Equilibria of Round-Robin: Computational Hardness and Fairness for Few Subadditive Agents

2026-09-16

AI Summary

研究了次可加代理人在线循环赛中的策略行为及计算子博弈完美纳什均衡的复杂性，揭示了其在公平性上的局限与特性。

Abstract

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.

Problem

• round-robin
• subadditive agents
• subgame perfect Nash equilibrium
• computational hardness
• fairness

Innovation

• subgame perfect Nash equilibrium
• computational hardness
• fairness criteria
• round-robin procedure
• subadditive agents