Pradeep Dubey

Value Theory Without Efficiency

A semivalue is a symmetric positive linear operator on a space of games, which leaves the additive games fixed. Such an operator satisfies all of the axioms defining the Shapley value, with the possible exception of the efficiency axiom. The class of semivalues is completely characterized for the space of finite-player games, and for the space pNA of nonatomic games.

A theory of money and financial institutions. 28. The non-cooperative equilibria of a closed trading economy with market supply and bidding strategies

Abstract : In several previous papers Shubik, Shapley and Shapley and Shubik have proposed and investigated a model of exchange in many markets with the manner of price formation completely formulated and with trade utilizing a money. The basic model analyzed previously was extremely simple; in some ways not completely satisfactory and certainly not unique in its portrayal of price formation. Shapley and Shubik and Shubik have suggested several alternative models. This paper is devoted to examining a noncooperative equilibrium solution to one of the alternative models and to contrasting this with the noncooperative equilibrium solution to the original model.

Totally balanced games arising from controlled programming problems

A cooperative game in characteristic-function form is obtained by allowing a number of individuals to esercise partial control over the constraints of a (generally nonlinear) mathematical programming problem, either directly or through committee voting. Conditions are imposed on the functions defining the programming problem and the control system which suffice to make the game totally balanced. This assures a nonempty core and hence a stable allocation of the full value of the programming problem among the controlling palyers. In the linear case the core is closely related to the solutions of the dual problem. Applications are made to a variety of economic models, including the transferable utility trading economies of Shapley and Shubik and a multishipper one-commodity transshipment model with convex cost functions and concave revenue functions. Dropping the assumption of transferable utility leads to a class of controlled multiobjective or ‘Pareto programming’ problems, which again yield totally balanced games.

A Closed Economic System with Production and Exchange Modelled as a Game of Strategy

Abstract : ;Contents: A strategic model of exchange and production; The Existence of noncooperative equilibrium points; Limit equilibrium points and competitive equilibria; Discussion and further problems--(The role of credit, Capital goods, The trading of shares, A comment on existence of oligopolistic equilibria, A variation of the model).

Inefficiency of smooth market mechanisms

Abstract We examine the efficiency properties of an abstractly given market mechanism. This consists of a smooth map from traders’ strategy-choices to their net trades. When the number of traders is finite (the oligopolistic case), it is shown that Nash equilibria ‘tend to be’ inefficient for generic utilities. The phenomenon is analyzed via a certain set of ‘optimal points’ that are determined solely by the mechanism. In the last section we apply our results to the Hurwicz and Shapely–Shubik mechanisms by way of an illustration.

Bankruptcy and optimality in a closed trading mass economy modelled as a non-cooperative game

Abstract In this paper we establish the existence of (a) an optimal bankruptcy rule which enables us to describe the Walrasian trading economy as a game with trade in fiat money; and (b) non- cooperative equilibrium points of this game which (in terms of prices and the final allocation yielded) include the competitive equilibrium points, and the accompanying money rate of interest (induced by borrowing at a central bank), when the bankruptcy rule is different from optimal.

Information Conditions, Communication and General Equilibrium

It is shown that if the information sets of one game are a refinement of the information sets of the other, then the set of pure strategy equilibrium points of the game with less information is contained within the set of pure strategy equilibrium points of the game with more information.

Perfect competition in strategic market games with interlinked preferences

Abstract When the competitive system is viewed as a strategic market game with a continuum of agents, concern for others need not influence outcomes. The generalization of preference conditions is noted and discussed.

An Axiomatic Approach to the Equivalence Phenomenon

It is a striking fact that different solutions (such as Walrasian, core and value allocations) become equivalent in perfectly competitive economies (see, e.g., [1], [2], [3], [7], [8], [9], [10], [11], [12], [13], [14], [15], [19], [20]). We attempt to understand this phenomenon by making explicit certain crucial properties that are common across these solutions and on which — at bottom — the equivalence depends.