Mutual Knowledge of Rationality in the Electronic Mail Game

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.

Computational Complexity in the Design of Voting Rules

This paper discusses an aspect of computational complexity in social choice theory. We consider the problem of designing voting rules, which is formulated in terms of simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not.

Mutual knowledge of rationality in the electronic mail game

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

Computational complexity in the design of voting systems

This paper discusses an aspect of computational complexity in social choice theory. We consider the problem of designing voting rules, which is formulated in terms of simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not

Genome-wide SNP analysis reveals population structure and demographic history of the ryukyu islanders in the southern part of the Japanese archipelago.

The Ryukyu Islands are located to the southwest of the Japanese archipelago. Archaeological evidence has revealed the existence of prehistoric cultural differentiation between the northern Ryukyu islands of Amami and Okinawa, and the southern Ryukyu islands of Miyako and Yaeyama. To examine a genetic subdivision in the Ryukyu Islands, we conducted genome-wide single nucleotide polymorphism typing of inhabitants from the Okinawa Islands, the Miyako Islands, and the Yaeyama Islands. Principal component and cluster analyses revealed genetic differentiation among the island groups, especially between Okinawa and Miyako. No genetic affinity was observed between aboriginal Taiwanese and any of the Ryukyu populations. The genetic differentiation observed between the inhabitants of the Okinawa Islands and the Miyako Islands is likely to have arisen due to genetic drift rather than admixture with people from neighboring regions. Based on the observed genetic differences, the divergence time between the inhabitants of Okinawa and Miyako islands was dated to the Holocene. These findings suggest that the Pleistocene inhabitants, whose bones have been found on the southern Ryukyu Islands, did not make a major genetic contribution, if any, to the present-day inhabitants of the southern Ryukyu Islands

Computational complexity in the design of voting rules

This paper considers the computational complexity of the design of voting rules, which is formulated by simple games. We prove that it is an NP-complete problem to decide whether a given simple game is stable, or not

Computational complexity in the design of voting rules

ISER discussion paperMarch 2006 Revised July 2006 (Originally entitled "Computational Complexity in the Design of Voting Systems."