  We investigate how distorted, yet structured, beliefs can persist in
strategic situations. Specifically, we study two-player games in which each
player is endowed with a biased-belief function that represents the discrepancy
between a player's beliefs about the opponent's strategy and the actual
strategy. Our equilibrium condition requires that (i) each player choose a
best-response strategy to his distorted belief about the opponent's strategy,
and (ii) the distortion functions form best responses to one another. We obtain
sharp predictions and novel insights into the set of stable outcomes and their
supporting stable biases in various classes of games.
