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309
The Evolution of Social and Economic Networks
 JOURNAL OF ECONOMIC THEORY 106, 265–295
, 2002
"... We examine the dynamic formation and stochastic evolution of networks connecting individuals. The payoff to an individual from an economic or social activity depends on the network of connections among individuals. Over time individuals form and sever links connecting themselves to other individuals ..."
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Cited by 889 (37 self)
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We examine the dynamic formation and stochastic evolution of networks connecting individuals. The payoff to an individual from an economic or social activity depends on the network of connections among individuals. Over time individuals form and sever links connecting themselves to other individuals based on the improvement that the resulting network offers them relative to the current network. In addition to intended changes in the network there is a small probability of unintended changes or errors. Predictions can be made regarding the likelihood that the stochastic process will lead to any given network at some time, where the stochastic process selects from among the statically stable networks and cycles. We apply these results to examples including the Gale–Shapley marriage problem. Thus the paper achieves two goals. First, it outlines a dynamic solution concept for networks. Second, it applies this concept to matching problems.
Agentbased computational economics: Growing economies from the bottomup
 Artificial Life
, 2002
"... Abstract: Agentbased computational economics (ACE) is the computational study of economies modeled as evolving systems of autonomous interacting agents. Thus, ACE is a specialization to economics of the basic complex adaptive systems paradigm. This study outlines the main objectives and defining ch ..."
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Cited by 192 (5 self)
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Abstract: Agentbased computational economics (ACE) is the computational study of economies modeled as evolving systems of autonomous interacting agents. Thus, ACE is a specialization to economics of the basic complex adaptive systems paradigm. This study outlines the main objectives and defining characteristics of the ACE methodology, and discusses similarities and distinctions between ACE and artificial life research. Eight ACE research areas are identified, and a number of publications in each area are highlighted for concrete illustration. Open questions and directions for future ACE research are also considered. The study concludes with a discussion of the potential benefits associated with ACE modeling, as well some potential difficulties. Keywords: Agentbased computational economics; artificial life; learning; evolution of norms; markets; networks; parallel experiments with humans and computational agents; computational laboratories. 1
Evolutionary games on graphs
, 2007
"... Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to ..."
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Cited by 152 (0 self)
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Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in nonequilibrium statistical physics. This review gives a tutorialtype overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by nonmeanfieldtype social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner’s Dilemma, the Rock–Scissors–Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.
Basins of attraction, longrun stochastic stability, and the speed of stepbystep evolution
 Review of Economic Studies
"... The paper examines the behaviour of ‘‘evolutionary’ ’ models with εnoise like those which have been used recently to discuss the evolution of social conventions. The paper is built around two main observations: that the ‘‘long run stochastic stability’ ’ of a convention is related to the speed with ..."
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Cited by 130 (1 self)
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The paper examines the behaviour of ‘‘evolutionary’ ’ models with εnoise like those which have been used recently to discuss the evolution of social conventions. The paper is built around two main observations: that the ‘‘long run stochastic stability’ ’ of a convention is related to the speed with which evolution toward and away from the convention occurs, and that evolution is more rapid (and hence more powerful) when it may proceed via a series of small steps between intermediate steady states. The formal analysis uses two new measures, the radius and modified coradius, to characterize the long run stochastically stable set of an evolutionary model and to bound the speed with which evolutionary change occurs. Though not universally powerful, the result can be used to make many previous analyses more transparent and extends them by providing results on waiting times. A number of applications are also discussed. The selection of the risk dominant equilibrium in 2B2 games is generalized to the selection of 1 2dominant equilibria in arbitrary games. Other applications involve twodimensional local interaction and cycles as long run stochastically stable sets. 1.
The Statistical Mechanics of BestResponse Strategy Revisions
 GAMES AND ECONOMIC BEHAVIOR
, 1995
"... I continue the study, begun in Blume (1993), of stochastic strategy revision processes in large player populations where the range of interaction between players is small. Each player interacts directly with only a finite set of neighbors, but any two players indirectly interact through a finite cha ..."
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Cited by 102 (2 self)
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I continue the study, begun in Blume (1993), of stochastic strategy revision processes in large player populations where the range of interaction between players is small. Each player interacts directly with only a finite set of neighbors, but any two players indirectly interact through a finite chain of direct interactions. The purpose of this paper is to compare local strategic interaction with global strategic interaction when players update their choice according to the (myopic) bestresponse rule. I show that randomizing the order in which players update their strategic choice is sufficient to achieve coordination on the riskdominant strategy in symmetric 2 x 2 coordination games. The "persistant randomness" which is necessary to achieve similar coordination when the range of interaction is global is replaced by spatial variation in choice in the initial condition when strategic interactions are local. An extension of the riskdominance idea gives the same convergence result for K x K games with strategic complementarities. Similar results for K x K pure coordination games and potential games are also presented.
Evolutionary Game Dynamics in Finite Populations
, 2004
"... We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are ..."
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Cited by 97 (18 self)
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We introduce a model of stochastic evolutionary game dynamics in finite populations which is similar to the familiar replicator dynamics for infinite populations. Our focus is on the conditions for selection favoring the invasion and/or fixation of new phenotypes. For infinite populations, there are three generic selection scenarios describing evolutionary game dynamics among two strategies. For finite populations, there are eight selection scenarios. For a fixed payoff matrix a number of these scenarios can occur for different population sizes. We discuss several examples with unexpected behavior.
The Indirect Evolutionary Approach To Explaining Fair Allocations
, 1996
"... Experimental results on the ultimatum game show clearly that (1) large fractions of players offer a 'fair' allocation and (2) that unfair (but positive) offers are systematically rejected. We offer an explanation of this behavior using the 'indirect evolutionary approach' whic ..."
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Cited by 85 (6 self)
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Experimental results on the ultimatum game show clearly that (1) large fractions of players offer a 'fair' allocation and (2) that unfair (but positive) offers are systematically rejected. We offer an explanation of this behavior using the 'indirect evolutionary approach' which is based on the assumption that players behave rationally for given preferences but that their preferences change through an evolutionary process. We prove that despite anonymous interaction a preference for punishing unfair offers is an evolutionarily successful strategy if players interact in groups. This leads players to split the resource equally almost always. However, the equal split is not due to 'true fairness' (or 'altruism') but is entirely caused by the (justified) fear that unfair offers might be rejected. Our result can be interpreted as presenting an evolutionary foundation for the emergence of social norms. JEL classification numbers: C73, D 83. We thank Georg Noldeke, Karl Schlag,...