“Backward” coinduction, Nash equilibrium and the rationality of escalation
“Backward” coinduction, Nash equilibrium and the rationality of escalation
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“后向”共归纳、纳什均衡与升级的合理性
DOI：
10.1007/s00236-012-0153-3
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发表时间：
2012
期刊：
影响因子：
0.6
通讯作者：
Matthieu Perrinel
中科院分区：
文献类型：
--
作者：
P. Lescanne;Matthieu Perrinel
我们研究了共归纳的一个新的应用，即升级，这是一个典型的功能的无限游戏。因此，为研究无限数学结构而设计的工具，也就是那些从共归纳中推导出来的工具是必不可少的。在这里，我们使用共归纳，或反向共归纳（以显示其与有限博弈的相同概念的连接），以仔细和正式研究无限博弈，特别是所谓的美元拍卖，这被认为是升级的范式。不像什么是公认的，我们表明，假设其他代理人将永远停止，投标是理性的，因为它会导致一个子博弈完美均衡。我们证明了这不是唯一的理性策略（唯一的子博弈完美均衡）。事实上，如果一个行动者停下来，并且每走一步都会停下来，我们就可以说他也是理性的，只要他承认他的对手永远不会停下来，因为这对应于一个子博弈完美均衡。令人惊讶的是，在无限美元拍卖博弈中，两个代理人在每一步都停止的行为不是纳什均衡，因此不是子博弈完美均衡，因此不是理性的。我们获得的合理性的正确概念符合常识和经验，并消除了所有的矛盾感。
We study a new application of coinduction, namely escalation which is a typical feature of infinite games. Therefore tools conceived for studying infinite mathematical structures, namely those deriving from coinduction are essential. Here we use coinduction, or backward coinduction (to show its connection with the same concept for finite games) to study carefully and formally infinite games especially the so-called dollar auction, which is considered as the paradigm of escalation. Unlike what is commonly admitted, we show that, provided one assumes that the other agent will always stop, bidding is rational, because it results in a subgame perfect equilibrium. We show that this is not the only rational strategy profile (the only subgame perfect equilibrium). Indeed if an agent stops and will stop at every step, we claim that he is rational as well, if one admits that his opponent will never stop, because this corresponds to a subgame perfect equilibrium. Amazingly, in the infinite dollar auction game, the behavior in which both agents stop at each step is not a Nash equilibrium, hence is not a subgame perfect equilibrium, hence is not rational. The right notion of rationality we obtain fits with common sense and experience and removes all feeling of paradox.