More and more economists are finding both empirical and experimental evidence of economic behavior that is well beyond classical economics. In particular, empirical evidence (Jullien and Salanié (2000)) and experimental evidence (Kahneman and Tversky (1979)) supported the importance of risk loving, ambiguity loving, and related behavior in economics. However, these types of preferences have not been analyzed in the general equilibrium literature with a finite number of agents because non‐convexity of preferences creates difficulty in proving existence of equilibrium. The main result in this paper provides a set of conditions under which equilibrium exists in such economies.