Jingang Zhao

The Equilibria of a Multiple Objective Game

For a multiple objective game, we introduce its cooperative, non-cooperative, hybrid and quasi-hybrid solution concepts and prove their existence. JEL #: C70, C71, C72

The hybrid solutions of an N-person game

We introduce a solution concept intermediate between the cooperative and noncooperative solutions of an n-person game in normal form. Consider a partition p of the players, with each s in p a coalition. A joint strategy x = {x_{s}|s in p} is a hybrid solution for the partition p if, for each s in p, x_{s} is a core solution of the corresponding parametric subgame, where this game is played by the players in s and is parameterized by x_{-s}, the strategies played by all outside players. This assumes that players behave cooperatively within each coalition and competitively across coalitions. Sufficient conditions are given for a general n-person game to have hybrid solutions for any partition.

A characterization for the negative welfare effects of cost reduction in Cournot oligopoly

Abstract This paper characterizes the welfare effects of cost reductions in a Cournot model with linear costs. Under linear demand, a small reduction in a firm’s marginal cost reduces welfare if and only if its market share is less than 1/(2n+2), or equivalently, its marginal cost exceeds a critical level determined by the market. A large cost reduction by the firm increases welfare if and only if its magnitude is at least twice the difference between the current marginal cost and its critical value. The paper also extends the results to non-linear demand, but the characterizations become less tractable.

A necessary and sufficient condition for the convexity in oligopoly games

Abstract This paper establishes a necessary and sufficient condition for the convexity (or supermodularity) in oligopoly games.

The relative interior of the base polyhedron and the core

Summary. This note provides two necessary and sufficient conditions for the relative interior of the core (and the base polyhedron) to be non-empty: (i) the second largest excess of the prenucleolus is negative; (ii) the grand coalitions payoff is greater than the minimum no-blocking payoff. Such conditions imply an intuitive method in proving core existence, they also imply results on the sensitivity of the base polyhedron and the core.

Cooperative processing of information via choice at an information set

A specific structure is added to the model of Bayesian society, and the associated (more involved) version of the Bayesian incentive compatible strong equilibrium concept is proposed. The equilibrium endogenously explains whether or not playerj in coalitionS, in pursuit of his self-interest, decides to pass on his private information to the other members ofS, and if he does, which part of his private information he decides to pass on. Generic existence theorems for this equilibrium are established.

The labor market effects of non-wage compensations

Abstract Contrary to the argument that non-wage compensation is a tax on labor reducing employment, we find that employment may increase in response to an increased demand for benefits (a decreased cost of providing benefits or increased government-mandated benefit levels), under the assumption of strong cross-economies of scale. When there are strong cross-diseconomies of scale, employment and hours both decrease. The secular increase in employer-provided insurance and the growth in U.S. employment may well reflect the role of cross-economies of scale, which seems to exist in larger firms with lower marginal non-wage benefit costs.

The existence of TU -core in normal form games

Abstract. This paper provides a TU α-core existence result in a large class of normal form games. In the oligopoly markets of a homogeneous good, the TU α-core is non-empty if all profit functions are continuous and concave. In a general game, the existence of TU α-core follows from the weak separability, the compactness and convexity of choice sets, and the concavity and continuity of payoff functions.

Three little-known and yet still significant contributions of Lloyd Shapley

Abstract This paper makes three corrections in the literature by restating three little-known and yet still significant contributions of Lloyd Shapley: 1) Shapley (1955) , not Gillies, 1953 , Gillies, 1959 , first defined the core solution; 2) Shapley (1956) first defined and studied the noncooperative solution in multiobjective games; and 3) Shapley (1987) revealed a fundamental error in existing noncooperative game theory.

The hybrid equilibria and core selection in exchange economies with externalities

Abstract This paper introduces a hybrid equilibrium concept that combines the elements of cooperative and non-cooperative behaviors in an exchange economy with externalities. For a fixed coalition structure (or a partition of traders), the hybrid equilibrium is a price and consumption bundle such that each coalition chooses a core solution from its budget set and the consumption bundles are feasible. It becomes the competitive equilibrium when the position is the finest, and it selects a core allocation when the partition is the coarsest. The paper provides sufficient conditions for the existence of a hybrid equilibrium for any coalition structure.