Research on the Foundation of Interactive Decision Theory from Epistemic Logical Aspect.

从认知逻辑角度研究交互决策理论基础。

• 批准号: 14540145
• 负责人: MATSUHISA Takashi
• 金额: $ 2.56万
• 依托单位: Ibaraki National College of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540145/
• 关键词: Epistemic logics; Information structure; Nash equilibrium; Core equivalence theorem; Economy under uncertainty; Rational expectations equilibrium; Communication; Protocol; 期待均衡; コア同値定理; 行動予測; 戦略型ゲーム; 認識論理; 合意定理

The purposes of this research is to investigate two points :(i) The foundation of the epistemic process reaching consensus, and its application to Game Theory ;(ii) The epistemic foundation of exchange economy under uncertainty with incomplete information, where traders have a multi-modal logic of awareness and belief.We obtained the following results :(1) We present the pre-play communication-process leading to a Nash equilibrium of a strategic form game. The stage sets up as follows : The players start with the same prior distribution on a finite state-space. In addition they have the private information given by the non-partition structure corresponding to the modal logic S4. Each player communicates privately his/her belief about the other players' actions through messages according to a communication-graph, and the receiver of the message updates her/his belief. When a player communicates with another, the other players are not informed about the contents of the message. In these … More circumstances we can show thatTheorem 1 : The players' predictions about the other players' actions regarding as the future beliefs converge in the long run, and those convergent beliefs constitute a Nash equilibrium of the game even when the communication-graph is not acyclic.(2) We propose the multi-modal logic KT by which the traders use making their decision, secondly to establish the extended notion of rational expectations equilibrium for the economy, and finally to investigate the relationship between the ex-post core and the rational expectations equilibrium allocations with emphasis on modal logical point of view. The stage is set by the following : Suppose that the trader have the multi-agent modal logic KT : It is an extension of the propositional logic with many modal operators requiring only the axiom (T) "each traders does not know a sentence whenever it is not true." The logic have non-partitional information structures, each of which gives an interpretation of the logic. Each trader has own utility function which is measurable, but he/she is not assumed to know the function completely. It is shown thatTheorem 2 : In a pure exchange atomless economy under generalized information, assume that the traders have the multi-modal logic KT and they are risk averse. Then the ex-post core coincides with the set of all rational expectations equilibrium allocations for the economy.(3) We present an extended notion of economy under uncertainty, called an economy with awareness structure, where each trader makes decision in his/her awareness and belief under incomplete information. We show the 'no trade theorem' under generalized expectations equilibrium in the extended economy :Theorem 3: In a pure exchange economy under uncertainty, the traders are assumed to have an awareness structure and to have strictly monotone preferences. If the initial endowment is ex-ante Pareto optimal then there exists no other expectations equilibrium in awareness. Less

The purposes of this research is to investigate two points:(i) The foundation of the epistemic process reaching consensus, and its application to Game Theory;(ii) The epistemic foundation of exchange economy under uncertainty with incomplete information, where trades have a multi-modal logic of awareness and belief.We obtained the following results:(1) We present the pre-play communication-process leading to a Nash equivalent of a strategic form game.舞台设置如下：玩家以有限状态空间的相同先前分布开始。此外，它们还具有与模态逻辑S4相对应的非分区结构给出的私人信息。每个玩家都通过沟通图表来私下传达对其他玩家对其他玩家行动的信念，并且消息的接收者更新了她/他的信仰。当玩家与另一个玩家交流时，其他玩家不会知道消息的内容。在这些……更多的情况下，我们可以证明理论1：从长远来看，随着未来信念的融合，参与者对其他玩家的行为的预测构成了与游戏的纳什相当于游戏的纳什，即使沟通方式不是无性的。（2）我们提出了多模式的逻辑，以实现他们的决策，以确定其决定，以确定其决定，以确定其决定，以使他们的决策建立了次要的，其次是使他们的决定，其次是在制定次数的情况下，使得交易所构成了次数，而又要建立次数的策略，并提出了次要的决定，并确定了次要的逻辑。研究前核心核心与理性期望平衡分配之间的关系，重点是模态逻辑的观点。阶段由以下阶段设置：假设交易者具有多代理模态逻辑kt：它是命题逻辑的扩展，许多模态运算符仅需要公理（t）“每个交易者在不正确的情况下都不知道句子。”逻辑具有非分区信息结构，每个信息结构都提供了逻辑的解释。每个交易者都有自己的效用功能，这是可衡量的，但他/她不被认为完全了解该功能。结果表明，理论2：在广义信息下的纯交易所无原子经济中，假设交易具有多模式逻辑KT，并且它们是避开风险的。然后，前核心核心与对经济的所有理性期望平衡分配的一组相吻合。（3）我们在不确定性下发表了延长的经济通知，称为具有意识结构的经济，每个贸易都在其意识中做出决定，并相信不完整的信息。我们在扩展经济中的普遍期望平衡下显示了“无贸易定理”：定理3：在不确定性下的纯交换经济中，交易者被认为具有意识结构，并且严格具有单调偏好。如果初始捐赠是前帕累托最佳的，那么就没有其他期望的意识平衡。较少的

项目成果

Takashi Matsuhisa: "Robust models for Nash equilibrium"Game Theory and Applications -Satellite Conference of ICM 2002, Proceedings, Qingdao (China). 474-476 (2002)

Takashi Matsuhisa：“纳什均衡的鲁棒模型”博弈论与应用 - ICM 2002 卫星会议，论文集，青岛（中国）。

Core equivalence in economy for modal logic

模态逻辑经济中的核心等价

• 发表时间: 2003
• 期刊: Computational Science-ICCS2003, Springer Lecture Notes of Computer Sciences 2568
• 作者: K.Horie;T.Matsuhisa;T.Matsuhisa;Emiko Fukuda;Ryuichiro Ishikawa;Takashi Matsuhisa;Takashi Matsuhisa
• 通讯作者: Takashi Matsuhisa

Rational expectations equilibrium in economy for modal logic

模态逻辑经济中的理性预期均衡

• 发表时间: 2003
• 期刊: Abstracts of Stony Brook Conference of Game Theory, SUNY (USA) 2003.
• 作者: K.Horie;T.Matsuhisa;T.Matsuhisa;Emiko Fukuda;Ryuichiro Ishikawa;Takashi Matsuhisa;Takashi Matsuhisa;Takashi Matsuhisa;Takashi Matsuhisa;Takashi Matsuhisa;Takashi Matsuhisa
• 通讯作者: Takashi Matsuhisa

Welfare in Economy under Awareness

意识下的经济福利

• 发表时间: 2005
• 期刊: R.I.M.S Symposium of Algebras, Language and Computation, Kyoto University, February 20-23, 2005
• 作者: Takashi MATSUHISA

Takashi Matsuhisa: "Model-robustness of equilibrium in game for modal logics"京都大学数理解析研究所講究録「代数系のアルゴリズムと計算論」. 1268. 151-154 (2002)

Takashi Matsuhisa：“模态逻辑博弈中的模型鲁棒性”京都大学数学科学研究所Kokyuroku“代数算法和计算理论”1268。151-154（2002）。