论文标题

安全的子游戏解决广泛形式相关的平衡

Safe Subgame Resolving for Extensive Form Correlated Equilibrium

论文作者

Ling, Chun Kai, Fang, Fei

论文摘要

相关平衡是一种解决方案概念,比NASH平衡(NE)更一般,并且可以带来更好的社会福利结果。但是,它的自然扩展到顺序设置,\ textIt {广泛形式相关的平衡}(efce)也需要二次量的空间来解决,即使在自然界中没有随机性的限制设置中。为了减轻这些问题,我们应用\ textit {subgame nesolving},这是一种在零和游戏中找到NE的技术来解决通用和EFCE。子游戏的解决方案以\ textit {在线}方式完善了相关计划:而不是为完整的游戏预先求解,而是解决了在实际游戏中达到的子游戏中的策略,从而导致了显着的计算收益。在本文中,我们(i)根据\ textit {社会福利}和\ textit {textit {可剥削性}的基础阐明了基础来量化精致策略的质量,(ii)EFCES表明,EFCE具有足够的独立性,并提供了两种较高的独立性,以提供两个Algols的行动,以实现有效的方案,并(IIII)进行了统一,并提供了(IIII),以及III III insments,并提供了足够的独立性。最小化。两种方法都保证\ textit {安全},即,它们永远不会适得其反。我们的方法是第一次将在线方法应用于相关的通用和设置。

Correlated Equilibrium is a solution concept that is more general than Nash Equilibrium (NE) and can lead to outcomes with better social welfare. However, its natural extension to the sequential setting, the \textit{Extensive Form Correlated Equilibrium} (EFCE), requires a quadratic amount of space to solve, even in restricted settings without randomness in nature. To alleviate these concerns, we apply \textit{subgame resolving}, a technique extremely successful in finding NE in zero-sum games to solving general-sum EFCEs. Subgame resolving refines a correlation plan in an \textit{online} manner: instead of solving for the full game upfront, it only solves for strategies in subgames that are reached in actual play, resulting in significant computational gains. In this paper, we (i) lay out the foundations to quantify the quality of a refined strategy, in terms of the \textit{social welfare} and \textit{exploitability} of correlation plans, (ii) show that EFCEs possess a sufficient amount of independence between subgames to perform resolving efficiently, and (iii) provide two algorithms for resolving, one using linear programming and the other based on regret minimization. Both methods guarantee \textit{safety}, i.e., they will never be counterproductive. Our methods are the first time an online method has been applied to the correlated, general-sum setting.

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