Akihiko Matsui

Social Stability and Equilibrium

This paper constructs a two-country (Home and Foreign) general equilibrium model of Schumpeterian growth without scale effects. The scale effects property is removed by introducing two distinct specifications in the knowledge production function: the permanent effect on growth (PEG) specification, which allows policy effects on long-run growth; and the temporary effects on growth (TEG) specification, which generates semi-endogenous long-run economic growth. In the present model, the direction of the effect of the size of innovations on the pattern of trade and Homes relative wage depends on the way in which the scale effects property is removed. Under the PEG specification, changes in the size of innovations increase Homes comparative advantage and its relative wage, while under the TEG specification, an increase in the size of innovations increases Homes relative wage but with an ambiguous effect on its comparative advantage.

Toward a Theory of International Currency

Our goal is to provide a theoretical framework in which both positive and negative aspects of international currency can be addressed in a systematic way. To this end, we use the framework of random matching games and develop a two country model of the world economy, in which two national fiat currencies compete and may be circulated as media of exchange. There are multiple equilibrium which differ in the areas of circulation of the two currencies. In one equilibrium, the two national currencies are circulated only locally. In another, one of the national currencies is circulated as an international currency. There is also an equilibrium in which both currencies are accepted internationally. We also find an equilibrium in which the two currencies are directly exchanged. The existence conditions of these equilibria are characterized, using the relative country size and the degree of economic integration as the key parameters. In order to generate sharper predictions in he presence of multiple equilibria, we discuss an evolutionary approach to equilibrium selection, which is used to explain the evolution of the international currency as the two economies become more integrated. Some welfare implications are also discussed. For example, a country can improve its national welfare by letting its own currency circulated internationally, provided the domestic circulation is controlled for. When the total supply is fixed, however, a resulting currency shortage may reduce the national welfare.

Best response dynamics and socially stable strategies

Abstract An evolutionarily stable strategy (Maynard Smith and Price, Nature (London) 246 (1973), 15–18) is a strategy which is robust against a tiny invasion of mutants. Best response dynamics is a dynamic process in which the frequency of a strategy increases only if it is a best response to the present strategy distribution. Gilboa and Matsui (Econometrica 59 (1991), 859–867) proposed a stability concept directly derived from this dynamic process. Modifying the above two stability concepts, this paper shows the equivalence between the static concept and the dynamic one. Their set-valued versions always exist. Examples are given to see their usefulness in analyzing forward induction and preplay communication.

Cheap-Talk and Cooperation in a Society

Does cheap-talk matter? Does costless communication necessarily yield Pareto optimal outcomes? When is it that the voices of those with disabilities reach the majority, or persons without disability? These questions are relevant in the context of economy and disability. In many situations, persons without disability do not see the barriers that persons with disability are faced with. If the barriers were removed simply by pointing them out, life would be easier for persons with disability than now.

Asynchronous Choice in Repeated Coordination Games

The standard model of repeated games assumes perfect synchronization in the timing of decisions between the players. In many natural settings, however, choices are made synchronously so that only one player can move at a given time. This paper studies a family of repeated settings in which choices are asynchronous. Initially, we examine, as a canonical model, a simple two person alternating move game of pure coordination. There, it is shown that for sufficient patient players, there is a unique perfect equilibrium payoff which Pareto dominates all other payoffs. The result generalizes to any finite number of players and any game in a class of asynchronously repeated games which includes both stochastic and deterministic repetition. The result complement a recent Folk Theorem by Dutta (1995) for stochastic games which can be applied to asynchronously repeated games if a full dimensionality condition holds. A critical feature of the model is the inertia in decisions. We show how the inertia in asynchronous decisions determines the set of equilibrium payoffs.

Inductive Game Theory: Discrimination and Prejudices

This paper proposes a new theory, which we call inductive game theory. In this theory, the individual player does not have a priori knowledge of the structure of the game that he plays repeatedly. Instead, he accumulates experiences induced by occasional random trials in the repeated play. A stationary state is required to be stable against intentional deviations based on the players experiences, and then it turns out to be a Nash equilibrium. The main part of the paper is the consideration of possible individual views of the society based on individual experiences. This view is defined to be a model of the society which the player builds from his experiences. Coherency with these experiences and a condition called rationalization are required for a model. As concrete objects of the theory, this paper analyzes the phenomena of discrimination and prejudice. The development of the new theory is undertaken by contrasting its observational and behavioral aspects with mental and judgmental aspects. The relationship between discrimination and prejudice will emerge in this dichotomous consideration. Copyright 1999 by Blackwell Publishing Inc.

Learning aspiration in repeated games

Abstract We study infinitely repeated symmetric 2 × 2 games played by bounded rational agents who follow a simple rule of thumb: each agent continues to play the same action if the current payoff exceeds the average of the past payoffs, and switches to the other action with a positive probability otherwise. By applying the stochastic approximation technique, we characterize the asymptotic outcomes for all 2×2 games. In the prisoners’ dilemma game, for example, the players cooperate in the limit if and only if the gain from defecting against cooperation is “modest.”

Information leakage forces cooperation

Abstract This paper considers a two-person repeated game in which there is a small probability of espionage, i.e., that one or both of the players will be informed of the others supergame strategy and have a chance to revise his strategy on the basis of this information before the game begins. It is shown that in such a game any subgame perfect equilibrium pair of payoffs is Pareto efficient provided that the probability of espionage is sufficiently small. Different from preceding studies, the present paper assumes neither “collective deviation” nor “bounded rationality” in deriving the result.

Organizations and Overlapping Generations Games: Memory, Communication, and Altruism

This paper studies the role of memory and communication in overlapping generations (OLG) games between ongoing organizations. In each organization, each individual, upon entry into the game, replaces his predecessor who has the same preferences and faces the same strategic possibilities. An individual has no prior memory - that is, he does not directly witness the events that occur before his tenure. Instead, each individual relies on information about the past from his predecessor via cheap talk. This paper highlights the role of communication as a surrogate for memory. It has been shown elsewhere that Folk Theorems hold in OLG games with long enough lived individuals who can perfectly observe the past. However, the Folk Theorem fails for many games when individuals have no prior memory. We show that for OLG games without prior memory but with costly communication, a Folk Theorem holds only when there is some altruistic link between cohorts in an organization. Our main result asserts that if communication costs are sufficiently small, or if altruistic weights on successors are sufficiently large, then a strongly stationary Folk Theorem (i.e., equilibrium payoffs are time invariant) obtains if a manager’s message is public information. The equilibria in this Folk Theorem require a special form of intergenerational sanctions. In these sanctions, punishment is sometimes carried out long after both victim and perpetrator have left the game. Without this special structure, altruism may in fact destroy cooperation when it would otherwise be possible. Copyright Springer-Verlag Berlin/Heidelberg 2004

Expected utility and case-based reasoning

Abstract This paper presents an equivalence result between expected utility theory (EU) and a modified version of case-based decision theory (CBDT). To be precise, it shows that a model constructed in EU can be embedded in a CBDT model, and vice versa. CBDT, proposed and axiomatized by Gilboa and Schmeidler (1995, Case-based decision theory, Quarterly Journal of Economics 110, 605–639), is related to case-based reasoning in psychology and artificial intelligence and considered as a descriptive theory of human behavior. In CBDT a decision maker remembers situations similar to the current problem and uses them to help solve it. This idea stems from bounded rationality and is similar in spirit to the satisficing theory of March and Simon (1958, Organizations, Wiley, New York) in the sense that the decision maker tends to satisfice rather than optimize.