Iterated continuous prisoner´s dilemma game and its usefulness in analyzing multi-agent systems

In multi-agent systems, each agent has his own objective, sometimes conflicts with others, and there exists no supervisor which controls the entire system. The iterated prisoner´s dilemma game was studied as a model for analyzing interactions between agents under such situation. In this game, each agent chooses his action from ´Cooperate´ and ´Defect´, but this is unsatisfactory when we consider complex multi-agent systems such as cyberworlds. We extend this game so that each agent can take intermediate actions from the range between ´Cooperate´ and ´Defect´. The purpose of this research is to clarify the profitability of taking intermediate actions using the iterated prisoner´s dilemma game extended to a continuous domain, and to show the usefulness of this game in analyzing elastic interactions between agents. Several knowledge has been obtained as results of analysis. For example, a cooperative strategy taking intermediate actions invades a group of identical strategies taking discrete actions, and a group of cooperative strategies taking intermediate ones also. Note that being a cluster is less profitable in this case.