Some recent results in bargaining theory

Abstract

Two person bargaining situations are very frequent in economic life. Among the most natural examples, one can think of wage-negotiations between an employer and a person he wishes to hire; another example, at a more aggregate level, concerns wage-renegotiations that take place periodically in large firms between the manager and the workers’ representative. As a final example let me mention the simple and very usual situation of a seller and a potential buyer who bargain over the price of some indivisible object. Unlike for competitive markets, economic theory (and especially mathematical economics) has not, until recently, been very helpful in explaining how prices are determined in these bargaining situations. The usual explanations refer to a vague notion of ‘respective bargaining powers’ of the two agents. There is a clear need to precise the relations between this mysterious notion and quantifiable economic data like preferences (what bargainers can get in case of an agreement), outside options (what they can get if agreement fails), impatience, risk aversion, and finally information of bargainers about each other. After the seminal contributions of Hicks and Zeuthen in the thirties, John Nash (1950,1953) was the first to adopt, in the early fifties, a systematic theoretical approach to the bargaining problem. Nash introduced a distinction between the axiomatic (or normative) approach on the one hand, and the strategic (or positive) approach on the other hand. Of course, the two approaches must not be viewed as independent. What has come to be known as the Nash program can be described as follows: starting from an axiomatic solution having desirable normative properties (like the solution proposed by Nash himself) is it possible to design a particular bargaining process that would naturally lead ‘rational’ negotiators to the outcome prescribed by the axiomatic solution? Behind the word ‘rational’ hides the main difficulty of this program: find a satisfactory concept of non-cooperative equilibrium for bargaining games.