Abraham Neyman. Bounded complexity justifies cooperation in finitely repeated prisoner's dilemma. Economic Letters, pages 227--229, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... mechanisms (that lead to desirable outcomes) 10, 40] and the complexity of deciding what information to elicit from the players in various mechanisms [11] Another avenue involves studying more sophisticated equilibrium notions which take into account that players have limited memory (e.g. [1, 14, 32, 39, 41]) or limited capability to solve optimization problems (e.g. 19, 23, 24, 34] There are also open issues on communication complexity in games (e.g. 7, 8, 17, 35, 50] and on the complexity of computing general equilibria ( market equilibria ) e.g. 50] and other solutions. There are ....

A Neyman. Bounded complexity justifies cooperation in finitely repeated prisoner's dilemma. Economic Letters, pages 227--229, 1985.

....n Gamma 1 states (see Lemma 4) Bounded rationality seems to indeed foster collaboration, albeit with unreasonably restrictive complexity bounds. A. Neyman was the first to study bounds beyond n on the sizes of automata for which collaboration is enabled. An important theorem announced in 1985 [Ne1] states that if both size bounds s I and s II lie in a range [n 1 k ; n k ] for some k 1, that is, between a root and a power of n, then collaboration can be approximated in equilibrium. Section 2 contains the precise statement) A similar result for Turing machines, conditional on an ....

....unbounded (by the continuous defection strategy for both players) and if ffl 2, then c ffl ffl=36; thus, the theorem holds as long as one of the state bounds is smaller than 2 ffln=36 . 6 As we mentioned in the introduction, our starting point was the following theorem by Abraham Neyman [Ne1]. Neyman s Theorem: For every integer k there is an integer N 0 such that if n N 0 and n 1 k minfs I (n) s II (n)g maxfs I (n) s II (n)g n k then there is an equilibrium in the n round prisoner s dilemma played by automata with sizes bounded by s I (n) and s II (n) with payoff greater ....

A. Neyman "Bounded complexity justifies cooperation in the finitely repeated prisoners ' dilemma," Economics Letters 19, pp. 227-229, 1985.

....most, if not all, of our results can easily be generalized to a wider class of two person non zero sum games. 1. 1 Related Work Finite automata players were suggested as a model of bounded rationality, and as a means of resolving the prisoner s dilemma paradox, by Rubinstein [7] and by Neyman [5]. An extensive survey of the relevant literature appears in [3] The basic concept underlying this trend is that the players are rational, but are constrained to submit automata of limited size as their agents in the game. The number of states in the automata is accepted as a measure of their ....

A. Neyman. Bounded complexity justifies cooperation in finitely repeated prisoner's dilemma. Economic Letters, pages 227--229, 1985.

....be rational even though the game has a finite and known ending point. Much research work going back at least to [3] has been done on finding strategies which lead to cooperative behavior. Modifications of the basic 2 player iterated game such as bounded rationality and noisy communication channels [20, 14, 12, 24] lead to interesting observations for the emergence of cooperative behavior in complex systems. 3 Games on lattices and local interaction It is obvious that it is rare that only two players play against each other. Further, it is also rare that all agents play all other agents. Typically, there ....

....however, did not occur either. Instead of strict cooperation, we observed widespread local coordination. This is what one often observes from the operation of decentralized economic processes. The issue of bounded rationality on a lattice is more complex than in the two person repeated game (re: [20, 14]) The need to respond at the same time to cooperators and defectors changes the nature of the problem. We argue that this is a more realistic model of many economic environments. Because agents play each other simultaneously, our results seem to contradict Axelrod s [4] proposition that it is no ....

Neyman, A. "Bounded complexity justifies cooperation in the finitely repeated prisoner's dilemma." Economics Letters 19 (1985):227-229.

....their own coalition. Emphases on other principles lead to different solution concepts for cooperative games [43] In addition, the thesis of bounded rationality is introduced as a crucial concept for game theoretical solutions to have practically meanful implementations in real life situations [44, 33, 38]. Informally, this principle of bounded rationality states that players would not spend an unbounded amount of resources to gain a small amount of improvements in the outcome. We are particularly interested in the computational resources required for questions related to a solution. There have ....

....of improvements in the outcome. We are particularly interested in the computational resources required for questions related to a solution. There have been more and more studies on the computational aspects of game theory problems, though early works may even be traced back to two decades ago [29, 20, 33, 36, 24, 31, 37, 6, 28, 38, 14, 32, 27]. An extensive discussion can be found in a review by Kalai on interplays of operations research, game theories, and theoretical computer science [23] There is another important observation that applying computational issues to game theory problems will be fruitful and enlightening. Like many ....

A. Neyman, "Bounded Complexity Justifies Cooperation in the Finitely Repeated Prisoner's Dilemma," Economics Letters 19, pp. 227--229, 1985.

....non zero sum games. A B D C D P P T S C S T R R Figure 2: The Prisoner s dilemma game 1. 1 Related Work Finite automata players were suggested as a model of bounded rationality, and as a means of resolving the prisoner s dilemma paradox, by Rubinstein [ Rubinstein, 1985 ] and by Neyman [ Neyman, 1985 ] An extensive survey of the relevant literature appears in [ Kalai, 1990 ] The basic concept underlying this trend is that the players are rational, but are constrained to submit automata of limited size as their agents in the game. The number of states in the automata is accepted as a ....

....DFSs, the set of equilibria change. We will always interpret the notion of equilibrium with respect to the set of strategies available to each player. For instance, in the repeated PD game, if all players are rational, the only equilibrium is mutual defection throughout the game. However Neyman [ Neyman, 1985 ] Rubinstein [ Rubinstein, 1985 ] and others have shown that even if only one player is restricted to an Automaton with a limited number of states, any payoff pair in the Individually Rational Region (Fig. 4) can be accomplished as an equilibrium payoff. S P R T S P R T H H H H H H T T T T T T ....

A. Neyman. Bounded complexity justifies cooperation in finitely repeated prisoner's dilemma. Economic Letters, pages 227--229, 1985.

....of interactive proofs and zero knowledge proofs [GMR89] can be viewed as precursors of this work. Although our model is significantly different, it is in the spirit of [Mos88, HMT88] There have also been many attempts in the game theoretical literature to model resource bounded agents, e.g. [Meg89, MW86, Ney85, Rub85] (see [Bin90] Chapters 5 6) for a foundational discussion) our formal model is much different from any proposed in this literature. 2 Knowledge in multi agent systems We briefly review the framework of [FHMV95] for modeling multi agent systems. We assume that at each point in time, each agent ....

A. Neyman. Bounded complexity justifies cooperation in finitely repated prisoner's dilemma. Economic Letters, pages 227--229, 1985.

....design. In the theory of games, bounds on the complexity of players have become a topic of intense interest. For example, it is a troubling fact that defection is the only equilibrium strategy for unbounded agents playing a fixed number of rounds of the Prisoners Dilemma game. Neyman s theorem (Neyman, 1985), recently proved by Papadimitriou and Yannakakis (1994) shows that an essentially cooperative equilibrium exists if each agent is a finite automaton with a number of states that is less than exponential in the number of rounds. This is essentially a bounded optimality result, where the bound is ....

Neyman, A. (1985). Bounded complexity justifies cooperation in the finitely repeated prisoners ' dilemma. Economics Letters, 19, 227--229.

.... a survey on the area of bounded rationality , see the paper of Kalai [5] While most previous papers examine how various aspects of classical game theory change in this setting (for example, whether cooperation is a stable solution for prisoner s dilemma when the adversary is a finite automaton [8, 10]) some have examined the natural question of learning to play optimally against a computationally bounded adversary [4] These works usually do not explicitly take into account the computational efficiency of the learning algorithm, and often give algorithms whose running time is exponential in ....

A. Neyman. Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma. Economics Letters, 19:227--229, 1985.

.... the area of bounded rationality , see the paper of Kalai [4] Many previous papers examine how various aspects of classical game theory change in this setting; a good example is the question of whether cooperation is a stable solution for prisoner s dilemma when both players are finite automata [6, 8]. Some authors have examined the further problem of learning to play optimally against an adversary whose precise strategy is unknown, but is constrained to lie in some known class of strategies (for instance, see Gilboa and Samet [3] It is this research that forms our starting point. The ....

Abraham Neyman. Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma. Economics Letters, 19:227--229, 1985.

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Abraham Neyman. Bounded complexity justifies cooperation in finitely repeated prisoner's dilemma. Economic Letters, pages 227--229, 1985.

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A. Neyman, Bounded complexity justifies cooperation in the finitely repeated prisoner's dilemma, Econ. Lett. 19 (1985), 227#229.

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Neyman A. 1985, Bounded complexity justifies cooperation in the finitely repeated Prisoners' Dilemma, Economics Letters, 19: 227--229.

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