# Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairness, and Truthful Contribution

arXiv: https://arxiv.org/abs/2407.15881 · HTML: https://mlsanity.com/paper/2407.15881/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 30 references that are in the map.
- First posted on arXiv 20 Jul 2024.

## Builds on (most cited first, 19 of 19)

- [Towards Efficient Data Valuation Based on the Shapley Value](https://mlsanity.com/paper/1902.10275/) (2019)
- [Strategic Classification](https://mlsanity.com/paper/1506.06980/) (2015)
- [A Principled Approach to Data Valuation for Federated Learning](https://mlsanity.com/paper/2009.06192/) (2020)
- [A Marketplace for Data: An Algorithmic Solution](https://mlsanity.com/paper/1805.08125/) (2018)
- [Collaborative Machine Learning with Incentive-Aware Model Rewards](https://mlsanity.com/paper/2010.12797/) (2020)
- [Model-sharing Games: Analyzing Federated Learning Under Voluntary Participation](https://mlsanity.com/paper/2010.00753/) (2020)
- [Free-rider Attacks on Model Aggregation in Federated Learning](https://mlsanity.com/paper/2006.11901/) (2020)
- [Free-riders in Federated Learning: Attacks and Defenses](https://mlsanity.com/paper/1911.12560/) (2019)
- [Incentive Mechanisms for Federated Learning: From Economic and Game Theoretic Perspective](https://mlsanity.com/paper/2111.11850/) (2021)
- [One for One, or All for All: Equilibria and Optimality of Collaboration in Federated Learning](https://mlsanity.com/paper/2103.03228/) (2021)
- [Mechanisms that Incentivize Data Sharing in Federated Learning](https://mlsanity.com/paper/2207.04557/) (2022)
- [Optimum Statistical Estimation with Strategic Data Sources](https://mlsanity.com/paper/1408.2539/) (2014)
- [Truthful Data Acquisition via Peer Prediction](https://mlsanity.com/paper/2006.03992/) (2020)
- [Towards Data Auctions with Externalities](https://mlsanity.com/paper/2003.08345/) (2020)
- [Buying Private Data without Verification](https://mlsanity.com/paper/1404.6003/) (2014)
- [Evaluating and Incentivizing Diverse Data Contributions in Collaborative Learning](https://mlsanity.com/paper/2306.05592/) (2023)
- [Mechanism Design for Collaborative Normal Mean Estimation](https://mlsanity.com/paper/2306.06351/) (2023)
- [Incentivizing Honesty among Competitors in Collaborative Learning and Optimization](https://mlsanity.com/paper/2305.16272/) (2023)
- [Unravelling in Collaborative Learning](https://mlsanity.com/paper/2407.14332/) (2024)

## Built on by (most cited first, 4 of 4)

- [Incentivized Symbiosis: A Paradigm for Human-Agent Coevolution](https://mlsanity.com/paper/2412.06855/) (2024)
- [TheoremForge: Scaling up Formal Data Synthesis with Low-Budget Agentic Workflow](https://mlsanity.com/paper/2601.17332/) (2026)
- [A Cram'er-von Mises Approach to Incentivizing Truthful Data Sharing](https://mlsanity.com/paper/2506.07272/) (2025)
- [Gradient Manipulation in Distributed Stochastic Gradient Descent with Strategic Agents: Truthful Incentives with Convergence Guarantees](https://mlsanity.com/paper/2603.27962/) (2026)

## Abstract (arXiv)

We study a collaborative learning problem where m agents aim to estimate a vector μ =(μ1,ldots,μd)∈ ℝd by sampling from associated univariate normal distributions N(μk, σ2)k∈[d]. Agent i incurs a cost ci,k to sample from N(μk, σ2). Instead of working independently, agents can exchange data, collecting cheaper samples and sharing them in return for costly data, thereby reducing both costs and estimation error. We design a mechanism to facilitate such collaboration, while addressing two key challenges: ensuring individually rational (IR) and fair outcomes so all agents benefit, and preventing strategic behavior (e.g. non-collection, data fabrication) to avoid socially undesirable outcomes. We design a mechanism and an associated Nash equilibrium (NE) which minimizes the social penalty-sum of agents' estimation errors and collection costs-while being IR for all agents. We achieve a O(√m)-approximation to the minimum social penalty in the worst case and an O(1)-approximation under favorable conditions. Additionally, we establish three hardness results: no nontrivial mechanism guarantees (i) a dominant strategy equilibrium where agents report truthfully, (ii) is IR for every strategy profile of other agents, (iii) or avoids a worst-case Omega(√m) price of stability in any NE. Finally, by integrating concepts from axiomatic bargaining, we demonstrate that our mechanism supports fairer outcomes than one which minimizes social penalty.