant probability. That is, agents play, for instance, MBR most of the time but occasionally deviate with some constant rate (Kandori et al., M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208 1971993; Young, 1993).1 In two-by-two coordination games, MBR dynamics that are perturbed by constant errors select, in the sense of “stochastic stability” (Foster and Young, 1990), the risk-dominant (Harsanyi and Selten, 1988) Nash equilibrium as errors vanish (Young, 1993; Blume, 1996; Peski, 2010). Second, we tested whether deviation rates are decreasing in their costliness vis-à-vis the prevalent choice. The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998; Blume, 2003; Myatt and Wallace, 2004; Alós-Ferrer and Netzer, 2010), particularly with regard to convergence times (Ellison, 1993; Yo... |

700 |
Re-examination of the perfectness concept for equilibrium points in extensive games
- Selten
- 1975
(Show Context)
Citation Context ...ve terminologies for deviations from an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word with regard to causality. There is a related but separate literature on noise in static situations of stochastic choice under risk (for example, Wilcox, 2008; Butler et al., 2012). These contributions study the effects of random perturbations of utility functions, rather than deviations from dynamic strategy protocols. Related static notions are the trembling-hand perfect (Selten, 1975), quantal response (McKelvey and Palfrey, 1995, 1998) and proper (Myerson, 1978) equilibrium concepts, which are static analogues of various dynamics. Our paper complements this line of research with the study of evolutionary dynamics. 2. Competing deviation assumptions We tested three competing deviation assumptions as used in theoretical models. First, we tested the assumption that deviations occur with constant probability. That is, agents play, for instance, MBR most of the time but occasionally deviate with some constant rate (Kandori et al., M. Mäs, H.H. Nax / Journal of Economic Theory ... |

644 | Quantal response equilibria for normal form games
- McKelvey, Palfrey
- 1995
(Show Context)
Citation Context ...rom an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word with regard to causality. There is a related but separate literature on noise in static situations of stochastic choice under risk (for example, Wilcox, 2008; Butler et al., 2012). These contributions study the effects of random perturbations of utility functions, rather than deviations from dynamic strategy protocols. Related static notions are the trembling-hand perfect (Selten, 1975), quantal response (McKelvey and Palfrey, 1995, 1998) and proper (Myerson, 1978) equilibrium concepts, which are static analogues of various dynamics. Our paper complements this line of research with the study of evolutionary dynamics. 2. Competing deviation assumptions We tested three competing deviation assumptions as used in theoretical models. First, we tested the assumption that deviations occur with constant probability. That is, agents play, for instance, MBR most of the time but occasionally deviate with some constant rate (Kandori et al., M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208 1971993; Young, 1993).1 In ... |

618 | Predicting how people play games: Reinforcement learning in experimental games with unique, mixed strategy equilibria
- Erev, Roth
- 1998
(Show Context)
Citation Context ...ung, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1995; Erev and Roth, 1998) make virtually identical predictions in our experiment. Hence, while we cannot be certain as to which precise underlying decision rule the subjects applied, we can be certain that decisions identified as deviations indeed deviated from the decision rule, whichever was applied by the subject. Alternative terminologies for deviations from an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word with regard to causality. There is a related but separate literature on n... |

525 | The Evolution of Conventions
- Young
- 1993
(Show Context)
Citation Context ...et.2015.12.010 0022-0531/© 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 196 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–2081. Introduction Individuals occasionally deviate from their prevailing behavioral rules because of, for instance, mistakes, misperceptions, inertia, or trial-and-error experiments. Evolutionary game theory demonstrates that the exact nature of such individual-level deviations can crucially influence equilibrium selection (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with p... |

462 |
Individual Strategy and Social Structure: An Evolutionary Theory of Institutions
- Young
- 2001
(Show Context)
Citation Context ...erturbed by constant errors select, in the sense of “stochastic stability” (Foster and Young, 1990), the risk-dominant (Harsanyi and Selten, 1988) Nash equilibrium as errors vanish (Young, 1993; Blume, 1996; Peski, 2010). Second, we tested whether deviation rates are decreasing in their costliness vis-à-vis the prevalent choice. The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998; Blume, 2003; Myatt and Wallace, 2004; Alós-Ferrer and Netzer, 2010), particularly with regard to convergence times (Ellison, 1993; Young, 1998, 2011a).2 A third set of deviation assumptions stems from payoff-based learning models (Hart and Mas-Colell, 2003, 2006; Foster and Young, 2006; Young, 2009), which share the assumption that agents adjust their behavior based on trial-and-error heuristics rather than bestresponse considerations. Consequently, deviations are assumed to depend on agents’ past experiences. Deviation rates have been assumed to increase when players enter an experimental s... |

347 |
The statistical mechanics of strategic interaction
- Blume
- 1993
(Show Context)
Citation Context ... (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). To study deviations, it is fundamental to justify the behavioral model relative to which a decision is considered a deviation. Most evolutionary game theory models focus on variants on myopic best-response (MBR) behavior, which assumes that agents maximize their individual payoffs in the current period by best-responding to others’ actions as previously sampled. The concept of myopic best response dates back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on m... |

308 | Learning, mutation, and the long run equilibria in games
- Kandori, Mailath, et al.
- 1993
(Show Context)
Citation Context ...dx.doi.org/10.1016/j.jet.2015.12.010 0022-0531/© 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 196 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–2081. Introduction Individuals occasionally deviate from their prevailing behavioral rules because of, for instance, mistakes, misperceptions, inertia, or trial-and-error experiments. Evolutionary game theory demonstrates that the exact nature of such individual-level deviations can crucially influence equilibrium selection (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii... |

255 |
Evolutionary stable strategies and game dynamics
- Taylor, Jonker
- 1978
(Show Context)
Citation Context ...tes have been assumed to increase when players enter an experimental state of mind, which may be due to payoff losses or recent action changes (Young, 2009; Pradelski and Young, 2012). Related trial-and-error dynamics (Thuijsman et al., 1995; Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria (Pradelski and Young, 2012).3 Although the empirical literature on the three deviation assumptions is very limited, there are related strands of literature. There is empirical research on evolutionary dynamics related to replicator dynamics (Taylor and Jonker, 1978; Weibull, 1995). Examples include the evolutionary interpretation by Crawford (1991) of the seminal study by Van Huyck et al. (1990), as well as more recent experiments by Friedman and Ostrov (2013), Xu et al. (2013), Cason et al. (2014), Hoffman et al. (2015). These studies show that replication makes macro-predictions that correspond to observed system behavior such as cyclical patterns in rock-paper-scissor games. However, in contrast to our study, these studies test macro-predictions that follow from competing deviation assumptions and were not designed to directly test the behavioral ass... |

247 |
Stochastic models of learning
- Bush, Mosteller
- 1955
(Show Context)
Citation Context ...usly sampled. The concept of myopic best response dates back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1995; Erev and Roth, 1998) make virtually identical predictions in our experiment. Hence, while we cannot be certain as to which precise underlying decision rule the subjects applied, we can be certain that decisions identified as deviations indeed deviated from the decision rule, whichever was applied by the subject. Alternative terminologies for deviations from an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviatio... |

231 | Tacit coordination games, strategic uncertainty, and coordination - Huyck, Battalio, et al. - 1990 |

215 | Quantal Response Equilibria in Extensive Form Games - McKelvey, Palfrey - 1998 |

205 |
Refinements of the Nash Equilibrium Concept,"
- MYERSON
- 1978
(Show Context)
Citation Context ...“trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word with regard to causality. There is a related but separate literature on noise in static situations of stochastic choice under risk (for example, Wilcox, 2008; Butler et al., 2012). These contributions study the effects of random perturbations of utility functions, rather than deviations from dynamic strategy protocols. Related static notions are the trembling-hand perfect (Selten, 1975), quantal response (McKelvey and Palfrey, 1995, 1998) and proper (Myerson, 1978) equilibrium concepts, which are static analogues of various dynamics. Our paper complements this line of research with the study of evolutionary dynamics. 2. Competing deviation assumptions We tested three competing deviation assumptions as used in theoretical models. First, we tested the assumption that deviations occur with constant probability. That is, agents play, for instance, MBR most of the time but occasionally deviate with some constant rate (Kandori et al., M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208 1971993; Young, 1993).1 In two-by-two coordination games, MBR... |

152 |
Learning, local interaction, and coordination
- Ellison
- 1993
(Show Context)
Citation Context ...and Selten, 1988) Nash equilibrium as errors vanish (Young, 1993; Blume, 1996; Peski, 2010). Second, we tested whether deviation rates are decreasing in their costliness vis-à-vis the prevalent choice. The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998; Blume, 2003; Myatt and Wallace, 2004; Alós-Ferrer and Netzer, 2010), particularly with regard to convergence times (Ellison, 1993; Young, 1998, 2011a).2 A third set of deviation assumptions stems from payoff-based learning models (Hart and Mas-Colell, 2003, 2006; Foster and Young, 2006; Young, 2009), which share the assumption that agents adjust their behavior based on trial-and-error heuristics rather than bestresponse considerations. Consequently, deviations are assumed to depend on agents’ past experiences. Deviation rates have been assumed to increase when players enter an experimental state of mind, which may be due to payoff losses or recent action changes (Young, 2009; Pradelski and Young, 2012). Related trial-an... |

143 | Stochastic evolutionary game dynamics,”
- Foster, Young
- 1990
(Show Context)
Citation Context ...s line of research with the study of evolutionary dynamics. 2. Competing deviation assumptions We tested three competing deviation assumptions as used in theoretical models. First, we tested the assumption that deviations occur with constant probability. That is, agents play, for instance, MBR most of the time but occasionally deviate with some constant rate (Kandori et al., M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208 1971993; Young, 1993).1 In two-by-two coordination games, MBR dynamics that are perturbed by constant errors select, in the sense of “stochastic stability” (Foster and Young, 1990), the risk-dominant (Harsanyi and Selten, 1988) Nash equilibrium as errors vanish (Young, 1993; Blume, 1996; Peski, 2010). Second, we tested whether deviation rates are decreasing in their costliness vis-à-vis the prevalent choice. The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998; Blume, 2003; Myatt and Wallace, 2004; Alós-Ferrer and Netzer, 2010), particularly with... |

140 |
Population Games and Evolutionary Dynamics.
- Sandholm
- 2010
(Show Context)
Citation Context ...cess article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 196 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–2081. Introduction Individuals occasionally deviate from their prevailing behavioral rules because of, for instance, mistakes, misperceptions, inertia, or trial-and-error experiments. Evolutionary game theory demonstrates that the exact nature of such individual-level deviations can crucially influence equilibrium selection (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). ... |

85 |
Evolution of Equilibria in the Long Run: A General Theory and Applications
- Kandori, Rob
- 1995
(Show Context)
Citation Context ... 2015 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 196 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–2081. Introduction Individuals occasionally deviate from their prevailing behavioral rules because of, for instance, mistakes, misperceptions, inertia, or trial-and-error experiments. Evolutionary game theory demonstrates that the exact nature of such individual-level deviations can crucially influence equilibrium selection (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-... |

84 | Uncoupled dynamics do not lead to nash equilibrium,”
- Hart, Colell
- 2003
(Show Context)
Citation Context ...her deviation rates are decreasing in their costliness vis-à-vis the prevalent choice. The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998; Blume, 2003; Myatt and Wallace, 2004; Alós-Ferrer and Netzer, 2010), particularly with regard to convergence times (Ellison, 1993; Young, 1998, 2011a).2 A third set of deviation assumptions stems from payoff-based learning models (Hart and Mas-Colell, 2003, 2006; Foster and Young, 2006; Young, 2009), which share the assumption that agents adjust their behavior based on trial-and-error heuristics rather than bestresponse considerations. Consequently, deviations are assumed to depend on agents’ past experiences. Deviation rates have been assumed to increase when players enter an experimental state of mind, which may be due to payoff losses or recent action changes (Young, 2009; Pradelski and Young, 2012). Related trial-and-error dynamics (Thuijsman et al., 1995; Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfa... |

48 | How noise matters.
- Blume
- 2003
(Show Context)
Citation Context ...ished by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 196 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–2081. Introduction Individuals occasionally deviate from their prevailing behavioral rules because of, for instance, mistakes, misperceptions, inertia, or trial-and-error experiments. Evolutionary game theory demonstrates that the exact nature of such individual-level deviations can crucially influence equilibrium selection (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavio... |

41 | Regret testing: learning to play nash equilibrium without knowing you have an opponent. Theoretical Economics,
- Foster, Young
- 2006
(Show Context)
Citation Context ...g in their costliness vis-à-vis the prevalent choice. The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998; Blume, 2003; Myatt and Wallace, 2004; Alós-Ferrer and Netzer, 2010), particularly with regard to convergence times (Ellison, 1993; Young, 1998, 2011a).2 A third set of deviation assumptions stems from payoff-based learning models (Hart and Mas-Colell, 2003, 2006; Foster and Young, 2006; Young, 2009), which share the assumption that agents adjust their behavior based on trial-and-error heuristics rather than bestresponse considerations. Consequently, deviations are assumed to depend on agents’ past experiences. Deviation rates have been assumed to increase when players enter an experimental state of mind, which may be due to payoff losses or recent action changes (Young, 2009; Pradelski and Young, 2012). Related trial-and-error dynamics (Thuijsman et al., 1995; Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria ... |

40 |
Learning the evolutionarily stable strategy.
- Harley
- 1981
(Show Context)
Citation Context ...es back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1995; Erev and Roth, 1998) make virtually identical predictions in our experiment. Hence, while we cannot be certain as to which precise underlying decision rule the subjects applied, we can be certain that decisions identified as deviations indeed deviated from the decision rule, whichever was applied by the subject. Alternative terminologies for deviations from an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word with regard to ca... |

40 | Stochastic uncoupled dynamics and Nash equilibrium. - Hart, Mas-Colell - 2006 |

37 | An evolutionary interpretation of Van Huyck, Battalio and Beil’s experimental results on coordination.
- Crawford
- 1991
(Show Context)
Citation Context ... be due to payoff losses or recent action changes (Young, 2009; Pradelski and Young, 2012). Related trial-and-error dynamics (Thuijsman et al., 1995; Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria (Pradelski and Young, 2012).3 Although the empirical literature on the three deviation assumptions is very limited, there are related strands of literature. There is empirical research on evolutionary dynamics related to replicator dynamics (Taylor and Jonker, 1978; Weibull, 1995). Examples include the evolutionary interpretation by Crawford (1991) of the seminal study by Van Huyck et al. (1990), as well as more recent experiments by Friedman and Ostrov (2013), Xu et al. (2013), Cason et al. (2014), Hoffman et al. (2015). These studies show that replication makes macro-predictions that correspond to observed system behavior such as cyclical patterns in rock-paper-scissor games. However, in contrast to our study, these studies test macro-predictions that follow from competing deviation assumptions and were not designed to directly test the behavioral assumptions about micro-level deviations.4 The empirical study that comes closest to our... |

36 |
The spread of innovations in social networks.
- Montanari, Saberi
- 2010
(Show Context)
Citation Context ...vier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 196 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–2081. Introduction Individuals occasionally deviate from their prevailing behavioral rules because of, for instance, mistakes, misperceptions, inertia, or trial-and-error experiments. Evolutionary game theory demonstrates that the exact nature of such individual-level deviations can crucially influence equilibrium selection (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski an... |

33 | The logit-response dynamics.
- Alos-Ferrer, Netzer
- 2010
(Show Context)
Citation Context ... “stochastic stability” (Foster and Young, 1990), the risk-dominant (Harsanyi and Selten, 1988) Nash equilibrium as errors vanish (Young, 1993; Blume, 1996; Peski, 2010). Second, we tested whether deviation rates are decreasing in their costliness vis-à-vis the prevalent choice. The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998; Blume, 2003; Myatt and Wallace, 2004; Alós-Ferrer and Netzer, 2010), particularly with regard to convergence times (Ellison, 1993; Young, 1998, 2011a).2 A third set of deviation assumptions stems from payoff-based learning models (Hart and Mas-Colell, 2003, 2006; Foster and Young, 2006; Young, 2009), which share the assumption that agents adjust their behavior based on trial-and-error heuristics rather than bestresponse considerations. Consequently, deviations are assumed to depend on agents’ past experiences. Deviation rates have been assumed to increase when players enter an experimental state of mind, which may be due to payoff losses or recent action chan... |

33 | Global nash convergence of foster and young’s regret testing.
- Germano, Lugosi
- 2007
(Show Context)
Citation Context ...cting have been proposed by Newton (2012a) (constant errors) and Newton (2012b), Sawa (2014) (logit response). 3 A dynamic is “uncoupled” when not dependent on information about others’ utility functions (Hart and Mas-Colell, 2003), strengthened to “completely uncoupled” when only information about own actions and own payoffs is considered (Foster and Young, 2006). Uncoupled dynamics, in general, do not lead to Nash equilibrium (Hart and Mas-Colell, 2003, 2006). However, under certain genericity conditions, many completely uncoupled dynamics do select Nash equilibrium (Foster and Young, 2006; Germano and Lugosi, 2007; Marden et al. 2009, 2014; Pradelski and Young, 2012; Skyrms, 2012; Huttegger and Skyrms, 2012; Huttegger et al., 2014). 4 A companion paper (Maes and Helbing, 2014) uses our data to test competing macro predictions of deterministic and noisy micro-models. 198 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208Fig. 1. Network types: Illustration of the two network structures studied in the experiment. Letters and colors depict the option for which the assigned participant earned payoff P . In the left-hand-side network nodes have mixed neighborhoods (Case ONE), whereas nodes are ... |

33 | Payoff-based dynamics for multi-player weakly acyclic games.
- Marden, Young, et al.
- 2009
(Show Context)
Citation Context ...y Newton (2012a) (constant errors) and Newton (2012b), Sawa (2014) (logit response). 3 A dynamic is “uncoupled” when not dependent on information about others’ utility functions (Hart and Mas-Colell, 2003), strengthened to “completely uncoupled” when only information about own actions and own payoffs is considered (Foster and Young, 2006). Uncoupled dynamics, in general, do not lead to Nash equilibrium (Hart and Mas-Colell, 2003, 2006). However, under certain genericity conditions, many completely uncoupled dynamics do select Nash equilibrium (Foster and Young, 2006; Germano and Lugosi, 2007; Marden et al. 2009, 2014; Pradelski and Young, 2012; Skyrms, 2012; Huttegger and Skyrms, 2012; Huttegger et al., 2014). 4 A companion paper (Maes and Helbing, 2014) uses our data to test competing macro predictions of deterministic and noisy micro-models. 198 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208Fig. 1. Network types: Illustration of the two network structures studied in the experiment. Letters and colors depict the option for which the assigned participant earned payoff P . In the left-hand-side network nodes have mixed neighborhoods (Case ONE), whereas nodes are isolated in the righ... |

32 | Learning by trial and error
- Young
- 2009
(Show Context)
Citation Context ...ontaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). To study deviations, it is fundamental to justify the behavioral model relative to which a decision is considered a deviation. Most evolutionary game theory models focus on variants on myopic best-response (MBR) behavior, which assumes that agents maximize their individual payoffs in the current period by best-responding to others’ actions as previously sampled. The concept of myopic best response dates back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately om... |

26 |
A Theory of Adaptive Economic Behavior.
- Cross
- 1983
(Show Context)
Citation Context ... Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1995; Erev and Roth, 1998) make virtually identical predictions in our experiment. Hence, while we cannot be certain as to which precise underlying decision rule the subjects applied, we can be certain that decisions identified as deviations indeed deviated from the decision rule, whichever was applied by the subject. Alternative terminologies for deviations from an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word with regard to causality. Ther... |

23 |
Stochastic Models for Binary Discrete Choice under Risk: A Critical Primer and Econometric Comparison.”
- Wilcox
- 2008
(Show Context)
Citation Context ... cannot be certain as to which precise underlying decision rule the subjects applied, we can be certain that decisions identified as deviations indeed deviated from the decision rule, whichever was applied by the subject. Alternative terminologies for deviations from an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word with regard to causality. There is a related but separate literature on noise in static situations of stochastic choice under risk (for example, Wilcox, 2008; Butler et al., 2012). These contributions study the effects of random perturbations of utility functions, rather than deviations from dynamic strategy protocols. Related static notions are the trembling-hand perfect (Selten, 1975), quantal response (McKelvey and Palfrey, 1995, 1998) and proper (Myerson, 1978) equilibrium concepts, which are static analogues of various dynamics. Our paper complements this line of research with the study of evolutionary dynamics. 2. Competing deviation assumptions We tested three competing deviation assumptions as used in theoretical models. First, we tested t... |

21 | Achieving Pareto optimality through distributed learning - Marden, Young, et al. - 2012 |

17 | Automata, matching, and foraging behavior in bees,”
- Thuijsman, Peleg, et al.
- 1995
(Show Context)
Citation Context ...1a).2 A third set of deviation assumptions stems from payoff-based learning models (Hart and Mas-Colell, 2003, 2006; Foster and Young, 2006; Young, 2009), which share the assumption that agents adjust their behavior based on trial-and-error heuristics rather than bestresponse considerations. Consequently, deviations are assumed to depend on agents’ past experiences. Deviation rates have been assumed to increase when players enter an experimental state of mind, which may be due to payoff losses or recent action changes (Young, 2009; Pradelski and Young, 2012). Related trial-and-error dynamics (Thuijsman et al., 1995; Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria (Pradelski and Young, 2012).3 Although the empirical literature on the three deviation assumptions is very limited, there are related strands of literature. There is empirical research on evolutionary dynamics related to replicator dynamics (Taylor and Jonker, 1978; Weibull, 1995). Examples include the evolutionary interpretation by Crawford (1991) of the seminal study by Van Huyck et al. (1990), as well as more recent experiments by Friedman and Ostrov (2013), Xu et al. (2013),... |

16 | Learning efficient Nash equilibria in distributed systems
- Pradelski, Young
- 2012
(Show Context)
Citation Context ...Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). To study deviations, it is fundamental to justify the behavioral model relative to which a decision is considered a deviation. Most evolutionary game theory models focus on variants on myopic best-response (MBR) behavior, which assumes that agents maximize their individual payoffs in the current period by best-responding to others’ actions as previously sampled. The concept of myopic best response dates back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published versi... |

12 | The dynamics of social innovation.
- Young
- 2011
(Show Context)
Citation Context ...e costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). To study deviations, it is fundamental to justify the behavioral model relative to which a decision is considered a deviation. Most evolutionary game theory models focus on variants on myopic best-response (MBR) behavior, which assumes that agents maximize their individual payoffs in the current period by best-responding to others’ actions as previously sampled. The concept of myopic best response dates back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1995; Erev and ... |

10 | Cycles and instability in a rock–paper–scissors population game: a continuous time experiment.
- Cason, Friedman, et al.
- 2014
(Show Context)
Citation Context ... Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria (Pradelski and Young, 2012).3 Although the empirical literature on the three deviation assumptions is very limited, there are related strands of literature. There is empirical research on evolutionary dynamics related to replicator dynamics (Taylor and Jonker, 1978; Weibull, 1995). Examples include the evolutionary interpretation by Crawford (1991) of the seminal study by Van Huyck et al. (1990), as well as more recent experiments by Friedman and Ostrov (2013), Xu et al. (2013), Cason et al. (2014), Hoffman et al. (2015). These studies show that replication makes macro-predictions that correspond to observed system behavior such as cyclical patterns in rock-paper-scissor games. However, in contrast to our study, these studies test macro-predictions that follow from competing deviation assumptions and were not designed to directly test the behavioral assumptions about micro-level deviations.4 The empirical study that comes closest to ours is a recent experiment on two-by-two coordination games under random re-matching by Lim and Neary (2014). These games have the advantage that most of t... |

7 | Generalized risk-dominance and asymmetric dynamics.
- Peski
- 2010
(Show Context)
Citation Context ...ssumptions as used in theoretical models. First, we tested the assumption that deviations occur with constant probability. That is, agents play, for instance, MBR most of the time but occasionally deviate with some constant rate (Kandori et al., M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208 1971993; Young, 1993).1 In two-by-two coordination games, MBR dynamics that are perturbed by constant errors select, in the sense of “stochastic stability” (Foster and Young, 1990), the risk-dominant (Harsanyi and Selten, 1988) Nash equilibrium as errors vanish (Young, 1993; Blume, 1996; Peski, 2010). Second, we tested whether deviation rates are decreasing in their costliness vis-à-vis the prevalent choice. The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998; Blume, 2003; Myatt and Wallace, 2004; Alós-Ferrer and Netzer, 2010), particularly with regard to convergence times (Ellison, 1993; Young, 1998, 2011a).2 A third set of deviation assumptions stems from payoff... |

6 |
Recontracting and stochastic stability in cooperative games.
- Newton
- 2012
(Show Context)
Citation Context ...er the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 196 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–2081. Introduction Individuals occasionally deviate from their prevailing behavioral rules because of, for instance, mistakes, misperceptions, inertia, or trial-and-error experiments. Evolutionary game theory demonstrates that the exact nature of such individual-level deviations can crucially influence equilibrium selection (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). To study devia... |

5 |
Adaptive play by idiosyncratic agents.
- Myatt, Wallace
- 2004
(Show Context)
Citation Context ...s select, in the sense of “stochastic stability” (Foster and Young, 1990), the risk-dominant (Harsanyi and Selten, 1988) Nash equilibrium as errors vanish (Young, 1993; Blume, 1996; Peski, 2010). Second, we tested whether deviation rates are decreasing in their costliness vis-à-vis the prevalent choice. The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998; Blume, 2003; Myatt and Wallace, 2004; Alós-Ferrer and Netzer, 2010), particularly with regard to convergence times (Ellison, 1993; Young, 1998, 2011a).2 A third set of deviation assumptions stems from payoff-based learning models (Hart and Mas-Colell, 2003, 2006; Foster and Young, 2006; Young, 2009), which share the assumption that agents adjust their behavior based on trial-and-error heuristics rather than bestresponse considerations. Consequently, deviations are assumed to depend on agents’ past experiences. Deviation rates have been assumed to increase when players enter an experimental state of mind, which may be due to payo... |

5 |
Coalitional Stochastic Stability in Games, Networks
- Sawa
- 2013
(Show Context)
Citation Context ...ddresses related macro-effects. However, two-by-two coordination games imply little variance in the deviation costs that players face, which makes it difficult, if not impossible, to 1 The subtle difference between Kandori et al. (1993) and Young (1993) is that of mistakes from “imitation” (Kandori et al., 1993) versus MBR (Young, 1993; Kandori and Rob, 1995). We focus on the latter, because our subjects were not informed about others’ payoffs, which precluded imitation. 2 Generalizations with coalitional recontracting have been proposed by Newton (2012a) (constant errors) and Newton (2012b), Sawa (2014) (logit response). 3 A dynamic is “uncoupled” when not dependent on information about others’ utility functions (Hart and Mas-Colell, 2003), strengthened to “completely uncoupled” when only information about own actions and own payoffs is considered (Foster and Young, 2006). Uncoupled dynamics, in general, do not lead to Nash equilibrium (Hart and Mas-Colell, 2003, 2006). However, under certain genericity conditions, many completely uncoupled dynamics do select Nash equilibrium (Foster and Young, 2006; Germano and Lugosi, 2007; Marden et al. 2009, 2014; Pradelski and Young, 2012; Skyrms, 2012;... |

5 | Markov Learning Models for Multiperson Situations, I. The Theory,"
- SUPPES, ATKINSON
- 1959
(Show Context)
Citation Context ...of myopic best response dates back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1995; Erev and Roth, 1998) make virtually identical predictions in our experiment. Hence, while we cannot be certain as to which precise underlying decision rule the subjects applied, we can be certain that decisions identified as deviations indeed deviated from the decision rule, whichever was applied by the subject. Alternative terminologies for deviations from an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word wit... |

4 | Cycle frequency in standard rock–paper–scissors games: evidence from experimental economics.
- Xu, Zhou, et al.
- 2013
(Show Context)
Citation Context ...sman et al., 1995; Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria (Pradelski and Young, 2012).3 Although the empirical literature on the three deviation assumptions is very limited, there are related strands of literature. There is empirical research on evolutionary dynamics related to replicator dynamics (Taylor and Jonker, 1978; Weibull, 1995). Examples include the evolutionary interpretation by Crawford (1991) of the seminal study by Van Huyck et al. (1990), as well as more recent experiments by Friedman and Ostrov (2013), Xu et al. (2013), Cason et al. (2014), Hoffman et al. (2015). These studies show that replication makes macro-predictions that correspond to observed system behavior such as cyclical patterns in rock-paper-scissor games. However, in contrast to our study, these studies test macro-predictions that follow from competing deviation assumptions and were not designed to directly test the behavioral assumptions about micro-level deviations.4 The empirical study that comes closest to ours is a recent experiment on two-by-two coordination games under random re-matching by Lim and Neary (2014). These games have the adv... |

3 |
Evolutionary dynamics over continuous action space for population games that arise from symmetric two-player games.
- Friedman, Ostrov
- 2013
(Show Context)
Citation Context ...al-and-error dynamics (Thuijsman et al., 1995; Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria (Pradelski and Young, 2012).3 Although the empirical literature on the three deviation assumptions is very limited, there are related strands of literature. There is empirical research on evolutionary dynamics related to replicator dynamics (Taylor and Jonker, 1978; Weibull, 1995). Examples include the evolutionary interpretation by Crawford (1991) of the seminal study by Van Huyck et al. (1990), as well as more recent experiments by Friedman and Ostrov (2013), Xu et al. (2013), Cason et al. (2014), Hoffman et al. (2015). These studies show that replication makes macro-predictions that correspond to observed system behavior such as cyclical patterns in rock-paper-scissor games. However, in contrast to our study, these studies test macro-predictions that follow from competing deviation assumptions and were not designed to directly test the behavioral assumptions about micro-level deviations.4 The empirical study that comes closest to ours is a recent experiment on two-by-two coordination games under random re-matching by Lim and Neary (2014). These ... |

3 | Evolutionary bargaining with intentional idiosyncratic play.
- Naidu, Bowles, et al.
- 2010
(Show Context)
Citation Context ...: the type of the subject (w or g), the decision period t , and a dummy measuring whether (coded 1) or not (coded 0) the MBR was the same color as the type of the subject and, thus, resulted in payoff P . Demonstrating the robustness of our findings, including the three control variables did not affect the findings from the final model. Subject type and period t did not have significant effects, but deviation rates were significantly lower when subjects faced a decision where the MBR was the subject’s preferred option, which lends support to the assumption that deviations can be directed (Naidu et al., 2010; Hwang and Newton, 2014). When the MBR was the subject’s M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208 205preferred option, the overall deviation rate was 1%. Otherwise, subjects deviate with a rate of about 9%. The period effect from the control-variable model from Table 2 is small and insignificant, which shows that the changes in deviation rates over time depicted in Fig. 2 are explained by the independent variables of the model and the evolutionary dynamics they imply (related to stochastic stability, Foster and Young, 1990). For example, decreasing deviation rates resu... |

3 |
Non-Cooperative Games,” Ph.D. thesis,
- Nash
- 1950
(Show Context)
Citation Context ... depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). To study deviations, it is fundamental to justify the behavioral model relative to which a decision is considered a deviation. Most evolutionary game theory models focus on variants on myopic best-response (MBR) behavior, which assumes that agents maximize their individual payoffs in the current period by best-responding to others’ actions as previously sampled. The concept of myopic best response dates back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1... |

2 |
Coalitional stochastic stability.
- Newton
- 2012
(Show Context)
Citation Context ...er the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 196 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–2081. Introduction Individuals occasionally deviate from their prevailing behavioral rules because of, for instance, mistakes, misperceptions, inertia, or trial-and-error experiments. Evolutionary game theory demonstrates that the exact nature of such individual-level deviations can crucially influence equilibrium selection (Kandori et al., 1993; Young, 1993, 1998, 2011a; Kandori and Rob, 1995; Blume, 2003; Montaneri and Saberi, 2010; Sandholm, 2010; Newton, 2012a; Bergin and Lipman, 1996). In this paper, we therefore tested competing assumptions regarding the nature of deviations, analyzing data from a laboratory experiment on coordination games played in fixed networks. Using classical discrete-choice estimation techniques (McFadden, 1974), we tested, in particular, the assumptions that deviations (i) occur with a constant probability (Kandori et al., 1993; Young, 1993), (ii) depend on the costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). To study devia... |

2 |
Commentary: John Nash and evolutionary game theory.
- Young
- 2011
(Show Context)
Citation Context ...e costs of deviating (Blume, 1993), and (iii) vary with payoff patterns related to trial-and-error behavior (Young, 2009; Pradelski and Young, 2012). To study deviations, it is fundamental to justify the behavioral model relative to which a decision is considered a deviation. Most evolutionary game theory models focus on variants on myopic best-response (MBR) behavior, which assumes that agents maximize their individual payoffs in the current period by best-responding to others’ actions as previously sampled. The concept of myopic best response dates back to the Nash equilibrium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1995; Erev and ... |

1 |
Testing the ‘standard’ model of stochastic choice under risk.
- Butler, Isoni, et al.
- 2012
(Show Context)
Citation Context ...tain as to which precise underlying decision rule the subjects applied, we can be certain that decisions identified as deviations indeed deviated from the decision rule, whichever was applied by the subject. Alternative terminologies for deviations from an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word with regard to causality. There is a related but separate literature on noise in static situations of stochastic choice under risk (for example, Wilcox, 2008; Butler et al., 2012). These contributions study the effects of random perturbations of utility functions, rather than deviations from dynamic strategy protocols. Related static notions are the trembling-hand perfect (Selten, 1975), quantal response (McKelvey and Palfrey, 1995, 1998) and proper (Myerson, 1978) equilibrium concepts, which are static analogues of various dynamics. Our paper complements this line of research with the study of evolutionary dynamics. 2. Competing deviation assumptions We tested three competing deviation assumptions as used in theoretical models. First, we tested the assumption that dev... |

1 |
An experimental investigation of evolutionary dynamics in the rock–paper–scissors game.
- Hoffman, Suetens, et al.
- 2015
(Show Context)
Citation Context ...ve been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria (Pradelski and Young, 2012).3 Although the empirical literature on the three deviation assumptions is very limited, there are related strands of literature. There is empirical research on evolutionary dynamics related to replicator dynamics (Taylor and Jonker, 1978; Weibull, 1995). Examples include the evolutionary interpretation by Crawford (1991) of the seminal study by Van Huyck et al. (1990), as well as more recent experiments by Friedman and Ostrov (2013), Xu et al. (2013), Cason et al. (2014), Hoffman et al. (2015). These studies show that replication makes macro-predictions that correspond to observed system behavior such as cyclical patterns in rock-paper-scissor games. However, in contrast to our study, these studies test macro-predictions that follow from competing deviation assumptions and were not designed to directly test the behavioral assumptions about micro-level deviations.4 The empirical study that comes closest to ours is a recent experiment on two-by-two coordination games under random re-matching by Lim and Neary (2014). These games have the advantage that most of the theoretical literatu... |

1 |
Emergence of a signaling network with “probe and adjust”. In: Signaling, Commitment, and Emotion.
- Huttegger, Skyrms
- 2012
(Show Context)
Citation Context ...(logit response). 3 A dynamic is “uncoupled” when not dependent on information about others’ utility functions (Hart and Mas-Colell, 2003), strengthened to “completely uncoupled” when only information about own actions and own payoffs is considered (Foster and Young, 2006). Uncoupled dynamics, in general, do not lead to Nash equilibrium (Hart and Mas-Colell, 2003, 2006). However, under certain genericity conditions, many completely uncoupled dynamics do select Nash equilibrium (Foster and Young, 2006; Germano and Lugosi, 2007; Marden et al. 2009, 2014; Pradelski and Young, 2012; Skyrms, 2012; Huttegger and Skyrms, 2012; Huttegger et al., 2014). 4 A companion paper (Maes and Helbing, 2014) uses our data to test competing macro predictions of deterministic and noisy micro-models. 198 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208Fig. 1. Network types: Illustration of the two network structures studied in the experiment. Letters and colors depict the option for which the assigned participant earned payoff P . In the left-hand-side network nodes have mixed neighborhoods (Case ONE), whereas nodes are isolated in the right-hand-side network (Case TWO). test individual-level phenomena such as cos... |

1 |
Probe and adjust in information transfer games.
- Huttegger, Skyrms, et al.
- 2014
(Show Context)
Citation Context ...c is “uncoupled” when not dependent on information about others’ utility functions (Hart and Mas-Colell, 2003), strengthened to “completely uncoupled” when only information about own actions and own payoffs is considered (Foster and Young, 2006). Uncoupled dynamics, in general, do not lead to Nash equilibrium (Hart and Mas-Colell, 2003, 2006). However, under certain genericity conditions, many completely uncoupled dynamics do select Nash equilibrium (Foster and Young, 2006; Germano and Lugosi, 2007; Marden et al. 2009, 2014; Pradelski and Young, 2012; Skyrms, 2012; Huttegger and Skyrms, 2012; Huttegger et al., 2014). 4 A companion paper (Maes and Helbing, 2014) uses our data to test competing macro predictions of deterministic and noisy micro-models. 198 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208Fig. 1. Network types: Illustration of the two network structures studied in the experiment. Letters and colors depict the option for which the assigned participant earned payoff P . In the left-hand-side network nodes have mixed neighborhoods (Case ONE), whereas nodes are isolated in the right-hand-side network (Case TWO). test individual-level phenomena such as cost-sensitive deviation rat... |

1 | A classification of bargaining solutions by evolutionary origin. Working paper no. 2.
- Hwang, Newton
- 2014
(Show Context)
Citation Context ...subject (w or g), the decision period t , and a dummy measuring whether (coded 1) or not (coded 0) the MBR was the same color as the type of the subject and, thus, resulted in payoff P . Demonstrating the robustness of our findings, including the three control variables did not affect the findings from the final model. Subject type and period t did not have significant effects, but deviation rates were significantly lower when subjects faced a decision where the MBR was the subject’s preferred option, which lends support to the assumption that deviations can be directed (Naidu et al., 2010; Hwang and Newton, 2014). When the MBR was the subject’s M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208 205preferred option, the overall deviation rate was 1%. Otherwise, subjects deviate with a rate of about 9%. The period effect from the control-variable model from Table 2 is small and insignificant, which shows that the changes in deviation rates over time depicted in Fig. 2 are explained by the independent variables of the model and the evolutionary dynamics they imply (related to stochastic stability, Foster and Young, 1990). For example, decreasing deviation rates result from decreases in the ... |

1 |
An experimental investigation of stochastic stability. Working paper.
- Lim, Neary
- 2014
(Show Context)
Citation Context ...y Friedman and Ostrov (2013), Xu et al. (2013), Cason et al. (2014), Hoffman et al. (2015). These studies show that replication makes macro-predictions that correspond to observed system behavior such as cyclical patterns in rock-paper-scissor games. However, in contrast to our study, these studies test macro-predictions that follow from competing deviation assumptions and were not designed to directly test the behavioral assumptions about micro-level deviations.4 The empirical study that comes closest to ours is a recent experiment on two-by-two coordination games under random re-matching by Lim and Neary (2014). These games have the advantage that most of the theoretical literature, beginning with Kandori et al. (1993) and Young (1993), addresses related macro-effects. However, two-by-two coordination games imply little variance in the deviation costs that players face, which makes it difficult, if not impossible, to 1 The subtle difference between Kandori et al. (1993) and Young (1993) is that of mistakes from “imitation” (Kandori et al., 1993) versus MBR (Young, 1993; Kandori and Rob, 1995). We focus on the latter, because our subjects were not informed about others’ payoffs, which precluded imita... |

1 |
Noise in behavioral models can improve macro-predictions when micro-theories fail.
- Maes, Helbing
- 2014
(Show Context)
Citation Context ...tion about others’ utility functions (Hart and Mas-Colell, 2003), strengthened to “completely uncoupled” when only information about own actions and own payoffs is considered (Foster and Young, 2006). Uncoupled dynamics, in general, do not lead to Nash equilibrium (Hart and Mas-Colell, 2003, 2006). However, under certain genericity conditions, many completely uncoupled dynamics do select Nash equilibrium (Foster and Young, 2006; Germano and Lugosi, 2007; Marden et al. 2009, 2014; Pradelski and Young, 2012; Skyrms, 2012; Huttegger and Skyrms, 2012; Huttegger et al., 2014). 4 A companion paper (Maes and Helbing, 2014) uses our data to test competing macro predictions of deterministic and noisy micro-models. 198 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208Fig. 1. Network types: Illustration of the two network structures studied in the experiment. Letters and colors depict the option for which the assigned participant earned payoff P . In the left-hand-side network nodes have mixed neighborhoods (Case ONE), whereas nodes are isolated in the right-hand-side network (Case TWO). test individual-level phenomena such as cost-sensitive deviation rates. In our experiment, in contrast, subjects p... |

1 | Learning in a black box.
- Nax, Burton-Chellew, et al.
- 2013
(Show Context)
Citation Context ...iation assumptions stems from payoff-based learning models (Hart and Mas-Colell, 2003, 2006; Foster and Young, 2006; Young, 2009), which share the assumption that agents adjust their behavior based on trial-and-error heuristics rather than bestresponse considerations. Consequently, deviations are assumed to depend on agents’ past experiences. Deviation rates have been assumed to increase when players enter an experimental state of mind, which may be due to payoff losses or recent action changes (Young, 2009; Pradelski and Young, 2012). Related trial-and-error dynamics (Thuijsman et al., 1995; Nax et al., 2013) have been shown to select Nash equilibria (Young, 2009), even welfare-maximizing Nash equilibria (Pradelski and Young, 2012).3 Although the empirical literature on the three deviation assumptions is very limited, there are related strands of literature. There is empirical research on evolutionary dynamics related to replicator dynamics (Taylor and Jonker, 1978; Weibull, 1995). Examples include the evolutionary interpretation by Crawford (1991) of the seminal study by Van Huyck et al. (1990), as well as more recent experiments by Friedman and Ostrov (2013), Xu et al. (2013), Cason et al. (2014... |

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Learning in extensive-form games—experimental data and simple dynamic models in the intermediate term.
- Roth, Erev
- 1995
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Citation Context ...rium (Nash, 1950b; Young, 2011b) but the section on myopic best-response dynamics from Nash’s PhD thesis (Nash, 1950a) was unfortunately omitted in its published version (Nash, 1951). Based on our experimental data, statistical tests revealed that MBR (confined to a minimal memory length of one) accurately describes 96% of subjects’ decisions, leading us to define deviations as the remaining decisions. It is noteworthy that best-response models with longer memories and also simple models of reinforcement learning (Bush and Mosteller, 1955; Suppes and Atkinson, 1959; Harley, 1981; Cross, 1983; Roth and Erev, 1995; Erev and Roth, 1998) make virtually identical predictions in our experiment. Hence, while we cannot be certain as to which precise underlying decision rule the subjects applied, we can be certain that decisions identified as deviations indeed deviated from the decision rule, whichever was applied by the subject. Alternative terminologies for deviations from an underlying rule are “noise”, “errors”, “trembles”, “experiments” or “mistakes” (Kandori et al., 1993; Young, 1993). We shall prefer the terminology of “deviation”, a more neutral word with regard to causality. There is a related but se... |

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Learning to signal with probe and adjust.
- Skyrms
- 2012
(Show Context)
Citation Context ..., Sawa (2014) (logit response). 3 A dynamic is “uncoupled” when not dependent on information about others’ utility functions (Hart and Mas-Colell, 2003), strengthened to “completely uncoupled” when only information about own actions and own payoffs is considered (Foster and Young, 2006). Uncoupled dynamics, in general, do not lead to Nash equilibrium (Hart and Mas-Colell, 2003, 2006). However, under certain genericity conditions, many completely uncoupled dynamics do select Nash equilibrium (Foster and Young, 2006; Germano and Lugosi, 2007; Marden et al. 2009, 2014; Pradelski and Young, 2012; Skyrms, 2012; Huttegger and Skyrms, 2012; Huttegger et al., 2014). 4 A companion paper (Maes and Helbing, 2014) uses our data to test competing macro predictions of deterministic and noisy micro-models. 198 M. Mäs, H.H. Nax / Journal of Economic Theory 162 (2016) 195–208Fig. 1. Network types: Illustration of the two network structures studied in the experiment. Letters and colors depict the option for which the assigned participant earned payoff P . In the left-hand-side network nodes have mixed neighborhoods (Case ONE), whereas nodes are isolated in the right-hand-side network (Case TWO). test individual... |