Fuzzy utility and equilibria

A decision maker is frequently confronted with fuzzy constraints, fuzzy utility maximization, and fuzziness about the state of competitors. In this paper we present a framework for fuzzy decision-making, using techniques from fuzzy logic, game theory, and micro-economics. In the first part, we study the rationality of fuzzy choice. We introduce fuzzy constraints, and show that this can easily be combined with maximizing a fuzzy utility. The second part of the paper analyzes games with uncertainty about the state of the competitors. We implement fuzzy Cournot adjustment, define equilibria, and study their stability. Finally, we show how a play progresses where the players have uncertainty about the state of the other players, and about their utility. For a likely procedure of utility maximization, the equilibria are the same as for the game without utility maximization.