分析平均收益竞标博弈中最优策略的相互作用
Analyzing the Interaction of Optimal Strategies in Mean-Payoff Bidding Games
AI总结：
本文针对多智能体系统中智能体互动分析的挑战，聚焦两智能体图上的平均收益竞标博弈，分析对抗优化策略的互动，证明特定条件下博弈最终周期性并开发效用计算算法。
AI中文摘要：
在多智能体系统中设计智能体时，一个常见假设是其他智能体表现出对抗性行为，这使得设计者在无法控制或了解其他智能体行为时能获得最强的保证。然而，当所有智能体都在这种对抗假设下设计时，它们的实际互动并非对抗性（例如，当所有玩家都采取防御性策略时，没有玩家实际发起攻击）。在这种情况下，我们希望知道多智能体系统中会产生何种行为，但分析智能体之间的互动在数学和算法上都极具挑战性。本文针对这一问题展开分析，聚焦于由两个智能体在图上进行的竞标博弈：一个标记被放置在顶点上，每一轮通过拍卖（竞标）决定哪个智能体移动标记，从而生成决定智能体效用的无限路径。我们考虑平均收益目标：每个顶点与每个智能体的奖励相关联，无限博弈中的效用是奖励的极限平均值。我们分析每个智能体遵循针对对抗者优化的策略时产生的博弈，并考虑两种已知的最优策略显式构造。技术挑战源于竞标博弈的无限多配置及其复杂动态。我们证明，在某些限制下，产生的博弈最终是周期性的，并开发算法来计算其中智能体的效用。
英文摘要：
A common assumption when designing an agent in a multi-agent system is that the other agents behave adversarially. This allows a designer to obtain the strongest guarantees when they have no control over nor knowledge about the other agents' behavior. However, when all agents are designed under this adversarial assumption, their actual interaction is not adversarial (e.g., when all players play defensively, no player actually attacks). In such settings, we would like to know what behavior arises in the multi-agent system. However, analyzing the interaction among agents is notoriously challenging, both mathematically and algorithmically. In this paper, we provide such an analysis, focusing on bidding games, played by two agents on a graph as follows. A token is placed on a vertex, and in each turn an auction (bidding) determines which agent moves the token, thus generating an infinite path that determines the agents' utilities. We consider mean-payoff objectives; each vertex is associated with a reward for each player, and the utility in an infinite play is the limit average of the rewards. We analyze the play that is generated when each agent follows a strategy that optimizes against an adversary, and consider the two known explicit constructions of optimal strategies. The technical challenge stems from the infinitely-many configurations of a bidding game and their complicated dynamics. We show that, under some restrictions, the generated play is ultimately periodic, and develop algorithms to compute the players' utilities in it.
