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We present a framework that incorporates the idea of bounded rationality into dynamic stochastic pursuit-evasion games. The solution of a stochastic game is characterized, in general, by its (Nash) equilibria in feedback form. However, computing these Nash equilibrium strategies may require extensive computational resources. In this paper, the agents are modeled as bounded rational entities having limited computational resources. We illustrate the framework by applying it to a pursuit-evasion game between two vehicles in a stochastic wind field, where both the pursuer and the evader are bounded rational. We show how such a game may be analyzed by properly casting it as an iterative sequence of finite-state Markov Decision Processes (MDPs). Leveraging tools and algorithms from cognitive hierarchy theory ("level-$k$ thinking") we compute the solution of the ensuing discrete game, while taking into consideration the rationality level of each agent. We also present an online algorithm for each agent to infer its opponent rationality level.