An Impossibility Theorem on Beliefs in Games
An Impossibility Theorem on Beliefs in Games
复制标题
游戏信念的不可能定理
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
H. Keisler
中科院分区：
文献类型：
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作者：
Adam Brandenburger;H. Keisler
确定了博弈中信念中的自我参照悖论，得到了类似于拉塞尔悖论的博弈论不可能性定理。这一悖论的一个非正式版本是，以下信念的配置是不可能的：安认为鲍勃假设安认为鲍勃的假设是错误的。这是形式化的，以表明任何特定类型的信念模型都必须有一个‘洞’。对结果的一种解释是，如果游戏中的玩家可以使用分析师的工具，那么玩家可以考虑但不能假设的陈述。与博弈论基础中的一些问题有联系。
A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell’s Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob’s assumption is wrongThis is formalized to show that any belief model of a certain kind must have a ‘hole.’ An interpretation of the result is that if the analyst’s tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.