# A Mechanism for Mutual Fairness in Cooperative Games with Replicable Resources -- Extended Version

arXiv: https://arxiv.org/abs/2508.13960 · HTML: https://mlsanity.com/paper/2508.13960/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Social simulation and multi-agent debate, one of 16 directions in LLM agents and tool use.
- Builds on 5 of its 26 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Placed in

- LLM agents and tool use / [Social simulation and multi-agent debate](https://mlsanity.com/agents/social-simulation-and-multi-agent-debate/)

## Builds on (most cited first, 5 of 5)

- [Data Banzhaf: A Robust Data Valuation Framework for Machine Learning](https://mlsanity.com/paper/2205.15466/) (2022)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [Social Choice Should Guide AI Alignment in Dealing with Diverse Human Feedback](https://mlsanity.com/paper/2404.10271/) (2024)
- [Collaborative Machine Learning with Incentive-Aware Model Rewards](https://mlsanity.com/paper/2010.12797/) (2020)
- [Mechanisms that Incentivize Data Sharing in Federated Learning](https://mlsanity.com/paper/2207.04557/) (2022)

## Abstract (arXiv)

The latest developments in AI focus on agentic systems where artificial and human agents cooperate to realize global goals. An example is collaborative learning, which aims to train a global model based on data from individual agents. A major challenge in designing such systems is to guarantee safety and alignment with human values, particularly a fair distribution of rewards upon achieving the global goal. Cooperative game theory offers useful abstractions of cooperating agents via value functions, which assign value to each coalition, and via reward functions. With these, the idea of fair allocation can be formalized by specifying fairness axioms and designing concrete mechanisms. Classical cooperative game theory, exemplified by the Shapley value, does not fully capture scenarios like collaborative learning, as it assumes nonreplicable resources, whereas data and models can be replicated. Infinite replicability requires a generalized notion of fairness, formalized through new axioms and mechanisms. These must address imbalances in reciprocal benefits among participants, which can lead to strategic exploitation and unfair allocations. The main contribution of this paper is a mechanism and a proof that it fulfills the property of mutual fairness, formalized by the Balanced Reciprocity Axiom. It ensures that, for every pair of players, each benefits equally from the participation of the other.