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Heterogeneous Data Game: Characterizing the Model Competition Across Multiple Data Sources

ICML 2025 · Learning theory and algorithms › Submodular and game algorithms · approach: Opponent modeling and subgame solving · 0 citations (OpenAlex)

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Proposes the Heterogeneous Data Game, a game-theoretic model of multiple ML providers competing across heterogeneous data sources, and characterizes pure Nash equilibria (non-existence, homogeneous, heterogeneous) under proximity and logit (probability) choice models, with synthetic experiments on temperature thresholds.

Problem

How multiple competing ML model providers choose models when data sources are heterogeneous (concept and covariate shift) and each data source selects a provider by its loss, and what equilibria (PNE) arise.

Approach

Extends competitive ML model-provider games from a single data distribution to multiple heterogeneous sources, modeling losses as squared Mahalanobis distances (MSE in linear models) and data-source choices via proximity or logit (temperature) models, then deriving existence and structure of pure Nash equilibria.

Key results

• Under the proximity model with N=2, a PNE exists iff w_1 >= 0.5, and (theta_1, theta_1) is the unique PNE when w_1 > 0.5.
• Under the probability model with N=2, any PNE must be homogeneous at the monopoly parameter, and it is a PNE iff t >= some threshold below 2*l_max.
• Synthetic experiments show the homogeneous PNE threshold is roughly 0.1 to 0.2 times 2*l_max, and heterogeneous and homogeneous PNE may coexist for small N.

Measured effects reported in the paper

Surprising findings

• Under the probability choice model, a PNE may fail to exist even when w_1 >= 0.5 for small t, so the probability model does not converge to the proximity model's PNE as t goes to 0 for N=2.
• Coexistence of homogeneous and heterogeneous PNE becomes less likely as N grows in the synthetic experiments.

Limitations

• Analysis is restricted to linear models with squared Mahalanobis loss; generalization to nonlinear models is not established.
• Closed-form expressions for the temperature thresholds are not derived; they are estimated empirically.
• Heterogeneous PNE under the probability model is shown only for small temperature with a sufficient-condition range of N, and experiments use only K=2 and D=2.

Experimental setup

Metrics: critical temperature threshold for homogeneous PNE maximal temperature for heterogeneous PNE

Builds on: competitive location models logit choice model competition among ML providers (best-response dynamics)

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