本論文主要研究在完全資訊的有限制預算--預算僅在該次拍賣有價值拍賣結束後失去價值，首價密封拍賣機制，兩玩家兩商品的競價模型下，所得到的混合策略納許均衡結果。其中的解析過程需要用到兩個步驟，第一步使用弱劣勢策略逐步消去法消去不會被選擇的弱劣勢策略，第二步使用各種納許均衡的求解方式求出混合策略納許均衡解。模型結果可分為三個部分來解析，分別為兩人預算限制很接近，相差較遠以及相差一點五倍以上，再以兩商品的相對價值作為參數得到混合策略的納許均衡解。經濟上的現象可以發現，擁有較多預算的優勢玩家會傾向於投標在高價值商品上，而另一名較少預算的劣勢玩家則傾向於將預算投標到低價值商品上，且分配機率與商品的相對價值有關。

This article mainly try to find the mixed strategy Nash equilibriums result on a complete in formation limited-use budget, which mean the budget only has value in the current auction and loses its value after the auction, first-price sealed bid auction, two players two commodities auction model. The analyzation needs two steps, first step is to use iterative elimination of weakly dominated strategies to eliminated the unchosen weakly dominated strategies, and the second step is to use various method to solve the mixed strategy Nash equilibriums. The result can be separated into three parts, two player’s budget constraint are close, further and different by 1.5 times, then uses the relative value of two commodities as a parameter to find the mixed strategy Nash equilibriums. In the economics point of view, we can find that the player who has higher budget tends to bid more often on the high value commodity and the one who has lower budget tends to bid more often on the low value commodity, and the distribution probabilities are related to the relative value of the commodities.

授權書 i
指導教授推薦書 ii
學位考試委員會審訂書 iii
中文摘要 iv
English Abstract v
序言 vi
目錄 vii
圖目錄 viii
第一章、緒論與文獻回顧 1
第二章、模型建構—出價策略連續下 6
第三章：出價策略不連續下的模型解析 11
第一節：弱劣勢策略逐步消去法 （iterative elimination of weakly dominated strategies） 11
第二節：第一部分的混合策略納許均衡 18
第三節：第二部分的混合策略納許均衡 25
第四節：第三部分的混合策略納許均衡 35
第四章：總結 41
參考文獻 42
附錄一：弱劣勢策略逐步消除法操作範例 44
附錄二：第一部分的混合機率納許均衡純策略機率 53
附錄三：第一步部份混合策略納許均衡解機率作圖 57

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