COOPERATION AND EFFECTIVE COMPUTABILITY

A common interest game is a game in which there exists a unique pair of payoffs which strictly Pareto-dominates all other payoffs. We consider the undiscounted repeated game obtained by the infinite repetition of such a two-player stage game. We show that if supergame strategies are restricted to be computable within Church's thesis, the only pair of payoffs which survives any computable tremble with sufficiently large support is the Pareto-efficient pair. The result is driven by the ability of the players to use the early stages of the game to communicate their intention to play cooperatively in the future.

[1]  L. Samuelson Stochastic Stability in Games with Alternative Best Replies , 1994 .

[2]  Robert J. Aumann,et al.  Long-Term Competition - A Game-Theoretic Analysis , 1994, Essays in Game Theory.

[3]  H. Young,et al.  The Evolution of Conventions , 1993 .

[4]  R. Rob,et al.  Learning, Mutation, and Long Run Equilibria in Games , 1993 .

[5]  L. Samuelson,et al.  Evolutionary stability in repeated games played by finite automata , 1992 .

[6]  L. Samuelson,et al.  Evolutionary Stability in Asymmetric Games , 1992 .

[7]  David Canning Rationality, Computability, and Nash Equilibrium , 1992 .

[8]  Luca Anderlini,et al.  Some notes on Church's thesis and the theory of games , 1990 .

[9]  John Nachbar “Evolutionary” selection dynamics in games: Convergence and limit properties , 1990 .

[10]  R. Aumann,et al.  Cooperation and bounded recall , 1989 .

[11]  H. Sabourian Repeated Games: A Survey , 1989 .

[12]  John C. Harsanyi,et al.  Общая теория выбора равновесия в играх / A General Theory of Equilibrium Selection in Games , 1989 .

[13]  Ken Binmore,et al.  Modeling Rational Players: Part II , 1987, Economics and Philosophy.

[14]  Drew Fudenberg,et al.  The Folk Theorem in Repeated Games with Discounting or with Incomplete Information , 1986 .

[15]  A. Rubinstein,et al.  The Structure of Nash Equilibrium in Repeated Games with Finite Automata (Now published in Econometrica, 56 (1988), pp.1259-1282.) , 1986 .

[16]  Vijay Krishna,et al.  Finitely Repeated Games , 1985 .

[17]  A. Neyman Bounded complexity justifies cooperation in the finitely repeated prisoners' dilemma , 1985 .

[18]  D. Fudenberg,et al.  Subgame-perfect equilibria of finite- and infinite-horizon games , 1981 .

[19]  R. Aumann Survey of Repeated Games , 1981 .

[20]  A. Rubinstein Equilibrium in supergames with the overtaking criterion , 1979 .

[21]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[22]  R. Myerson Refinements of the Nash equilibrium concept , 1978 .

[23]  John L. Bell,et al.  A course in mathematical logic , 1977 .

[24]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[25]  Jr. Hartley Rogers Theory of Recursive Functions and Effective Computability , 1969 .

[26]  Martin D. Davis,et al.  Computability and Unsolvability , 1959, McGraw-Hill Series in Information Processing and Computers.