A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information

TLDR

The paper extends Nash’s two‑person bargaining theory to settings with incomplete information, defines a formal bargaining model, and develops an axiomatic framework to select a unique solution from strict equilibrium payoff sets. The authors propose a noncooperative bargaining game, analyze its strict equilibrium points with special stability properties, and develop an axiomatic theory to select a unique solution from these equilibria. The axiomatic solution is the payoff vector that maximizes a generalized Nash product over the set of strict equilibrium payoffs.

Abstract

The paper extends Nash's theory of two-person bargaining games with fixed threats to bargaining situations with incomplete information. After defining such bargaining situations, a formal bargaining model (bargaining game) will be proposed for them. This bargaining game, regarded as noncooperative game, will be analyzed in terms of a certain class of equilibrium points with special stability properties, to be called “strict” equilibrium points. Finally an axiomatic theory will be developed in order to select a unique solution from the set X of payoff vectors corresponding to such strict equilibrium points (as well as to probability mixtures of the latter). It will be shown that the solution satisfying the axioms proposed in this paper is the point where a certain generalized Nash product is maximized over this set X.