Adaptive Properties and Memory of a System of Interactive Agents: A Game Theoretic Approach

In this work we present an evolving system of agents which interact with each other in game theoretic settings. The parameters of the game are considered as time dependent variables representing state of the external environment. The variation of these parameters covers four canonical examples from game theory: prisoners dilemma, hawk-dove, stag-hunt and harmony game. The process of selfadaptation of the proposed system as well as its adaptation to the changing parameters of the environment is considered. We have demonstrated that the introduced system can be in different states which determine the way the system adapts to the external conditions. Stability of these states with respect to the variation of the external conditions has been studied. An ability of the system to accumulate memory about its past experience has been reported. Keywords-complex adaptive systems; game theory; evolutionary game theory; Turing machines