纳什均衡策略的极大熵估计方法

基金项目: 国家社会科学基金资助项目(02BJY095)

详细信息

Estimating Mixed Nash Equilibrium Employing Maximum Entropy Inference

1.
School of Humanities and Economics Management, China University of Geosciences(Beijing), Beijing 100083, China
2. School of Economics and Management, Beijing University of Aeronautics and Aseronautics,Beijing 100083, China

摘要: 给出了策略熵的定义,论证了最大策略熵是纳什均衡的充分必要条件,并探讨了运用熵极大化准则来估计博弈参与者的混合策略的方法,得到了与传统方法相同的纳什均衡解,这表明纳什均衡策略是既定的收益约束条件的最大熵,为纳什均衡提供了基于信息论的解释,同时也为求解纳什均衡提供了一种极大熵估计方法,算例验证了该方法的可行性和有效性。
- 博弈论 /
- 纳什均衡 /
- 混合策略均衡 /
- 极大熵估计
Abstract: We presented the notion of strategic entropy at the beginning of this paper and discussed the relationship between the maximum strategic entropy and Nash Equilibria. Then we employed the maximum entropy inference to estimate mixed Nash equilibrium and got the same results as classical methods. And we demonstrated that strategic entropy under Nash Equilibrium is the maximum entropy, which produced an information-theoretic explanation of game theory and a new method to calculate mixed Nash equilibrium. A practical example ended our paper to confirm the feasibility and validity.
- Game Theory /
- Nash Equilibrium /
- Mixed Strategy Equilibrium /
- Maximum Entropy Inference

[1]	Kapur J N, Kesavan H K. Entropy Optimization Principles with Applications [M]. London: Academic Press, Inc., 1992.98-101.
[2]	邱菀华.管理决策与应用熵学[M]. 北京：机械工业出版社，2002.178-181.
[3]	罗杰 B 迈尔森.博弈论——矛盾冲突分析[M]. 于寅，费剑平译.北京：中国经济出版社，2001.36-39.
[4]	张维迎.博弈论与信息经济学[M]. 上海：上海三联书店/上海人民出版社，1996.108-109
[5]	Neyman A,Okada D. Strategic Entropy and Complexity in Repeated Games [J]. Games and Economic Behavior, 1999，(29):191-223.
[6]	Neyman A, Okada D. Repeated Games with Bounded Entropy [J]. Games and Economic Behavior, 2000,(30):228-247.