This paper provides an axiomatic model based on an extraneous random device generating objective probabilities for the derivation of expected utilities and subjective probabilities. Four basic axioms fully determine a real-valued utility function and a finitely additive subjective probability measure. The restrictions of these axioms to lotteries depending only upon events of the random device yield the von Neumann-Morgenstern axioms.
A generalization of assignment games, called partitioning games, is introduced. Given a finite set N of players, there is an a priori given subset pi of coalitions of N and only coalitions in pi play an essential role. Necessary and sufficient conditions for the non-emptiness of the cores of all games with essential coalitions pi are developed. These conditions appear extremely restrictive. However, when N is “large,” there are relatively few “types” of players, and members of pi are “small” and defined in terms of numbers of players of each type contained in subsets, then approximate cores are non-empty.
This paper applies the theory of the conventionally stable set to monopolistic and oligopolistic markets. A market model with a finite number of producers and a continuum of buyers is presented and then is formulated as a strategic game in which the producers’ strategies are prices and the buyers’ strategies are demands for commodities. It is shown that a conventionally stable set in this game corresponds to a conventionally stable one in a game where the producers are only players but the buyers are treated as a certain kind of demand function. Furthermore, it is shown that the theory of the conventionally stable set is compatible with the classical monopoly solution, the kinked-demand-curve solution and the leader-follower solution. This new theory makes their structures much more transparent.
It is argued that although the pathological multiplicity of Nash equilibria of super games stated by the folk theorem can be removed by introducing limited observations into super games with a continuum of players, the consideration of super games in terms of the Nash equilibrium concept involves a more fundamental and conceptual difficulty.
This paper attempts to define a new solution concept for n-person noncooperative games. The idea of the new concept is based on that of the von Neumann-Morgenstern stable set, or more precisely, rather on their interpretation of it which they call “standards of behavior.” This new approach enables us to consider new interesting problems of information. Further this approach gives us a plausible interpretation of Nash equilibrium. This paper provides the definition and considers the new solution concept for zero-sum two-person games, the prisoner’s dilemma, the battle of sexes and games with a continuum of players.
The purpose of this paper is to consider the problem of optimal income taxation in the domain of progressive (convex) income tax function. This paper proves the existence of an optimal tax function and that the optimal marginal and average tax rates tend asymptotically to 100 percent as income level becomes arbitrarily high.
In this paper we present a model of rental housing market in which houses are treated as indivisible commodities. We provide a recursive equation which determines a competitive equilibrium and argue that we can regard the competitive equilibrium as a representative of the set of all competitive equilibria. Using this representative equilibrium, we provide several propositions on comparative statics, that is, we consider how the competitive rents change when certain parameters of the model change.
Let N be a finite set of players and let ρ be a class of coalitions of N. We consider games with and without sidepayments such that only the coalitions in pi play essential roles but not the others. For an arbitrary ρ, we get the class of all such games. The purpose of this note is to provide a necessary and sufficient condition with respect to pi for the nonemptiness of the cores of all games in the class.