Evolutionary Game Theory based Cooperation Algorithm in Multi-agent System

A multi-agent system (MAS) that composed of multiple interacting intelligent agents can be used to solve problems which are difficult or impossible for an individual agent or monolithic system to solve. Since the agent is autonomous and intelligent, it is reasonable to assume that it choice the behavior to bring itself the maximal benefit. Thus, the cooperation and coordination can be achieved successfully if we can wisely design the utility function for every agent so that every agent can get the maximal reward from the cooperation to accomplish a given task. However, the utility function of one agent usually involves those of others for most “realworld” cooperation needed tasks. Moreover, it is not uncommon that the conflicts between the gains of these agents arise. In other words, the individual optimality is not always consistent with collective optimality in MAS. These conflicts will reduce the collective utility if there is no coordination among these decentralized, autonomous agents. This paper addresses the essential that in MAS the action of one agent may influence the action of others and there usually be conflicts among the payoff of one another. We investigated the optimal coordination approach for multi-agent foraging, a typical MAS task, from the point view of game theory. After introduced several concepts, we built the equivalence between the optimal solution of MAS and the equilibrium of the game corresponding to that situation, and then we introduced evolutionarily stable strategy into the approach hope that it maybe be of service in addressing the equilibrium selection problem of traditional game theory. Finally, based on the hawk-dove game model, an evolutionarily cooperation foraging algorithm (ECFA) is proposed to evolve a stable evolutionarily stable strategy (ESS) and bring the maximal reward for the group. If there be some change in the configuration of the environment, ECFA can, then, evolve to the new ESS automatically. And we also proposed a reinforcement factor to accelerate the convergence process of ECFA and thus make a new algorithm Accelerated ECFA (AECFA). These techniques were shown to be successful by the multi-agent foraging simulations.