Finite Two-player Game Research Articles

A note on pre-play communication

Consider a finite two-player game with one round of communication. Restrict players to a subset of “monotonic” strategies. The paper justifies this restriction. The paper provides sufficient conditions under which the strategies of the restricted game that survive iterative deletion of weakly dominated strategies favor the agent who can communicate.

Language, Meaning, and Games: A Model of Communication, Coordination, and Evolution

Language is a powerful coordination device. We generalize the cheap-talk approach to pre-play communication by way of introducing a meaning correspondence between messages and actions, and by postulating two axioms met by natural languages. Players have a lexicographic preference, second to material payoffs, against deviating from the meaning correspondence. Under two-sided communication in generic and symmetric n × n-coordination games, a Nash equilibrium component in such a lexicographic communication game is evolutionarily stable if and only if it results in the unique Pareto efficient outcome of the underlying game. We extend the analysis to one-sided communication in arbitrary finite two-player games. (JEL C72, C73, Z13)

Clever agents in adaptive learning

Saez-Marti and Weibull (J. Econom. Theory 86 (1999) 268) investigate the consequences of letting some agents play a myopic best reply to the myopic best reply in Young's (J. Econom. Theory 59 (1993) 145) bargaining model, which is how they introduce “cleverness” of players. I analyze such clever agents in general finite two-player games and show Young's (Individual Strategy and Social Structure, Princeton University Press, Princeton, NJ, 1998) prediction to be robust: adaptive learning with clever agents does select the same minimal curb set as in the absence of clever agents, if their population share is less than one. However, the long-run strategy distribution in such a curb set may vary with the share of clever agents.

An Evolutionary Approach to Pre-Play Communication

We add a round of pre-play communication to a finite two-player game played by a population of players. Pre-play communication is cheap talk in the sense that it does not directly enter the payoffs. The paper characterizes the set of strategies that are stable with respect to a stochastic dynamic adaptive process. Periodically players have an opportunity to change their strategy with a strategy that is more successful against the current population. Any strategy that weakly improves upon the current poorest performer in the population enters with positive probability. When there is no conflict of interest between the players, only the efficient outcome is stable with respect to these dynamics. For general games the set of stable payoffs is typically large. Every efficient payoff recurs infinitely often.