We propose a solution concept—satisficing equilibrium—in which each agent i does not necessarily optimize but selects one of their top ki actions in response to the actions of others. Our concept accounts for bounded rationality, which may vary across agents. We illustrate our solution concept in a number of games from the literature. We show that non-trivial satisficing equilibria may fail to exist. However, we introduce the class of approximate potential games where their existence is guaranteed and, moreover, we show that satisficing equilibrium in which all but one agent best-respond and the remaining agent plays at least a second-best action exist in asymptotically almost all games. We provide positive foundations analogous to Nash equilibrium and show that a simple dynamic converges to satisficing equilibrium in almost all large games. Moreover, we characterize satisficing equilibrium via decision theoretic axioms. Finally, we turn to the testable implications of satisficing equilibrium.