Studies on Properties of Cooperative Games with Restrictions on Coalitions and Their Solutions

联盟限制的合作博弈性质及其解研究

• 批准号: 16510114
• 负责人: TANINO Tetsuzo
• 金额: $ 1.79万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2006
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-16510114/
• 关键词: cooperative games; feasible coalitions; restricted games; cooperative fuzzy games; convex games; graded feasible coalitions; dividends; solutions of games; ファジィゲーム; 提携の実現可能度; 満場一致ゲーム; Shapley値

In this research we have discussed several properties of cooperative games with restrictions on coalitions and their solutions, i.e. rational allocation schemes of profits among players. Restrictions on coalitions can be described by feasible coalition systems which consist of admissible coalitions and are the same as functions from the power set of the player set to {0,1}. We have extended the concept of feasible coalition systems in two ways.The first extension is related to the concept of graded feasible coalition systems. This extension has enabled us to deal with degrees of feasibility of coalitions. We have defined so-called restricted games from ordinary cooperative games and graded feasible coalition systems. Inheritance of some properties of cooperative games from the original cooperative games to the obtained restricted games has been established under some appropriate conditions on the games and the graded feasible coalition systems. We can also consider some solution concepts of the original games under the graded feasible coalition systems via the restricted games.The second extension leads to cooperative fuzzy games with restrictions on fuzzy coalitions. This extension can be realized through the concept of feasible fuzzy coalition sets. With this concept we can deal with feasibility of partial cooperation of players in coalitions. We have defined restricted games obtained from cooperative fuzzy games and feasible fuzzy coalition sets and discussed some properties of the restricted games. We have also focused on some special classes of cooperative fuzzy games. We have also proposed some values as solutions of cooperative fuzzy games under appropriate feasible fuzzy coalition sets together with analysis of their properties..As future researches, we are planning to refine our results and apply our theory to interesting classes of cooperative games arising from optimization problems.

本文讨论了有联盟限制的合作对策的若干性质及其解，即局中人的合理利润分配方案。对联盟的限制可以用可行联盟系统来描述，该可行联盟系统由可允许的联盟组成，并且与从局中人集合的幂集到{0，1}的函数相同。我们从两个方面扩展了可行联盟系统的概念，第一个扩展涉及到分次可行联盟系统的概念。这种扩展使我们能够处理联盟的可行性程度。我们从普通的合作博弈和分级可行联盟系统中定义了所谓的限制博弈。在适当的条件下，证明了合作对策和分次可行联盟系统的某些性质从原来的合作对策到所得到的限制对策的继承.通过限制对策，我们还可以考虑原对策在分级可行联盟系统下的一些解的概念。第二种推广导致了对模糊联盟有限制的合作模糊对策。这种扩展可以通过可行模糊联盟集的概念来实现。有了这个概念，我们可以处理的可行性部分合作的球员在联盟。定义了合作模糊对策的限制对策和可行模糊联盟集，讨论了限制对策的一些性质。我们还重点研究了一些特殊的合作模糊对策。我们还提出了一些价值观的合作模糊对策的解决方案，在适当的可行模糊联盟集，并分析其性质。作为未来的研究，我们正计划完善我们的结果，并将我们的理论应用到有趣的合作游戏所产生的优化问题。

项目成果

Cooperative games restricted by graded feasible coalition systems

分级可行联盟系统限制的合作博弈

• 发表时间: 2007
• 期刊: Proceedings of the Fourth International Conference on Nonlinear Analysis and Convex Analysis
• 作者: V.Puripunyavanich;S.Myojo;Y.Kanazawa;Yuichiro KANAZAWA;Yuichiro KANAZAWA;Yuichiro KANAZAWA and Shinichiro WATANABE;Yuichiro KANAZAWA;Yuichiro KANAZAWA;金津雄一郎;金澤 雄一郎;金澤 雄一郎 他多数;Atsushi Moritani;Tetsuzo Tanino
• 通讯作者: Tetsuzo Tanino

Values for cooperative fuzzy games with restrictions on coalitions

具有联盟限制的合作模糊博弈的值

• 发表时间: 2011
• 作者: Yoshifumi Kusunoki;Yuto Nakai;Tetsuzo Tanino;Tetsuzo Tanino
• 通讯作者: Tetsuzo Tanino

Solutions of cooperative fuzzy games extended from ordinary cooperative games

普通合作博弈扩展的合作模糊博弈解

• 发表时间: 2006
• 期刊: Proceedings of 2006 International Symposium on Nonlinear-Theory and its Applications
• 作者: V.Puripunyavanich;S.Myojo;Y.Kanazawa;Yuichiro KANAZAWA;Yuichiro KANAZAWA;Yuichiro KANAZAWA and Shinichiro WATANABE;Yuichiro KANAZAWA;Yuichiro KANAZAWA;金津雄一郎;金澤 雄一郎;金澤 雄一郎 他多数;Atsushi Moritani;Tetsuzo Tanino;Atsushi Moritani;Tetsuzo Tanino;Tetsuzo Tanino;Atsushi Moritani;Tetsuzo Tanino;Tetsuzo Tanino
• 通讯作者: Tetsuzo Tanino

On dividends for cooperative games

关于合作游戏的分红

• 发表时间: 2006
• 期刊: 京都大学数理解析研究所講究録 1484
• 作者: V.Puripunyavanich;S.Myojo;Y.Kanazawa;Yuichiro KANAZAWA;Yuichiro KANAZAWA;Yuichiro KANAZAWA and Shinichiro WATANABE;Yuichiro KANAZAWA;Yuichiro KANAZAWA;金津雄一郎;金澤 雄一郎;金澤 雄一郎 他多数;Atsushi Moritani;Tetsuzo Tanino;Atsushi Moritani;Tetsuzo Tanino;Tetsuzo Tanino
• 通讯作者: Tetsuzo Tanino

提携に制限のあるファジィ協カゲームに対する値

有限联盟的模糊合作博弈的价值

• 发表时间: 2006
• 期刊: 京都大学数理解析研究所講究録 1526
• 作者: V.Puripunyavanich;S.Myojo;Y.Kanazawa;Yuichiro KANAZAWA;Yuichiro KANAZAWA;Yuichiro KANAZAWA and Shinichiro WATANABE;Yuichiro KANAZAWA;Yuichiro KANAZAWA;金津雄一郎;金澤 雄一郎;金澤 雄一郎 他多数;Atsushi Moritani;Tetsuzo Tanino;Atsushi Moritani;Tetsuzo Tanino;Tetsuzo Tanino;Atsushi Moritani;Tetsuzo Tanino;Tetsuzo Tanino;Atsushi Moritani;Tetsuzo Tanino
• 通讯作者: Tetsuzo Tanino