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Collaborative Mean Estimation Among Heterogeneous Strategic Agents: Individual Rationality, Fairness, and Truthful Contribution
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Designs a no-money data-sharing mechanism for collaborative univariate-normal mean estimation among heterogeneous strategic agents that is NIC and IR, achieving sqrt(m) (and O(1) under favorable conditions) efficiency to the IR social-penalty baseline, plus hardness results and a fairness extension via bargaining solutions.
Problem
Collaborative mean estimation where agents with heterogeneous sampling costs can share data, but must be incentivized to contribute sufficient data truthfully (no free-riding or fabrication) while remaining individually rational and reasonably fair.
Approach
Modify the social-penalty-optimal collection scheme (Compute-n-Approx) so enough agents collect each distribution to enable leverage-based validation, then use a corruption-based estimator (adapted from prior work) that penalizes deviations, yielding a Nash equilibrium that is IR and near-efficient; bargaining solutions (Nash, egalitarian, Kalai-Smorodinsky) plug in as alternative collection schem
Key results
- Mechanism is NIC, IR, and sqrt(m)-efficient in general, and 8-efficient when the favorable condition holds.
- Three hardness results: no DSIC or always-IR efficient mechanism; every agent gets at least half its working-alone penalty.
- Worst-case Omega(sqrt(m)) price of stability for any mechanism and any NE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Corrupt Based on Leverage with the IR-minimizing collection scheme | Collaborative heterogeneous Gaussian mean estimation · Worst-case instances | social-penalty approximation factor: √m in the worst case; 8 under favorable conditions | Mixed |
| Require a dominant-strategy profile | Mechanisms for collaborative mean estimation · Heterogeneous Gaussian mean estimation | agent penalty relative to working alone: ≥ penaliir/2 | Hurt |
| Require individual rationality regardless of other agents' strategies | Mechanisms for collaborative mean estimation · Heterogeneous Gaussian mean estimation | agent penalty relative to working alone: ≥ penaliir/2 | Hurt |
| Use the proposed mechanism instead of unconstrained minimum-social-penalty collection | Homogeneous scalar example with favorable condition · Homogeneous scalar example | social penalty: 2σ√c'm -> 16σ√c'm | Hurt |
| Use Nash bargaining or egalitarian bargaining to allocate collection work | Corrupt Based on Leverage · Heterogeneous Gaussian mean estimation | fairness of agent outcomes | Helped |
Surprising findings
- Naively minimizing social penalty subject to IR still leaves the lowest-cost agent no better than working alone, and without IR it is hopeless under strategic behavior.
- Agents can avoid collecting data and simply fabricate submissions to escape costs, so simple count-based checks fail.
Limitations
- Worst-case efficiency gap of sqrt(m) remains and is unavoidable for NE-based designs.
- Favorable condition required for constant-factor approximation; otherwise only sqrt(m).
Experimental setup
Metrics: social penalty agent penalty (estimation error plus collection cost) approximation ratio
Baselines: sample mean mechanism social penalty minimization without IR constraints
Builds on: Shapley-free collaborative learning with strategic agents (Karimireddy et al.-st Nash bargaining egalitarian bargaining Kalai-Smorodinsky solution
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