模糊多目標雙人零和賽局理論應用於無線網路市場分析

Abstract

本研究參考模糊單目標賽局理論之文獻，據以構建模糊多目標雙人零和賽局規劃模式。傳統雙人零和賽局模式中，報酬矩陣中各元素皆為定值，且未考慮決策者之期望水準。論文中引進模糊多目標賽局理論於雙人零和賽局模式，使模式能反映出決策者之期望水準與報酬矩陣中各元素的模糊性，使模式更符合現實且決策更富彈性，本研究並以模糊報酬值之賽局進行研究，以Sakawa所提出的模糊線性規劃求得多目標的最佳化，其中並利用Ramik提出將模糊區間轉換成數條明確限制式的想法，做為求解模糊線性規劃的方法，由數學限制式的推導，配合數學線性規劃軟體求解，求出雙人非合作賽局中，各玩家的最大期望報酬與混合策略機率值。 本論文並以無線區域網路市場競爭分析為例，由實際的市場資料，將國內外晶片商股價及出貨量對晶片價格和性能做研究，晶片的性能以無線網路速度代表，以指數成長曲線表示技術的成長趨勢，利用迴歸統計的方法得到晶片商股價對晶片價格/性能迴歸式的係數，表示調整晶片價格或提昇晶片性能對股價之影響程度，針對其定價策略及產品研發策略進行模糊非合作雙人賽局分析，求得提昇股價及增加出貨量為目標的最適解，以驗證本研究之實用性。由計算結果，無論是Sakawa模糊賽局模式或是Ramik的模糊線性規劃法，大部份的條件下，都是建議玩家(國內晶片供應商)採取提供產品性能的策略，目標的達成度較高。

This study is to construct a two-person fuzzy matrix game with multiple fuzzy goals and able to perform fuzzy element values of pay-off matrix in a traditional two-person zero-sum game model, so that the game model can reflect more facts and decision elasticity. According to the fuzzy game model and fuzzy linear programming method proposed by Sakawa and Ramik individually, the study is focused on two-person non-cooperative game, and combined with mathematic programming software to solve the fuzzy linear problems, and get the maxima expected pay-offs and mixed strategy ratios for each player. Finally, the fuzzy game model is applied in a case study of domestic and foreign wireless LAN market share analysis in Taiwan. The performance of the chip is represented by WLAN throughput, and the technology growth tendency is expressed by the exponential curve. Using the above two assumptions, the pay-off matrix parameters are obtained from the regression calculation result, which is to decide the optimize solution for marketing strategy to adjust the chip price or improve chip specs. According to the calculation results, using both Sakawa’s fuzzy game model and Ramik’s fuzzy programming method, under most circumstances, the conclusions are suggesting decision makers (IC vender) to adopt the strategy of improving product’s performance to achieve company’s goals.