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Melioration learning is an empirically well-grounded model of reinforcement learning. By means of computer simulations, this paper derives predictions for several repeatedly played two-person games from this model. The results indicate a likely convergence to a pure Nash equilibrium of the game. If no pure equilibrium exists, the relative frequencies of choice may approach the predictions of the mixed Nash equilibrium. Yet in some games, no stable state is reached.

本文研究一個賣家和多個潛在買家對於一個不可分割商品的議價，且賣家之間存在與身份相關的外部性。我們考察一個有限期的展開形式的博弈，此博弈採用內生的匹配機制，在每一期的博弈中，賣家選擇和哪一個買家進行議價。 / 此博弈有一個唯一的平衡，且無論外部性爲正或負，在平衡中，協議總是立即達成。只有兩個買家時，若外部性爲負，商品必然售予效率買家；若外部性爲正，當買家的議價能力提高時，平衡結果可能會從無效率變爲有效率。若有超過兩個買家存在，無效率結果出現的可能性將會提高。 / This paper studies bargaining between one seller and multiple potential buyers on the sale of one indivisible good, in which indentity-dependent exernalities exist among buyers. We consider an extensive game with nite horizon and endogenous matching procedure, that is, the seller chooses the buyer whom to bargain with during each period of the bargaining game. / The bargaining game has a unique equilibrium with immediate agreement regardless of whether externalities are positive or negative. In a two-buyer game, the good is sold to the efficient buyer when externalities are negative. When externalities are positive, the outcome may change from inefficient to efficient by increasing the bargaining power of the buyers. Inefficient outcomes arise with higher probability in a game with more than two buyers. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Zhang, Xuechao. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 37-38). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Abstract --- p.i / Abstract in Chinese --- p.ii / Acknowledgements --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.5 / Chapter 3 --- The Model --- p.8 / Chapter 3.1 --- Bargaining Procedure --- p.8 / Chapter 3.2 --- Histories and Strategies --- p.9 / Chapter 3.3 --- Outcomes and Payos --- p.10 / Chapter 4 --- Equilibrium Analysis --- p.13 / Chapter 4.1 --- Equilibrium Dynamics --- p.13 / Chapter 4.2 --- Effi ciency Analysis --- p.20 / Chapter 5 --- Further Extensions --- p.32 / Chapter 5.1 --- Buyer-active Protocol --- p.32 / Chapter 5.2 --- Innite-horizon Framework --- p.34 / Chapter 6 --- Conclusion --- p.36 / References --- p.37

Nash's Theorem is a famous and widely used result in non-cooperative game theory which can be applied to games where each player's mixed strategy payoff function is defined as an expectation. Current proofs of this Theorem neither justify why this constraint is necessary or satisfactorily identifies its origins. In this Thesis we change this and prove Nash's Theorem for abstract games where, in particular, the payoff functions can be replaced by total orders. The result of this is a combinatoric proof of Nash's Theorem. We also construct a generalised simplicial complex model and demonstrate a more general form of Nash's Theorem holds in this setting. This leads to the realisation Nash's Theorem is not a consequence of a fixed-point theorem but rather a combinatoric phenomenon existing in a much more general mathematical model.

Wong, Yat Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 41-43). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Literature Review --- p.6 / Chapter 3 --- Basic Model --- p.10 / Chapter 4 --- Perfect Equilibrium with Delay --- p.15 / Chapter 5 --- Perfect Equilibrium with Immediate Agreement --- p.21 / Chapter 6 --- Efficiency Loss Caused by Optimism --- p.26 / Chapter 7 --- Discussions --- p.31 / Chapter 8 --- Concluding Remarks --- p.33 / Chapter 9 --- Appendix --- p.34

Chan, Yon Sim Eddie. / Thesis submitted in: November 2008. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 89-92). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Background --- p.2 / Chapter 1.3 --- Literature Review --- p.5 / Chapter 2 --- Game Theoretic Models For Competing Operators --- p.10 / Chapter 2.1 --- Competitive Equilibrium Model --- p.12 / Chapter 2.1.1 --- Base Model Formulation --- p.12 / Chapter 2.1.2 --- Capacitated Model Formulation --- p.16 / Chapter 2.1.3 --- Solution Methods --- p.19 / Chapter 2.2 --- Net Profit Maximizing --- p.26 / Chapter 2.2.1 --- Equitable Route Assignment --- p.27 / Chapter 2.3 --- Congestion Game Model with Player- and Route-dependent Operating Cost --- p.31 / Chapter 2.3.1 --- Best-Response Algorithm --- p.34 / Chapter 2.3.2 --- Integer Programming Formulation --- p.41 / Chapter 2.3.3 --- Net Profit Maximizing --- p.43 / Chapter 3 --- Network Design --- p.45 / Chapter 3.1 --- Network Structure --- p.47 / Chapter 3.2 --- Comparison Between Two Network Structures --- p.49 / Chapter 3.2.1 --- Routes with Same Ridership --- p.49 / Chapter 3.2.2 --- Routes with Different Ridership --- p.65 / Chapter 3.2.3 --- Network with Player- and Route-specific Profit Function --- p.69 / Chapter 4 --- Elastic Demand --- p.71 / Chapter 4.1 --- Congestion Game Model with Service-Quality-Based Elastic Demand --- p.71 / Chapter 4.1.1 --- Network with Service-Quality-Based Elastic Demand --- p.82 / Chapter 5 --- Conclusion --- p.84 / Chapter 5.1 --- Future Work --- p.84 / Chapter 5.1.1 --- Impact of Network Design and structure --- p.84 / Chapter 5.1.2 --- Non-cooperative and Cooperative Games --- p.86 / Chapter 5.1.3 --- Joint game-theoretic model of both passenger and providers --- p.87 / Bibliography --- p.89