# The Coordination Gap: Multi-Agent Alternation Metrics for Temporal Fairness in Repeated Games

arXiv: https://arxiv.org/abs/2603.05789 · HTML: https://mlsanity.com/paper/2603.05789/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 57 references that are in the map.
- First posted on arXiv 6 Mar 2026.

## Builds on (most cited first, 11 of 11)

- [A multi-agent reinforcement learning model of common-pool resource appropriation](https://mlsanity.com/paper/1707.06600/) (2017)
- [Learning Fairness in Multi-Agent Systems](https://mlsanity.com/paper/1910.14472/) (2019)
- [Temporal Fair Division of Indivisible Items](https://mlsanity.com/paper/2410.14593/) (2024)
- [Temporal Fair Division](https://mlsanity.com/paper/2410.23416/) (2024)
- [Modeling the Formation of Social Conventions from Embodied Real-Time Interactions](https://mlsanity.com/paper/1802.06108/) (2018)
- [Weighted Fair Division with Matroid-Rank Valuations: Monotonicity and Strategyproofness](https://mlsanity.com/paper/2303.14454/) (2023)
- [Generalized binary utility functions and fair allocations](https://mlsanity.com/paper/2109.08461/) (2021)
- [Loss aversion fosters coordination among independent reinforcement learners](https://mlsanity.com/paper/1912.12633/) (2019)
- [Temporal Fair Division of Indivisible Goods with Scheduling](https://mlsanity.com/paper/2601.12835/) (2026)
- [Perpetually Fair Assignments Via Balanced Sequences of Permutations](https://mlsanity.com/paper/2602.21687/) (2026)
- [Purely vision-based collective movement of robots](https://mlsanity.com/paper/2406.17106/) (2024)

## Built on by (most cited first, 1 of 1)

- [Temporal Fair Division in Multi-Agent Systems: From Precise Alternation Metrics to Scalable Coordination Proxies](https://mlsanity.com/paper/2605.14879/) (2026)

## Abstract (arXiv)

Repeated multi-agent interactions require evaluation metrics that capture not only payoff distributions but also their temporal organization. Conventional outcome-based fairness measures can assign similar aggregate scores to temporally distinct coordination patterns, obscuring whether access to a shared resource is genuinely rotating or persistently monopolized. We study this problem in the Honey-Jar Game (HJG), a minimally dynamic repeated threshold-congestion Markov game in which n agents compete for exclusive access to a single high-reward resource. We introduce Perfect Alternation (PA), a reference turn-taking regime corresponding to the n-periodic round-robin picking sequence, together with six novel Alternation (ALT) metrics and a benchmarking methodology mapping ALT values to interpretable PA-equivalent performance. Using Q-learning agents as a minimal adaptive baseline against analytically derived random-policy baselines, we uncover a clear measurement failure: despite deceptively high traditional metrics (e.g., reward fairness often exceeding 0.9), learned policies perform worse than random on every ALT metric, by 34-74% on CALT and up to 92% on EALT, with PA-equivalent coordination falling to roughly one-fifth of the population at n=10. EALT further reveals two distinct failure patterns: without episodic memory (Type-A), the deficit grows from -20% at n=2 to -92% at n=10; with episodic memory (Type-B), it reaches a trough of -76% at n=5 before partially recovering to -10% at n=10. Conventional efficiency and fairness metrics do not reveal these differences. The ALT framework complements the temporal fair division and picking-sequence literature by diagnosing whether temporal fairness emerges spontaneously in decentralized adaptive systems rather than how to enforce it.