Game Theory: The Language of Social Science?

The present paper tries in a largely non-technical way to discuss the aim, the basic notions and methods as well as the limits of game theory under the aspect of providing a general modelling method or language for social sciences.

Unique Nash implementation for a class of bargaining solutions

bargaining;Nash equilibrium

An exact non-cooperative support for the sequential Raiffa solution

This article provides an exact non-cooperative foundation of the sequential Raiffa solution for two person bargaining games. Based on an approximate foundation due to Myerson (1997) for any two-person bargaining game (S, d) an extensive form game G^{S,d} is defined that has an infinity of weakly subgame perfect equilibria whose payoff vectors coincide with that of the sequential Raiffa solution of (S, d). Moreover all those equilibria share the same equilibrium path consisting of proposing the Raiffa solution and accepting it in the first stage of the game. By a modification of G^{S,d} the analogous result is provided for subgame perfect equilibria. Finally, it is indicated how these results can be extended to implementation of a sequential Raiffa (solution based) social choice rule in subgame perfect equilibrium.Raiffa solution, non-cooperative foundation Nash program, implementation, solution based social choice rule

A universal meta bargaining realization of the Nash solution

bargaining

On the Nash program for the Nash bargaining solution

bargaining

Core-Equivalence for the Nash Bargaining Solution.

Core equivalence and shrinking of the core results are well known for economies. The present paper establishes counterparts for bargaining economies, a specific class of production economies (finite and infinite) representing standard two-person bargaining games and their continuum counterparts as coalition production economies. Thereby we get core equivalence of the Nash solution. The results reconfirm the Walrasian approach to Nash bargaining of Trockel (1996). Moreover we establish the same speed of convergence as is known from Debreu (1975) and Grodal (1975) for replicated pure exchange economies and for regular purely competitive sequences of economies, respectively.

Game theory

game theory

On Maskin monotonicity of solution based social choice rules

Howard (1992) argues that the Nash bargaining solution is not Nash implementable, as it does not satisfy Maskin monotonicity. His arguments can be extended to other bargaining solutions as well. However, by de.ning a social choice correspondence that is based on the solution rather than on its realizations, one can overcome this shortcoming. We even show that such correspondences satisfy a stronger version of monotonicity that is even su.cient for Nash implementability.Maskin monotonicity, social choice rule, bargaining games, Nash program, mechanism, implementation