The equilibrium quantity and production strategy in a fuzzy random decision environment: Game approach and case study in glass substrates industries

This paper develops a two-stage Cournot production game that integrates strategic and operational planning under the fuzzy random environment, which to our best knowledge has not appeared in the literature. At the strategic level, two competing decision-makers determine the upper bound of a production quantity under a high-production strategy and the lower bound of the production quantity under a low-production strategy. Then at the operational level, the two competitors determine the range-type production quantity that is assumed to be a triangular fuzzy number represented by the apex and the entropies rather than a crisp value. The apex of a fuzzy equilibrium quantity can be obtained by the conventional Cournot game as the membership value is equal to one. A fuzzy random decision can be represented by entropies derived from the fuzzy random profit function of each firm in a specific production strategy. A case study of two leading firms in the glass substrates industry demonstrates the applicability of the proposed model. The finding that both firms would tend to adopt the common strategy coincides with observed real-world behavior. We conclude that our proposed method can provide decision-makers with a simple mathematical foundation for determining production quantity under a production strategy in a fuzzy random environment.