Equilibria Of Generalized Games Research Articles

On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem.

In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games.

Rationalizability in general situations

The main purpose of this paper is to present an analytical framework that can be used to study rationalizable strategic behavior in general situations—i.e., arbitrary strategic games with various modes of behavior. We show that, under mild conditions, the notion of rationalizability defined in general situations has nice properties similar to those in finite games. The major features of this paper are (1) our approach does not require any kind of technical assumptions on the structure of the game, and (2) the analytical framework provides a unified treatment of players’ general preferences, including expected utility as a special case. In this paper, we also investigate the relationship between rationalizability and Nash equilibrium in general games.