How to analyze a type of game problem between dissymmetrical players?

Abstract

We considered a type of game problem in which one player is full-rational individual, and the other is bounded rational population. Despite many social economy problems can be described by this game model between dissymmetrical players in the pyramidal social structure, the existing game theories have nothing to resolve this problems, because the existing game theory is divided into two branches, traditional game theory and evolutionary game theory, based on the playerpsilas characteristic and rational degree. In this paper we built a new game model that can connect traditional game with evolutionary game. In the game first phase, the bounded rationality population players takes the replicator dynamic behavior. In the second phase, the full-rational individual player decides himself response function by the strategies distribution of population players. At last, we discussed the modelpsilas application in some social economy problems.