鲁棒博弈理论的几点启示
Insights on the Theory of Robust Games
摘要：
鲁棒博弈是一种无分布模型，用于处理由参与者支付函数值的可能实现的有界集合所产生的模糊性。参与者是最坏情况下的优化者，并且通过标准正则性条件来保证称为鲁棒优化均衡的解决方案。本文研究了这种平衡的不确定性水平的敏感性。具体地说，我们证明了它是一个名义对应博弈的ε-纳什均衡，其中ε-近似度量了一个参与者通过降低他的不确定性水平而获得的额外利润。此外，给定一个名义博弈的鲁棒-纳什均衡，我们证明了总是可以引入不确定性，使得鲁棒-纳什均衡是一个鲁棒优化均衡。一个例子表明，一个鲁棒古诺双寡头模型可以允许多个和非对称的鲁棒优化均衡，尽管只有一个对称的纳什均衡存在的名义对应的游戏。
英文摘要：
A robust game is a distribution-free model to handle ambiguity generated by a bounded set of possible realizations of the values of players' payoff functions. The players are worst-case optimizers and a solution, called robust-optimization equilibrium, is guaranteed by standard regularity conditions. The paper investigates the sensitivity to the level of uncertainty of this equilibrium. Specifically, we prove that it is an epsilon-Nash equilibrium of the nominal counterpart game, where the epsilon-approximation measures the extra profit that a player would obtain by reducing his level of uncertainty. Moreover, given an epsilon-Nash equilibrium of a nominal game, we prove that it is always possible to introduce uncertainty such that the epsilon-Nash equilibrium is a robust-optimization equilibrium. An example shows that a robust Cournot duopoly model can admit multiple and asymmetric robust-optimization equilibria despite only a symmetric Nash equilibrium exists for the nominal counterpart game.
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