A pure-strategy equilibrium existence theorem is extended to include games with non-expected utility players. It is shown that to guarantee the existence of a Nash equilibrium in pure strategies, the linearity of preferences in the probabilities can be replaced by the weaker requirement of quasiconvexity in the probabilities.

Probability transformation functions were introduced into modelsof behavior toward risk to allow them to accommodate violations of the expected utility hypothesis.This paper examines the shape of the probability transformation function, its interpretation asoptimism or pessimism, and how the ranking of outcomes becomes important when probability transformationsare used. It also explores two behavioral implications: the overweighting of unlikely, extremeoutcomes, and intertia around certainty. Finally, the rationality of transforming the probabilitydistribution is discussed.

Probability transformation functions were introduced into modelsof behavior toward risk to allow them to accommodate violations of the expected utility hypothesis.This paper examines the shape of the probability transformation function, its interpretation asoptimism or pessimism, and how the ranking of outcomes becomes important when probability transformationsare used. It also explores two behavioral implications: the overweighting of unlikely, extremeoutcomes, and intertia around certainty. Finally, the rationality of transforming the probabilitydistribution is discussed.