Bounded-Rational Pursuit-Evasion Games

We present a framework that incorporates the principle of bounded rationality into a pursuit-evasion game between two aerial vehicles in a stochastic wind field. We initially formulate the problem as a continuous zero-sum stochastic game under perfect rationality. We then discretize the game via the Markov Chain Approximation Method. Leveraging the cognitive hierarchy theory ("level-k thinking") we relax the perfect rationality assumption and compute the solution of the ensuing discrete game, while taking into consideration the rationality level of each agent. We also present an online algorithm to infer the rationality of the opponent, which enables the agents to deploy appropriate countermeasures. Finally, we verify the efficacy of this framework through simulations.