模糊環境下之 Cournot 模型均衡產量

Abstract

由於現實決策環境中，模型中的參數估計往往具有不確定之因素，至使得傳統 Cournot 賽局的應用有所侷限。遂此，本研究延伸 Cournot 賽局於模糊環境中，求解各決策者之均衡產量與數量策略。再者，本研究所探討之問題可區分為二類：模糊環境下廠商之決策行為，以及模糊隨機環境下之廠商數量策略分析。 本研究在第一部分所建構之模糊 Cournot 賽局考量了決策者之主觀意識，以及提出了所得均衡產量之條件，以避免先前文獻之缺失。再者，本研究定義樂觀與悲觀狀態下之利潤函數，藉以分析決策者之主觀意識對於均衡產量與利潤函數的影響。接者，本研究在第二部份提出了，在模糊隨機環境下 Cournot 賽局，透過數量策略的概念，求解廠商之均衡產量之上、下限，並進一步探討廠商數量策略之 Nash 均衡條件。本研究為驗證所提出模型之實用性，利用了玻璃基版產業加以說明，所得之結果與當前產業狀況相符。

The conventional Cournot game may not be valid for business decision analysis when precise assessment data seldom exist. This research develops a decision-making procedure for multiple decision makers in determining the production quantity and production strategy under the fuzzy decision environment. This dissertation includes two major parts. The first part, Chapter 2, 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 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. Then the Cournot production model developed in Chapter 2 is extended to a competitive market with multiple firms to solve for the equilibrium quantity in Chapter 3. Furthermore, we relax the model assumption in Chapter 2 where the belief about uncertainty of each firm is a constant. The results show that the profit function of each firm plays a key role in interpreting the economics implications. In the second part, Chapter 4, we propose a two-stage Cournot game that integrates strategic and operational planning under the ambiguous environment. After determining a specific high- or low-production strategy at the strategic level, the decision-makers of two competing firms move to the operational level to determine the equilibrium production quantity with its upper or lower bound. We derive the conditions such that a production strategy combination in a duopoly can be a Nash equilibrium outcome in the long term. To demonstrate the applicability of our proposed model developed in Chapter 4, we collect the data from the glass substrates industry to conduct a case study in Chapter 5. The results indicate that both firms would determine the common strategy and it coincides with the real-world situation. Finally, in Chapter 6, the results from this dissertation raise new questions and several potential directions of future research.