Multi-stability and Analytical Results in Double Group Competition Games

Abstract

Generally behavioral diversity of individuals is one of the central propositions in ecology.+ Additionally coexistence of various strategies and evolution of cooperation have been subjects of interest in the framework that they consider evolution in the game theory. Here we approach these problems from introduction of hierarchical structure into dilemma games. This hierarchical structure game includes the conflict between within-group and between-group gamesmanship. Actually our model is abundantly simple and consists of plain rules and assumptions. However the evolutionary dynamics of players is very complicated and unpredictable.

There are some previous studies in economics. Rapoport and Amaldoss(1999) include between-group competitions for promoting cooperative behavior. In this paper, we give a generalized analysis of the hierarchical structure game based on Rapoport and Amaldoss’s game and discuss between-group effects from the point of view of evolutionary biology.