A New Approach to Incomplete Information Games

不完全信息博弈的新方法

• 批准号: 14530003
• 负责人: UI Takashi
• 金额: $ 1.09万
• 依托单位: YOKOHAMA NATIONAL UNIVERSITY
• 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 2003
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14530003/
• 关键词: potential games; multiple priors; team decision problems; no trade; incomplete information games; 不完備情報ゲーム; Choquet積分; maxmin期待効用理論; ナイト的不確実性; ベイジアンゲーム; ポテンシャルゲーム; チーム; 情報構造

We consider two new approaches to incomplete information games.In the first approach, we propose the use of Bayesian potential games as models of informationally decentralized organizations in order to study the efficient use of information. Applying techniques in team decision problems by Radner (1962), we characterize Bayesian Nash equilibria in terms of Bayesian potentials and demonstrates by examples that Bayesian potentials are useful tools in studying the efficient use of information in organizations.In the second approach, we present a model of incomplete information games with sets of priors. Upon arrival of private information, each player updates by the Bayes rule each of priors in this set to construct the set of posteriors consistent with the arrived piece of information. Then the player uses a possibly proper subset of this set of posteriors to form beliefs about the opponents' strategic choices. And finally the player evaluates his actions by the most pessimistic posterio … More r beliefs a la Gilboa and Schmeidler (1989). So each player's preferences may exhibit non-linearity in probabilities which can be interpreted as the player's aversion to ambiguity or uncertainty. In this setup, we define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players' views on uncertainty about the environment affect the strategic outcomes.We also present a general framework to understand the possibility of a purely speculative trade under asymmetric information, where the decision making rule of each agent conforms to the multiple priors model : the agents are interested in the minimum of the conditional expected value of trade where the minimum is taken over the set of posteriors. In this framework, we derive a necessary and sufficient condition on the sets of posteriors, thus implicitly on the updating rules adopted by the agents, for non-existence of trade such that it is always common knowledge that every agent expects a positive gain. Less

我们考虑了两种不完全信息博弈的新方法。在第一种方法中，我们提出使用贝叶斯势博弈作为信息分散型组织的模型，以研究信息的有效利用。将Radner(1962)的方法应用到团队决策问题中，我们用贝叶斯势刻画了贝叶斯-纳什均衡，并通过实例证明了贝叶斯势是研究组织中信息有效利用的有用工具。在私有信息到达时，每个玩家通过贝叶斯规则更新该集合中的每个先验，以构造与到达的信息片段一致的后验集合。然后，玩家使用这组后来者中可能合适的子集来形成对对手战略选择的信念。最后，玩家通过最悲观的Afterio…来评估他的行为更多的信仰来自吉尔博阿和施梅德勒()。因此，每个玩家的偏好可能在概率上表现出非线性，这可以被解释为玩家对模棱两可或不确定性的厌恶。在这个框架中，我们定义了几个均衡概念，建立了它们的存在性结果，并举例说明了参与者对环境不确定性的看法如何影响战略结果。我们还给出了一个一般框架来理解不对称信息下纯投机性交易的可能性，其中每个主体的决策规则符合多先验模型：主体对交易的条件期望值的最小值感兴趣，其中最小值取后验集合的最小值。在这个框架下，我们得到了后验集上的一个充要条件，从而隐含地得到了交易不存在的更新规则，使得每个代理期望一个正收益是众所周知的。较少