General Introduction

Abstract

In this chapter, we illustrate, by means of a series of examples, why the Nash equilibrium concept has to be refined and several refinements which have been proposed in the literature are introduced in an informal way (No formal definitions are given in this chapter). First, in section 1.1, it is motivated why the solution of a noncooperative game has to be a Nash equilibrium. In the sections 1.2–1.4, we consider games in extensive form and discuss the following refinements of the Nash equilibrium concept: subgame perfect equilibria, sequential equilibria and perfect equilibria. In the sections 1.5 and 1.6, we consider refinements of the Nash equilibrium concept for normal form games, such as perfect equilibria, proper equilibria, essential equilibria and regular equilibria. The contents of the monograph are summarized in section 1.7 and, finally, in section 1.8 some notations are introduced.