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Cross-Validation Equilibrium

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Listed:
  • Ran Spiegler
  • Stephan Waizmann

Abstract

We study strategic interaction when players delegate belief formation to predictive machine learning (ML). In a static Bayesian game, each player's ML agent predicts a payoff-relevant outcome variable as a function of the player's type. The ML agent's training sample is endogenous: it is drawn from the outcome distribution generated by players' ML-guided behavior. In Cross-Validation Equilibrium (CVE), each player's ML agent selects a predictive model to minimize expected out-of-sample squared error, given its realized training sample, and each player best-replies to the belief generated by the model her ML agent selected. We analyze CVE and relate it to other equilibrium concepts. We apply CVE to jury voting, speculative betting, and games with linear-quadratic payoffs. E.g., in a team-effort game, endogenous model selection can give rise to multiple equilibria.

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  • Ran Spiegler & Stephan Waizmann, 2026. "Cross-Validation Equilibrium," Papers 2606.12571, arXiv.org.
    • Handle: RePEc:arx:papers:2606.12571
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    References listed on IDEAS

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    1. Emilio Calvano & Giacomo Calzolari & Vincenzo Denicolò & Sergio Pastorello, 2020. "Artificial Intelligence, Algorithmic Pricing, and Collusion," American Economic Review, American Economic Association, vol. 110(10), pages 3267-3297, October.
    2. Jehiel, Philippe, 2005. "Analogy-based expectation equilibrium," Journal of Economic Theory, Elsevier, vol. 123(2), pages 81-104, August.
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