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，我们建议使用贝叶斯潜在博弈作为信息分散组织的模型，以研究信息的有效利用。运用Radner（1962）在团队决策问题中的技术，我们用贝叶斯潜力来描述贝叶斯纳什均衡，并通过实例证明贝叶斯潜力是研究组织中信息有效利用的有用工具。在第二种方法中，我们提出了一个具有先验集的不完全信息博弈模型。当私有信息到达时，每个玩家根据贝叶斯规则更新该集合中的每个先验，以构建与到达的信息一致的后验集合。然后，玩家使用这组后验的适当子集来形成关于对手战略选择的信念。最后，玩家通过最悲观的后验来评估自己的行为，这是Gilboa和Schmeidler（1989）的观点。所以每个玩家的偏好在概率上可能呈现非线性，这可以解释为玩家对模糊性或不确定性的厌恶。在这个设置中，我们定义了一些均衡概念，为它们建立存在结果，并通过例子展示玩家对环境不确定性的看法如何影响战略结果。我们还提出了一个一般框架来理解非对称信息下纯投机交易的可能性，其中每个代理的决策规则符合多先验模型：代理对交易条件期望值的最小值感兴趣，其中最小值占后置集合。在此框架中，我们推导出交易不存在的后验集上的充分必要条件，从而隐含地推导出agent所采用的更新规则，使得每个agent期望获得正收益始终是常识。少