论文标题
关于强大游戏理论的见解
Insights on the Theory of Robust Games
论文作者
论文摘要
强大的游戏是一个无分销模型，可以处理一组可能实现玩家回报功能值的可能实现的模棱两可。玩家是最差的优化器，并且由标准的规律性条件保证了一种称为强优化平衡的解决方案。该论文研究了对该平衡不确定性水平的敏感性。具体而言，我们证明这是名义上对手游戏的Epsilon-Nash均衡，在该游戏中，Epsilon-Approximation衡量了玩家通过降低其不确定性水平而获得的额外利润。此外，鉴于名义游戏的Epsilon-Nash平衡，我们证明可以始终引入不确定性，以使Epsilon-Nash平衡是一种强大的优化平衡。一个示例表明，尽管仅在标称对应者游戏中存在对称的NASH平衡，但强大的Cournot Dopoly模型仍可以接受多个和不对称的强智能平衡。
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.
