coordination in an email game without ``almost common knowledge推荐.pdf

Journal of Logic, Language and Information 12: 1–11, 2003. 1 © 2003 Kluwer Academic Publishers. Printed in the Netherlands. Coordination in an Email Game without “Almost Common Knowledge” NICOLA DIMITRI Dipartimento di Economia Politica, Università di Siena, Piazza San Francesco 7, 53100 Siena, Italy E-mail: dimitri@unisi.it (Received 24 September 2001; in final form 15 January 2002) Abstract. The paper presents a variation of the EMAIL Game, originally proposed by Rubinstein (American Economic Review , 1989), in which coordination of the more rewarding-risky joint course of actions is shown to obtain, even when the relevant game is, at most, “mutual knowledge.” In the example proposed, a mediator is introduced in such a way that two individuals are symmetrically informed, rather than asymmetrically as in Rubinstein, about the game chosen by nature. As long as the message failure probability is sufficiently low, with the upper bound being a function of the game payoffs, conditional beliefs in the opponent’s actions can allow players to choose a more rewarding- risky action. The result suggests that, for efficient coordination to obtain, the length of interactive knowledge on the game, possibly up to “almost common knowledge,” does not seem to be a major conceptual issue and that emphasis should be focused instead on the communication protocol and an appropriate relationship between the reliability of communication channels and the payoffs at stake. Key words: Choice, communication, coordination, efficiency, email, games, information, knowl- edge, mediation, risk-dominance 1. Introduction In a remarkable paper Rubinstein (1989), proposed a game-theoretic version of a coordination problem, also posed in the Artificial Intelligence literature (Gray, 1978), where it was made known as the “Coordinated Attack” (Halpern and Moses, 1990). Besides the interest in the matter per