Aspects of the bridge between optimization and game theory.
Both of the two major components of Game Theory, e.g., the non-cooperative game theory and the cooperative game theory, are becoming more and more closely related to the field of optimization, as the needs to study the analytical properties of games start to rise. The results presented in this thesi...
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| Format: | Others |
| Language: | English Chinese |
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c200
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| Online Access: | http://library.cuhk.edu.hk/record=b6074944 http://repository.lib.cuhk.edu.hk/en/item/cuhk-344577 |
| Summary: | Both of the two major components of Game Theory, e.g., the non-cooperative game theory and the cooperative game theory, are becoming more and more closely related to the field of optimization, as the needs to study the analytical properties of games start to rise. The results presented in this thesis illustrate several connections between Optimization and Game Theory, and attempts are made to build a bridge between the cooperative game theory and the non-cooperative game theory, to characterize the co-existence of competition and cooperation in practice. We start by applying the properties of Polymatroid Optimization to the cooperative game theory, and show that both of the joint replenish game and the one warehouse multi retailer game are submodular games. In the next part, we show that the strategies promoting learning from history are convergent under certain conditions. This result can also be viewed as an efficient algorithm to compute the Nash Equilibrium of the game. Because the competitive routing game satisfies the condition, we know that if every user adapts with good enough memory, then asymptotically the system converges to Nash Equilibrium. Therefore, if the decision of cooperation is difficult to reverse, then it can be justified for the farsighted players to use the cost structure in the Nash Equilibrium point to decide if they should cooperate or not, instead of reacting to the immediate consequences as a basis to make decisions. With the optimization tools applied, we are able to show that in parallel network, the social cost and the cost of other players tend to decrease if two players cooperate. Also, the price of anarchy is higher when the flow demand of players are more evenly distributed. Using that structural result, we derive the exact upper bound of the price of anarchy for a given parallel network with fixed number of players. The exact upper bound of the price of anarchy for arbitrary parallel network with given number of players, which is independent to the network structure and parameters, can be derived consequently. === Simai He. === Adviser: Shuzhong Zhang. === Source: Dissertation Abstracts International, Volume: 72-11, Section: B, page: . === Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. === Includes bibliographical references (leaves 97-103). === Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. === Abstract also in Chinese. |
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