Research on Foundation of Game Theory, Rationality and Human Behaviors from the view point of Epistemic Logic
认知逻辑视角下的博弈论基础、理性与人类行为研究
基本信息
- 批准号:12640145
- 负责人:
- 金额:$ 0.9万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2000
- 资助国家:日本
- 起止时间:2000 至 2001
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
(1) The logic of 'agreeing to disagree' with common-belief is presented which is an extension of a multi-modal logic of 'awareness and common-belief' in the logically non-omniscient point of view. It is shown that the sentence of the 'agreeing to disagree' theorem is provable in the logic and that the logic is sound for all finite models.(2) A pre-play communication-process is presented which leads to a Nash equilibrium of a strategic form game. In the communication process each player predicts the other players' actions, and he/she communicates privately his/her conjecture through message according to a protocol. All the players receiving the messages learn and revise their conjectures. After a long round of the communications they reach a Nash equilibrium: We show that the profile of players' conjectures in the revision process leads a Nash equilibrium of a game in the long run if the protocol contains no cycle.(3) The communication process in the $p$-belief system is presented which … More reaches consensus among many players : They communicate the events that they believe with probability greater than their own posteriors. We show that in the long run each sequence of revised posteriors converges to a limiting values and show that any two limiting values must be same.(4) The graph-theoretical conditions under which communication will lead to consensus among players about their decisions in circumstances are investigated where there are more than two players and they interact in pair without public announcement. It is shown that consensus on their decisions can be guaranteed if the communication graph contains no cycle. Where none of the requirements for player's knowledge is imposed as in the standard model of knowledge with partitional information structure.(5) The logic of 'utility maximizers' $L^{um}$ is proposed which is an extension of a system of modal logic for two players. The sound models according to $L^{um}$ are given in terms of game theory. It is shown for the models that two utility maximizing players must take the same action if they mutually believe that each takes a dominant action, even when they have different information. We remark that the logic $L^{um}$ has the finite model property.(6) In a pure exchange economy under uncertainty the traders are willing to trade of the amounts of state-contingent commodities and they know their expectations. Common-knowledge about these conditions among all traders can preclude trade if the initial endowments allocation is a rational expectations equilibrium, even when the traders have the non-partition structure of information without the common prior assumption. In the proof it plays essential role to extend the notion of a rational expectations equilibrium and to characterize ex-ante Pareto optimal endowments as the equilibrium. It is emphasized that the partition structure of information in the traders plays no roles in the no trade theorem. Less
(1)从逻辑非全知的角度,提出了“同意不同意”与“共同信念”的逻辑,这是对“意识与共同信念”的多模态逻辑的扩展。证明了“同意不同意”定理的语句在逻辑上是可证明的,并且该逻辑对所有有限模型都是合理的。(2)给出了一个导致策略型博弈的纳什均衡的博弈前沟通过程。在通信过程中,每个玩家预测其他玩家的动作,他/她按照协议通过消息私下交流他/她的猜测。所有收到信息的玩家都会学习并修改他们的猜想。在经过一轮长时间的沟通后,他们达到了纳什均衡:我们证明了在协议不包含循环的情况下,修改过程中的参与者猜想的轮廓在长期内导致博弈的纳什均衡。(3)给出了在$p$-信念系统中的通信过程,其中…More在许多玩家中达成了共识:他们交流他们相信的事件的可能性比他们自己的后人更大。我们证明了从长远来看,每个修正后的序列都收敛到一个极限值,并且证明了任何两个极限值一定是相同的。(4)研究了在有两个以上的参与者并且他们在没有公告的情况下成对互动的情况下,沟通将导致参与者对他们的决策达成共识的图论条件。结果表明,如果通信图不包含圈,则可以保证对他们的决策达成一致。提出了效用最大化逻辑,它是对两个参与者的模态逻辑系统的扩展。从博弈论的角度给出了《L》中的声音模型。模型表明,如果两个效用最大化的博弈者相互认为各自采取主导行动,即使他们拥有不同的信息,他们也必须采取相同的行动。我们注意到逻辑L具有有限模型性质。(6)在不确定的纯交换经济中,交易者愿意交易状态或有商品的数量,他们知道自己的预期。如果初始资产配置是理性预期均衡,即使交易者在没有共同先验假设的情况下具有非分割的信息结构,所有交易者之间关于这些条件的共同知识也可以排除交易。在证明中,推广了理性预期均衡的概念,并将事前帕累托最优禀赋刻画为均衡,发挥了至关重要的作用。强调了交易者的信息分割结构在无交易定理中不起作用。较少
项目成果
期刊论文数量(58)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Takashi MATSUHISA, T. Yanovskaya (Editor): "Communication leading to Nash equilibrium II"Logic, Games and Social Choices (LGS2), The Publish Coucil of St. Petersburg University. 174-179 (2001)
Takashi MATSUHISA、T. Yanovskaya(编辑):《通向纳什均衡 II 的通信》逻辑、博弈和社会选择 (LGS2),圣彼得堡大学出版委员会。
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- 影响因子:0
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- 通讯作者:
Emiko FUKUDA, Takashi MATSUHISA and Hisato SASANUMA: "Communication reaching consensus"Proceedings of The Second International Conference of Nonlinear Analysis and Convex Analysis NACA 2001, Hirosaki (Japan). 49-60 (2003)
Emiko FUKUDA、Takashi MATSUHISA 和 Hisato SASANUMA:“沟通达成共识”第二届国际非线性分析和凸分析会议记录 NACA 2001,弘前(日本)。
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- 影响因子:0
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Kazuki HIRASE and Takashi MATSUHISA: "Reasoning about dominant actions"R.I.M.S. Symposium Mathematical Economics, Kyoto University. (2000)
Kazuki HIRASE 和 Takashi MATSUHISA:“关于主导行为的推理”R.I.M.S.
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- 影响因子:0
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Ryuichiro ISHIKAWA, Takashi MATSUHISA and Yohsuke AKAGAWA: "consensus on p-belief communication"The Second International Conference of Nonlinear Analysis and Convex Analysis NACA 2001, Hirosaki (Japan). (2001)
Ryuichiro ISHIKAWA、Takashi MATSUHISA 和 Yohsuke AKAGAWA:“p-belief 沟通的共识”第二届非线性分析和凸分析国际会议 NACA 2001,弘前(日本)。
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:
- 通讯作者:
Takashi MATSUHISA: "Communication leading to Nash equilibrium II"T.Yanovskaya (Editor) : Logic, Games and Social Choices(LGS2), The Publishing Council of St. Petersburg University. 174-179 (2001)
松久隆:“通向纳什均衡 II 的通信”T.Yanovskaya(编辑):逻辑、游戏和社会选择(LGS2),圣彼得堡大学出版委员会。
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