  The paper studies one-shot two-player games with non-Bayesian uncertainty.
The players have an attitude that ranges from optimism to pessimism in the face
of uncertainty. Given the attitudes, each player forms a belief about the set
of possible strategies of the other player. If these beliefs are consistent,
one says that they form an uncertainty equilibrium. One then considers a
two-phase game where the players first choose their attitude and then play the
resulting game. The paper illustrates these notions with a number of games
where the approach provides a new insight into the plausible strategies of the
players.
