LEARNING-BEHAVIOR AND MIXED-STRATEGY NASH EQUILIBRIA
LEARNING-BEHAVIOR AND MIXED-STRATEGY NASH EQUILIBRIA
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DOI：
10.1016/0167-2681(85)90025-3
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发表时间：
1985-01-01
影响因子：
2.2
通讯作者：
CRAWFORD, VP
中科院分区：
文献类型：
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作者：
CRAWFORD, VP
本文考虑是否可以找到混合策略纳什均衡的自适应证明，就像通常用于非交互优化模型的那些证明一样。尽管人们知道这样的理由经常适用于纯策略均衡，但研究表明，在行为上看似合理的学习机制中，一大类成员肯定无法在均衡涉及混合策略的“几乎所有”博弈中收敛。发展了一个精确的形式类比，它允许这些学习机制被视为在适当选择的竞争性交易所经济中的离散的taˆ吨位过程。以此类推，这种不稳定性源于超额需求函数(边界除外)独立于“自身”价格。这种独立性是由于von Neumann-Morgenstein风险偏好的概率线性而产生的，因此一般不会扩展到纯策略均衡。因此，假设代理人将扮演均衡策略，当均衡涉及混合策略时，隐含地假设比只涉及纯策略时更复杂。
The paper considers whether an adaptive justification, like those commonly available for non-interactive optimization models, can be found for the mixed-strategy Nash equilibrium. Although it is known that such a justification is frequently available for pure-strategy equilibria, it is shown that all members of a wide class of behaviorally plausible learning mechanisms must fail to converge in ‘almost all’ games in which the equilibrium involves mixed strategies. An exact formal analogy is developed, which allows these learning mechanisms to be viewed as discrete taˆtonnement processes in properly chosen competitive exchange economies. In the analogy, the instability derives from the independence of excess demand functions (except at the boundaries) from ‘own’ prices. This independence arises because of the linearity in probabilities of von Neumann-Morgenstern risk preferences, and therefore does not extend to pure-strategy equilibria in general. Thus, assuming that agents will play equilibrium strategies implicitly assumes more sophistication when the equilibrium involves mixed strategies than when it involves only pure strategies.