A simple axiomatics of dynamic play in repeated games

Mathevet, Laurent (2012): A simple axiomatics of dynamic play in repeated games.

Abstract

This paper proposes an axiomatic approach to study two-player infinitely repeated games. A solution is a correspondence that maps the set of stage games into the set of infinite sequences of action profiles. We suggest that a solution should satisfy two simple axioms: individual rationality and collective intelligence. The paper has three main results. First, we provide a classification of all repeated games into families, based on the strength of the requirement imposed by the axiom of collective intelligence. Second, we characterize our solution as well as the solution payoffs in all repeated games. We illustrate our characterizations on several games for which we compare our solution payoffs to the equilibrium payoff set of Abreu and Rubinstein (1988). At last, we develop two models of players' behavior that satisfy our axioms. The first model is a refinement of subgame-perfection, known as renegotiation proofness, and the second is an aspiration-based learning model.

• Item Type: MPRA Paper
• Language: English
• Keywords: Axiomatic approach, repeated games, classification of games, learning, renegotiation
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C73 - Stochastic and Dynamic Games ; Evolutionary Games ; Repeated Games

References

Abreu D. and A. Rubinstein, "The Structure of Nash Equilibrium in Repeated Games with Finite Automata," Econometrica 56(6), 1988, p.1259-81.

Thomson W., "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare 18(2), 2001, p.327-386.