# Berk-Nash Equilibrium: A Framework for Modeling Agents with Misspecified Models

arXiv: https://arxiv.org/abs/1411.1152 · HTML: https://mlsanity.com/paper/1411.1152/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Nov 2014.

## Built on by (most cited first, 8 of 8)

- [Conjectural Online Learning with First-order Beliefs in Asymmetric Information Stochastic Games](https://mlsanity.com/paper/2402.18781/) (2024)
- [Automated Security Response through Online Learning with Adaptive Conjectures](https://mlsanity.com/paper/2402.12499/) (2024)
- [Symbiotic Game and Foundation Models for Cyber Deception Operations in Strategic Cyber Warfare](https://mlsanity.com/paper/2403.10570/) (2024)
- [In the Eye of the Beholder: Robust Prediction with Causal User Modeling](https://mlsanity.com/paper/2206.00416/) (2022)
- [Learning Underspecified Models](https://mlsanity.com/paper/2207.10140/) (2022)
- [Learned Collusion](https://mlsanity.com/paper/2304.12647/) (2023)
- [Belief formation and the persistence of biased beliefs](https://mlsanity.com/paper/2310.08466/) (2023)
- [Epistemic Traps: Rational Misalignment Driven by Model Misspecification](https://mlsanity.com/paper/2602.17676/) (2026)

## Abstract (arXiv)

We develop an equilibrium framework that relaxes the standard assumption that people have a correctly-specified view of their environment. Each player is characterized by a (possibly misspecified) subjective model, which describes the set of feasible beliefs over payoff-relevant consequences as a function of actions. We introduce the notion of a Berk-Nash equilibrium: Each player follows a strategy that is optimal given her belief, and her belief is restricted to be the best fit among the set of beliefs she considers possible. The notion of best fit is formalized in terms of minimizing the Kullback-Leibler divergence, which is endogenous and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self-confirming equilibrium constitute special cases where players have correctly-specified models. We provide a learning foundation for Berk-Nash equilibrium by extending and combining results from the statistics literature on misspecified learning and the economics literature on learning in games.