The Cournot production game with entropy spreads

Abstract

This paper extends the conventional Cournot model to fuzzy random environment, where the market demand and supply are with two-fold uncertainty of randomness and fuzziness.We propose a methodology for obtaining the equilibrium quantity in such environment. Different from previous studies, the equilibrium quantity of each firm is a fuzzy number rather than a crisp value. Our method follows two steps of the apex problem and the spreads problem to approach the equilibrium production quantity. In our model, the production quantity of each firm is intuitively a triangular fuzzy number due to the nature of uncertainty of randomness and fuzziness. We solve for the equilibrium quantity with the highest membership value from the apex problem. The resulting outcome derived from the apex problem is further utilized to solve the spreads problem. The fuzzy equilibrium quantity can be obtained from the solution of the apex problem and spreads problem.