The Cournot game under a fuzzy decision environment

Abstract

a b s t r a c tThe conventional precision-based decision analysis methodology is invalid for business decision analysis when precise assessment data seldom exist. This paper considers the Cournot game with fuzzy demand and fuzzy costs that are assumed to be triangular fuzzy numbers. Our model utilizes the weighted center of gravity (WCoG) method to defuzzify the fuzzy profit function into a crisp value. We derive the equilibrium Cournot quantity of each firm by simultaneously solving the first-order condition of each firm. Our model explicitly derives the necessary condition to avoid an unreasonable outcome of negative equilibrium quantities and lack of flexibility for modification of the ranking method. In addition, we examine the standard deviation of the fuzzy profit resulting from the fuzziness of each firm's cost and market demand functions. We conduct sensitivity analysis to investigate the effect of parameter perturbations on firms' outcomes. The results indicate that the center of parameter plays an important role in sensitivity analysis and dominates over variations in equilibrium quantity due to a perturbation of fuzzy parameters.

Revenue Sharing Contract in a Multi-Echelon Supply Chain with Fuzzy Demand and Asymmetric Information

“…20 40 0.5 (30,30,30) 266.67 1166.67 700.00 466.67 (29,30,31) From Tables 1 and 2, we Table 1 are the same in case 2 showed in Table 2. This is because the fuzzy retail price p  will not affect optimal wholesale prices, and the wholesale prices are impacted only by the operational costs 1 c  , 2 c  and 3 c  .…”

A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems

“…Fuzzy numbers are a special case of fuzzy sets and are of importance for fuzzy multiattribute decision making (MADM) problems [7][8][9][10][11][12][13][14][15][16]. As a generalization of fuzzy numbers [13], an intuitionistic fuzzy number (IFN) seems to suitably describe an ill-known quantity [17].…”

The Cournot production game with entropy spreads

“…(17), can be obtained by simultaneously solving these two best response functions, Eqs. (15) and (16) (17) It is clear that q i is the solution of the apex problem given the membership value is one. Then we utilize the result, q i , to solve the spreads problem because of the property of the triangular fuzzy number.…”

“…Liang et al [16] propose their duopoly model with fuzzy costs to obtain the optimal quantity of each firm. Recently, Dang and Hong [17] propose the fuzzy Cournot game model with rigorous definitions ensuring a positive equilibrium quantity and with a flexible controlling mechanism adjusted by decision makers. However, the resulting outcomes derived by previous studies are crisp values that are counter-intuitive outcomes of the problem in fuzzy sense.…”