Temporal Fair Division in Multi-Agent Systems: From Precise Alternation Metrics to Scalable Coordination Proxies
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910221817872384 |
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| author | Papadopoulos, Nikolaos Al. |
| author_facet | Papadopoulos, Nikolaos Al. |
| contents | A plethora real-world environments require agents to compete repeatedly for the same limited resource, calling for a temporal notion of fairness judged across entire interaction histories. This paper advances the theory of temporal fair division by introducing Rotational Periodicity (RP), a family of lightweight metrics, alongside the ALT family of sliding-window measures, within a unified framework for repeated multi-agent resource competition.
We formalise the Multi-Agent Battle of the Exes (MBoE) as a repeated fair division instance and establish Perfect Alternation (PA) as its canonical temporally fair solution, drawing connections to proportionality, envy-freeness, and n-periodic round-robin allocation. RP decomposes temporal fairness into two complementary sub-measures: Rotational Score (RS) and Waiting Periods Evaluation (WPE), achieving O(nu+n) time complexity versus the O(nu*n) of ALT, where nu is the episode count and n the agent count.
Empirical evaluation across n in {2,3,5,8,10} reveals three findings. First, both RP and ALT expose a coordination failure invisible to traditional metrics: Q-learning agents perform worse than random policies by 10-73% on RP and 7-35% on CALT, while Reward Fairness remains misleadingly high (above 0.92 for n>=3). Second, RP achieves 12-25x computational speedup over ALT, growing with n. Third, the two families are complementary: ALT provides richer discrimination for small populations; RP scales reliably where ALT becomes intractable. Together they form a diagnostic toolkit for temporal fair division. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_14879 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Temporal Fair Division in Multi-Agent Systems: From Precise Alternation Metrics to Scalable Coordination Proxies Papadopoulos, Nikolaos Al. Multiagent Systems Computer Science and Game Theory Machine Learning 91A20, 91B32, 68T42 I.2.11; F.2.2; J.4 A plethora real-world environments require agents to compete repeatedly for the same limited resource, calling for a temporal notion of fairness judged across entire interaction histories. This paper advances the theory of temporal fair division by introducing Rotational Periodicity (RP), a family of lightweight metrics, alongside the ALT family of sliding-window measures, within a unified framework for repeated multi-agent resource competition. We formalise the Multi-Agent Battle of the Exes (MBoE) as a repeated fair division instance and establish Perfect Alternation (PA) as its canonical temporally fair solution, drawing connections to proportionality, envy-freeness, and n-periodic round-robin allocation. RP decomposes temporal fairness into two complementary sub-measures: Rotational Score (RS) and Waiting Periods Evaluation (WPE), achieving O(nu+n) time complexity versus the O(nu*n) of ALT, where nu is the episode count and n the agent count. Empirical evaluation across n in {2,3,5,8,10} reveals three findings. First, both RP and ALT expose a coordination failure invisible to traditional metrics: Q-learning agents perform worse than random policies by 10-73% on RP and 7-35% on CALT, while Reward Fairness remains misleadingly high (above 0.92 for n>=3). Second, RP achieves 12-25x computational speedup over ALT, growing with n. Third, the two families are complementary: ALT provides richer discrimination for small populations; RP scales reliably where ALT becomes intractable. Together they form a diagnostic toolkit for temporal fair division. |
| title | Temporal Fair Division in Multi-Agent Systems: From Precise Alternation Metrics to Scalable Coordination Proxies |
| topic | Multiagent Systems Computer Science and Game Theory Machine Learning 91A20, 91B32, 68T42 I.2.11; F.2.2; J.4 |
| url | https://arxiv.org/abs/2605.14879 |