Adaptive Strategies: a Novel Game-theoretic Analysis for Autonomous Distributed Systems in Dynamic Environments

We propose a new concept of an adaptive strategy, and we consider its robustness against other strategies. On average, the adaptive strategy achieves a higher payoff than other strategies. The strength of a strategy is defined as an adaptive measure calculated on the basis of a payoff obtained through interactions among agents. An agent interacts with other agents by selecting various strategies in computer networks. For the adaptive strategy, we give a formal definition of the adaptive measure of how well it behaves against other strategies. In order to demonstrate a performance of the adaptive strategy, we present a calculation example of the adaptive measure for the iterated prisoner’s dilemma with three simple strategies. In the example, Trigger strategy is found to be the best strategy when we evaluate it by the adaptive measure, even if All-D (always defect) strategy achieves the highest expected payoff. Furthermore, we investigate the adaptive strategies for a self-repairing network consisting of agents with spatial strategies. According to simulations, under some conditions, the strategies obtaining the highest adaptive measures do not correspond to those with the highest averaged resources. The significance of the adaptive strategies is considered with a statistical analysis. The adaptive measure enables us to evaluate the behaviors of the adaptive strategies against those of other strategies. In addition, we discuss some open problems for polishing a notion of the adaptive strategies.