  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.
