Preliminaries

Abstract

The main theme of this book is axiomatic bargaining game theory, as initiated by Nash’s seminal paper of 1950. Axiomatic bargaining game theory is a mathematical discipline which studies the problem of bargaining between two or more parties by studying the mathematical properties of maps assigning an outcome to each bargaining game in some class of bargaining games. A bargaining game is a set of outcomes representing the utilities attainable by the parties or players involved, together with a disagreement outcome. The interpretation is that this last outcome results if the players are unable to reach a unanimous agreement on some other possible outcome. Maps as mentioned will be called bargaining solutions . Axiomatic bargaining game theory is concerned with a mathematical investigation of the properties of such bargaining solutions. Usually, following Nash (1950), one formulates desirable properties for these solutions, and then tries to characterize a solution or a class of solutions by its properties. Therefore, such properties are often referred to as axioms¹, which is a less neutral expression. We will use both terms, axioms as well as properties. In a nutshell, this is what this book is mainly about.