INTRODUCTION

The success of game theory in the 1980s has revolutionized economics. In addition to optimization and competitive market equilibrium, the concept of Nash equilibrium became a basic analytical tool and a common language of economists in almost all fields. In his famed text book (1948), Paul Samuelson quoted an epigram: “You can make even a parrot into a learned economist; all it must learn are the two words, 'supply' and 'demand.'” But now the parrot needs two more words, “Nash equilibrium,” to be academically correct.

As the game theoretic approach penetrated into many fields, however, some basic problems became apparent. First, it is not clear how players come to play a Nash equilibrium. Although Nash equilibrium was once perceived as the outcome of perfectly rational reasoning, active research in the past decade revealed that common knowledge of rationality only implies rationalizability, which is much weaker than Nash equilibrium. Second, game theoretic models quite often possess multiple equilibria which have markedly different properties. This is in contrast to the general equilibrium model where all equilibria are efficient. Hence in applications of game theory it is vital to pin down which equilibrium is selected. A host of refinements literature tried to solve this problem by defining a stronger notion of rationality than Nash equilibrium assumes, but it was not entirely successful. We are left with a number of new solution concepts, and there seems to be no clear consensus among economists as to which one is right.