Computational tractability and social welfare (aka. efficiency) of equilibria are two fundamental but in general orthogonal considerations in algorithmic game theory. Nevertheless, we show that when (approximate) full efficiency can be guaranteed via a smoothness argument \`a la Roughgarden, Nash equilibria are approachable under a family of no-regret learning algorithms, thereby enabling fast and decentralized computation. We leverage this connection to obtain new convergence results in large games -- wherein the number of players $n \gg 1$ -- under the well-documented property of full efficiency via smoothness in the limit. Surprisingly, our framework unifies equilibrium computation in disparate classes of problems including games with vanishing strategic sensitivity and two-player zero-sum games, illuminating en route an immediate but overlooked equivalence between smoothness and a well-studied condition in the optimization literature known as the Minty property. Finally, we establish that a family of no-regret dynamics attains a welfare bound that improves over the smoothness framework while at the same time guaranteeing convergence to the set of coarse correlated equilibria. We show this by employing the clairvoyant mirror descent algortihm recently introduced by Piliouras et al.

翻译：均衡的计算可计算性（即计算易处理性）与社会福利（即效率）是算法博弈论中两个基础但通常彼此正交的考量。然而，我们证明，当通过Roughgarden式的光滑性论证能够保证（近似）完全效率时，纳什均衡在一族无遗憾学习算法下是可逼近的，从而实现了快速且去中心化的计算。我们利用这一联系，在玩家数量$n \gg 1$的大型博弈中，基于极限下通过光滑性实现完全效率这一充分记录的性质，获得了新的收敛结果。令人惊讶的是，我们的框架统一了不同类别问题中的均衡计算，包括战略敏感性逐渐消失的博弈和两人零和博弈，并在此过程中揭示了一个直接但被忽视的等价关系——光滑性与优化文献中一个被称为Minty性质的研究充分条件等价。最后，我们证明一族无遗憾动力学能够达到一个超越光滑性框架的福利界，同时保证收敛到粗相关均衡集。我们通过采用Piliouras等人最新引入的先知镜像下降算法来证明这一点。