Nash equilibrium is often heralded as a guiding principle for rational decision-making in strategic interactions. However, it is well-known that Nash equilibrium sometimes fails as a reliable predictor of outcomes, with two of the most notable issues being the fact that it is not resilient to collusion and that there may be multiple Nash equilibria in a single game. In this paper, we show that a mechanism designer can get around these two issues for free by expanding the action sets of the original game. More precisely, given a normal-form or Bayesian game $\Gamma$ and a Nash equilibrium $\vec{\sigma}$ in $\Gamma$, a mechanism designer can construct a new game $\Gamma^{\vec{\sigma}}$ by expanding the action set of each player and defining appropriate utilities in the action profiles that were not already in the original game. We show that the designer can construct $\Gamma^{\vec{\sigma}}$ in such a way that (a) $\vec{\sigma}$ is a semi-strong Nash equilibrium of $\Gamma^{\vec{\sigma}}$, and (b) $\vec{\sigma}$ Pareto-dominates or quasi Pareto-dominates all other Nash equilibria of $\Gamma^{\vec{\sigma}}$.

翻译：纳什均衡常被视为战略互动中理性决策的指导原则。然而，众所周知，纳什均衡有时无法作为结果的可靠预测指标，其中最突出的两个问题包括：它对共谋缺乏鲁棒性，且单一博弈中可能存在多个纳什均衡。本文表明，机制设计者可以通过扩展原始博弈的行动集，无需额外成本即可绕过这两个问题。具体而言，给定一个规范形式或贝叶斯博弈 $\Gamma$ 及其中的纳什均衡 $\vec{\sigma}$，机制设计者可通过扩展每个参与者的行动集，并在原始博弈中未包含的行动组合上定义适当的效用函数，从而构建新博弈 $\Gamma^{\vec{\sigma}}$。我们证明，设计者能够以如下方式构造 $\Gamma^{\vec{\sigma}}$：(a) $\vec{\sigma}$ 是 $\Gamma^{\vec{\sigma}}$ 的半强纳什均衡；(b) $\vec{\sigma}$ 帕累托优于或拟帕累托优于 $\Gamma^{\vec{\sigma}}$ 中的所有其他纳什均衡。