Evolutionary asymmetric games for modeling systems of partially cooperative agents

Based on the tenet of Darwinism, we propose a general mechanism that guides agents (which can be partially cooperative) in selecting appropriate strategies in situations of complex interactions, in which agents do not have complete information about other agents. In the mechanism, each participating agent generates many instances of itself to help it find an appropriate strategy. The generated instances adopt alternative strategies from the agent's strategy set. While all instances generated by different agents meet randomly to complete a task, every instance adapts its strategy according to the difference between the average utilities of its current strategy and all its strategies. We give a complete analysis of the mechanism for the case with two agents when each agent has two strategies, and show that by the tenet of Darwinism, agents can find their appropriate strategies through evolution and adaptation: 1) if dominant strategies exist, then the proposed mechanism is guaranteed to find them; 2) if there are two or more strict Nash equilibrium strategies, the proposed mechanism is guaranteed to find them by using different initial strategy distributions; and 3) if there is no dominant strategy and no strict Nash equilibrium, then agents will oscillate periodically. Nevertheless, the mechanism allows agent designers to derive the appropriate strategies from the oscillation by integration. For cases with two agents when each agent has two or more strategies, it is shown that agents can reach a steady state where social welfare is optimum.