Takashi Matsuhisa

Bayesian communication leading to a nash equilibrium in belief

A Bayesian communication in the p-belief system is presented which leads to a Nash equilibrium of a strategic form game through messages as a Bayesian updating process. In the communication process each player predicts the other players’ actions under his/her private information with probability at least his/her belief. The players communicate privately their conjectures through message according to the communication graph, where each player receiving the message learns and revises his/her conjecture. The emphasis is on that both any topological assumptions on the communication graph and any common-knowledge assumptions on the structure of communication are not required.

Rational expectation can preclude trades

We reconsider the no trade theorem in an exchange economy where the traders have non-partition information. By introducing a new concept, rationality of expectations, we show some versions of the theorem different from previous works, such as Geanakoplos (http://cowles.econ.yale.edu, 1989). We also reexamine a standard assumption of the no trade theorem: the common prior assumption.

Moral hazard resolved by common-knowledge in S5n logic

This article investigates the role of common-knowledge in the principal-agent model under asymmetric information. We treat the problem: How the common-knowledge condition will be able to settle a moral hazard problem in the principal-agents model under asymmetric information. We shall propose a solution program for the moral hazard in the principal-agents model under asymmetric information by common-knowledge. Let us assume that the agents have the knowledge structure induced from a partition relation associated with the multimodal logic S5n. In particular we consider the situation that the agents commonly know all decision values of the other agents. Under certain assumptions we shall show the moral hazard can be resolved in the principal-agents model when all the expected marginal costs are common-knowledge among the principal and agents.

Communication in awareness reaching consensus without acyclic condition II

We present a communication process according to a protocol which is associated with an awareness and belief model. In the model we impose none of the requirements for players knowledge as those in the standard model with partition information structure. We show that consensus on the posteriors for an event among all players can still be guaranteed in the communication even when the protocol contains a cycle. AMS 2000 Mathematics Subject Classification: Primary 91B50, 91B60; Secondary 03B45. Journal of Economic Literature Classification: D51, C78, D61.

Communication Leading to Nash Equilibrium without Acyclic Condition

A pre-play communication-process is presented which leads to a Nash equilibrium of a strategic form game. In the communication process each player predicts the other players’ actions, and he/she communicates privately his/her conjecture through message according to a protocol. All the players receiving the messages learn and revise their conjectures. We show that after a long round of the communication the profile of players’ conjectures in the revision process leads a mixed strategy Nash equilibrium of the game.

Core equivalence in economy for modal logic

We investigate a pure exchange economy under uncertainty with emphasis on the logical point of view; the traders are assumed to have a multi-modal logic with non-partitional information structures.We propose a generalized notion of rational expectations equilibrium for the economy and we show the core equivalence theorem: The ex-post core for the economy coincides with the set of all its rational expectations equilibria.

Common-Knowledge and KP-Model

This paper starts epistemic approaches of studying the Bayesian routing problem in the frame work of the network game introduced by Koutsoupias and Papadimitriou [LNCS 1563, pp.404–413. Springer (1999)]. It highlights the role of common-knowledge on the users’ individual conjectures on the others’ selections of channels in the network game. Especially two notions of equilibria are presented in the Bayesian extension of the network game; expected delay equilibrium and rational expectations equilibrium, such as each user minimizes own expectations of delay and social cost respectively. We show that the equilibria have the properties: If all users commonly know them, then the former equilibrium yields a Nash equilibrium in the based KP-model and the latter equilibrium yields a Nash equilibrium for social cost in the network game.

Common-Knowledge and Cooperation Management I

Recently there are many issues of moral hazards and adverse selection presented in each and every contract, in which we have a self-interest and information that the other party does not possess. There is still a need for more information on how we handle a party to a contract with more information than us. This paper re-examines the issue in the framework of a principal-agent model under uncertainty based on S5n-knowledge. It highlights epistemic conditions for a possible resolution of the moral hazard between buyer and suppliers. We show that if the buyer and suppliers commonly know each agent’s belief on the others’ efforts, then all effort levels such that the expected marginal costs actually coincide for them can be characterised as the critical points of the refunded proportional rate function. This implies our recommendation that, for removing out such moral hazard in the buyer-supplier cooperation, the buyer and suppliers should commonly know their beliefs on the others’ effort levels.

Common-Knowledge and Cooperation Management II S4n-Knowledge Model Case

Issues of moral hazard and adverse selection abound in each and every contract where one has a self interest and information that the other party does not possess, and there is still need for more information on how you handle a party to a contract with more information than you. This paper re-examines the issue in the framework of a principal-agent model under uncertainty. We highlight epistemic conditions for a possible resolution of the moral hazard between the principal and the agents with S4n-knowledge, and we show that if the principalr and agents commonly know each agent’s belief on the others’ efforts, then all effort levels such that the expected marginal costs actually coincide for them can be characterised as the critical points of the refunded proportional rate function. This implies our recommendation that, for removing out such moral hazard in the principal-agents cooperation, the principal and agents should commonly know their beliefs on the others’ effort levels.

Network Communication Forming Coalition S4n-Knowledge Model Case

This paper is to introduce the new concept of coalition Nash equilibrium of a strategic game. A coalition Nash equilibrium for a strategic game consists of (1) a subset S of players, (2) independent mixed strategies for each member of S, and (3) the conjecture of the actions for the other players not in S with the condition that each member of S maximizes his/her expected payoff according to the product of all mixed strategies for S and the other players’ conjecture. Let us consider that each player communicates privately not only his/her belief about the others’ actions but also his/her rationality as messages according to a protocol and then the recipient updates their private information and revises her/his prediction. Then we show that the conjectures of the players in a coalition S regarding the future beliefs converge in the long run communication, which lead to a coalition Nash equilibrium for the strategic game.