Mutual knowledge of rationality in the electronic mail game

Arbeitspapier

This paper reexamines the paradoxical aspect of the electronic mail game (Rubinstein, 1989). The electronic mail game is a coordination game with payoff uncertainty. At a Bayesian Nash equilibrium of the game, players cannot achieve the desired coordination of actions even when a high order of mutual knowledge of payoff functions obtains. We want to make explicit the role of knowledge about rationality of players, not only that of payoff functions. For this purpose, we use an extended version of the belief system model developed by Aumann and Brandenburger (1995). We propose a certain way of embedding the electronic mail game in an belief system. And we show that for rational players to coordinate their actions, for any embedding belief systems, it is necessary that the upper bound order of mutual knowledge of payoff functions exceeds the upper bound order of mutual knowledge of rationality. This result implies that under common knowledge of rationality, the coordination never occurs, which is similar to Rubinstein's result. We point out, however, that there exists a class embedding belief systems for which the above condition is also sufficient for the desired coordination.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: ISER Discussion Paper ; No. 650

Classification and Topics

• Classification: Wirtschaft ; Noncooperative Games ; Criteria for Decision-Making under Risk and Uncertainty ; Asymmetric and Private Information; Mechanism Design
• Subject: electronic mail game ; mutual knowledge ; common knowledge ; rationality ; interactive belief system ; Spieltheorie ; Wissen ; Information

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Takamiya, Koji ; Tanaka, Akira
• Event: Veröffentlichung
• (who): Osaka University, Institute of Social and Economic Research (ISER)
• (where): Osaka
• (when): 2006

Further information

• Handle: http://hdl.handle.net/10419/92786
• Last update: 10.03.2025, 11:43 AM CET