The Nash Bargaining Solution

Abstract

Introduction A bargaining solution may be interpreted as a formula that determines a unique outcome for each bargaining situation in some class of bargaining situations. In this chapter I study the bargaining solution created by John Nash. The Nash bargaining solution is defined by a fairly simple formula, and it is applicable to a large class of bargaining situations — these features contribute to its attractiveness in applications. However, the most important of reasons for studying and applying the Nash bargaining solution is that it possesses sound strategic foundations: several plausible (game-theoretic) models of bargaining vindicate its use. These strategic bargaining models will be studied in later chapters where I shall address the issues of why, when and how to use the Nash bargaining solution. A prime objective of the current chapter, on the other hand, is to develop a thorough understanding of the definition of the Nash bargaining solution, which should, in particular, facilitate its characterization and use in any application. In the next section I define and characterize the Nash bargaining solution of a specific bargaining situation in which two players bargain over the partition of a cake (or ‘surplus’) of fixed size. Although this type of bargaining situation is not uncommon, a main purpose of this section is to introduce — in a relatively simple and concrete context — some of the main concepts involved in defining Nash's bargaining solution.