发表机构
University of Oxford; Technical University of Munich（牛津大学; 慕尼黑工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究轮转公平分配机制中次可加智能体的策略行为，证明计算子博弈完美纳什均衡在少量智能体下具有PSPACE或NP困难性，并揭示均衡公平性界限及均衡数量指数级增长。
AI 中文摘要
轮转程序是一种简单且被广泛研究的公平分配机制，其中智能体轮流选择物品。受体育联盟中选秀机制的启发，我们研究了次可加智能体在在线轮转中的策略行为。这产生了一个扩展形式博弈，我们研究了计算子博弈完美纳什均衡（SPNE）的计算问题。我们证明，仅对于两个次模智能体，计算SPNE是$\mathsf{PSPACE}$-困难的。即使对于$\mathit{OXS}$效用类（这是次模效用的一个特例），对于少量智能体，计算SPNE仍然是$\mathsf{NP}$-困难的。我们用规范性结果补充了我们的计算性结果。我们证明，仅对于三个加性智能体，存在每个均衡都违反EF1的实例。这区分了在线博弈和直接揭示博弈。在积极方面，我们证明对于加性智能体，每个均衡分配都是至多一件物品的比例分配（PROP1），并且对于两个加性智能体，它也是EF1。最后，通过证明轮转在均衡处是专横的，我们证明了即使智能体具有字典序偏好，均衡分配的数量也可能是指数级的。
英文摘要
The round-robin procedure is a simple and well-studied fair division mechanism where agents pick goods in turns. Motivated by draft mechanisms in sports leagues, we investigate strategic behaviour in online round-robin for subadditive agents. This gives rise to an extensive-form game, and we study the computational problem of computing a subgame perfect Nash equilibrium (SPNE). We show that for just two submodular agents, computing an SPNE is $\mathsf{PSPACE}$-hard. Even for the class of $\mathit{OXS}$ utilities, which are a special case of submodular utilities, computing an SPNE remains $\mathsf{NP}$-hard for a small number of agents. We complement our computational results with normative results. We show that for just three additive agents, there exist instances where every equilibrium violates EF1. This separates the online and the direct revelation games. On the positive side, we show that for additive agents every equilibrium allocation is proportional up to one good (PROP1) and for two additive agents it is also EF1. Finally, by showing that round-robin is bossy at equilibrium, we prove that the number of equilibrium allocations can be exponential even if agents have lexicographic preferences.
