  We study rational agents with different perception capabilities in strategic
games. We focus on a class of one-shot limited-perception games. These games
extend simultaneous-move normal-form games by presenting each player with an
individualized perception of all players' payoff functions. The accuracy of a
player's perception is determined by the player's capability level. Capability
levels are countable and totally ordered, with a higher level corresponding to
a more accurate perception. We study the rational behavior of players in these
games and formalize relevant equilibria conditions. In contrast to equilibria
in conventional bimatrix games, which can be represented by a pair of mixed
strategies, in our limited perception games a higher-order response function
captures how the lower-capability player uses their (less accurate) perception
of the payoff function to reason about the (more accurate) possible perceptions
of the higher-capability opponent. This response function characterizes, for
each possible perception of the higher-capability player (from the perspective
of the lower-capability player), the best response of the higher capability
player for that perception. Since the domain of the response function can be
exponentially large or even infinite, finding one equilibrium may be
computationally intractable or even undecidable. Nevertheless, we show that for
any $\epsilon$, there exists an $\epsilon$-equilibrium with a compact,
tractable representation whose size is independent of the size of the response
function's domain. We further identify classes of zero-sum limited-perception
games in which finding an equilibrium becomes a (typically tractable) nonsmooth
convex optimization problem.
