确保均等份额：一种学习多人对称博弈的原则性方法
Securing Equal Share: A Principled Approach for Learning Multiplayer Symmetric Games
AI总结：
本文针对多人对称常和博弈中均衡不唯一且不可利用性缺失的问题，提出以均等份额为目标，基于无悔学习设计可证明近似达到均等份额的算法，并通过理论下界和实验验证其有效性。
摘要：
本文研究竞争环境下超过两名参与者的多人对称常和博弈，包括麻将、扑克以及各种棋类和电子游戏等例子。与两人零和博弈不同，多人博弈中的均衡既不唯一也不具备不可利用性，当对手采用不同均衡或非均衡策略时，无法提供有意义的保证。这引发了多人博弈中一系列长期存在的基本问题，涉及合适的目标、解概念以及原则性算法。本文通过聚焦均等份额这一自然目标——在总收益为C的n人对称博弈中确保获得C/n的期望收益——为解决这些挑战迈出了初步一步。我们严格刻画了实现均等份额在理论上可处理的条件，并受无悔学习启发设计了一系列高效算法，这些算法在各种设定下可证明地达到近似均等份额。此外，我们提供了互补的下界，证明了理论结果的紧致性。实验结果展示了最坏情况场景，其中先前最先进的多人博弈系统的元算法未能确保均等份额，而我们的算法成功实现，证明了方法的有效性。
英文摘要：
This paper examines multiplayer symmetric constant-sum games with more than two players in a competitive setting, including examples like Mahjong, Poker, and various board and video games. In contrast to two-player zero-sum games, equilibria in multiplayer games are neither unique nor non-exploitable, failing to provide meaningful guarantees when competing against opponents who play different equilibria or non-equilibrium strategies. This gives rise to a series of long-lasting fundamental questions in multiplayer games regarding suitable objectives, solution concepts, and principled algorithms. This paper takes an initial step towards addressing these challenges by focusing on the natural objective of equal share -- securing an expected payoff of C/n in an n-player symmetric game with a total payoff of C. We rigorously identify the theoretical conditions under which achieving an equal share is tractable and design a series of efficient algorithms, inspired by no-regret learning, that provably attain approximate equal share across various settings. Furthermore, we provide complementary lower bounds that justify the sharpness of our theoretical results. Our experimental results highlight worst-case scenarios where meta-algorithms from prior state-of-the-art systems for multiplayer games fail to secure an equal share, while our algorithm succeeds, demonstrating the effectiveness of our approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
