Journal•ISSN: 0304-4068

# Journal of Mathematical Economics

About: Journal of Mathematical Economics is an academic journal. The journal publishes majorly in the area(s): General equilibrium theory & Nash equilibrium. It has an ISSN identifier of 0304-4068. Over the lifetime, 2379 publication(s) have been published receiving 53133 citation(s).

Topics: General equilibrium theory, Nash equilibrium, Expected utility hypothesis, Competitive equilibrium, Incomplete markets

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TL;DR: In this paper, the authors characterize preference relations over acts which have a numerical representation by the functional J(f) = min > {∫ uo f dP / P∈C } where f is an act, u is a von Neumann-Morgenstern utility over outcomes, and C is a closed and convex set of finitely additive probability measures on the states of nature.

Abstract: Acts are functions from states of nature into finite-support distributions over a set of 'deterministic outcomes'. We characterize preference relations over acts which have a numerical representation by the functional J(f) = min > {∫ uo f dP / P∈C } where f is an act, u is a von Neumann-Morgenstern utility over outcomes, and C is a closed and convex set of finitely additive probability measures on the states of nature. In addition to the usual assumptions on the preference relation as transitivity, completeness, continuity and monotonicity, we assume uncertainty aversion and certainty-independence. The last condition is a new one and is a weakening of the classical independence axiom: It requires that an act f is preferred to an act g if and only if the mixture of f and any constant act h is preferred to the same mixture of g and h. If non-degeneracy of the preference relation is also assumed, the convex set of priors C is uniquely determined. Finally, a concept of independence in case of a non-unique prior is introduced.

2,373 citations

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TL;DR: This paper examined the consequences of basing mixed strategies on subjective random devices, i.e. devices on the probabilities of whose outcomes people may disagree (such as horse races, elections, etc.).

Abstract: Subjectivity and correlation, though formally related, are conceptually distinct and independent issues. We start by discussing subjectivity. A mixed strategy in a game involves the selection of a pure strategy by means of a random device. It has usually been assumed that the random device is a coin flip, the spin of a roulette wheel, or something similar; in brief, an ‘objective’ device, one for which everybody agrees on the numerical values of the probabilities involved. Rather oddly, in spite of the long history of the theory of subjective probability, nobody seems to have examined the consequences of basing mixed strategies on ‘subjective’ random devices, i.e. devices on the probabilities of whose outcomes people may disagree (such as horse races, elections, etc.). Even a fairly superficial such examination yields some startling results, as follows :

1,603 citations

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TL;DR: In this paper, an economic model of trading in commodities that are inherently indivisible, like houses, is investigated from a game-theoretic point of view, and the concepts of balanced game and core are developed, and a general theorem of Scarf's is applied to prove that the market in question has a nonempty core, that is, at least one outcome that no subset of traders can improve upon.

Abstract: An economic model of trading in commodities that are inherently indivisible, like houses, is investigated from a game-theoretic point of view. The concepts of balanced game and core are developed, and a general theorem of Scarf's is applied to prove that the market in question has a nonempty core, that is, at least one outcome that no subset of traders can improve upon. A number of examples are discussed, and the final section reviews a series of other models involving indivisible commodities, with references to the literature.

1,109 citations

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TL;DR: In this paper, the existence and order structure of Nash equilibria of non-cooperative games where payoffs satisfy certain monotonicity properties (which are directly related to strategic complementarities) but need not be quasiconcave.

Abstract: Using lattice-theoretical methods, we analyze the existence and order structure of Nash equilibria of non-cooperative games where payoffs satisfy certain monotonicity properties (which are directly related to strategic complementarities) but need not be quasiconcave. In games with strategic complementarities the equilibrium set is always non-empty and has an order structure which ranges from the existence of a minimum and a maxinum element to being a complete lattice. Some stability properties of equilibria are also pointed out.

904 citations

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TL;DR: In this article, the principal can restrict himself to incentive-compatible direct coordination mechanisms, in which agents report their information to the principal, who then recommends to them decisions forming a correlated equilibrium.

Abstract: The general principal–agent problem is formulated, in which agents have both private information and private decisions, unobservable to the principal. It is shown that the principal can restrict himself to incentive-compatible direct coordination mechanisms, in which agents report their information to the principal, who then recommends to them decisions forming a correlated equilibrium. In the finite case, optimal coordination mechanisms can be found by linear programming. Some basic issues relating to systems with many principals are also discussed. Non-cooperative equilibria between interacting principals do not necessarily exist, so quasi-equilibria are defined and shown to exist.

873 citations