Misspecified learning and evolutionary stability
Abstract
We extend the indirect evolutionary approach to the selection of (possibly misspecified) models. Agents with different models match in pairs to play a stage game, where models define feasible beliefs about game parameters and about others' strategies. In equilibrium, each agent adopts the feasible belief that best fits their data and plays optimally given their beliefs. We define the stability of the resident model by comparing its equilibrium payoff with that of the entrant model, and provide conditions under which the correctly specified resident model can only be destabilized by misspecified entrant models that contain multiple feasible beliefs (that is, entrant models that permit inference). We also show that entrants may do well in their matches against the residents only when the entrant population is large, due to the endogeneity of misspecified beliefs. Applications include the selection of demand-elasticity misperception in Cournot duopoly and the emergence of analogy-based reasoning in centipede games.
Cite
@article{arxiv.2509.16067,
title = {Misspecified learning and evolutionary stability},
author = {Kevin He and Jonathan Libgober},
journal= {arXiv preprint arXiv:2509.16067},
year = {2025}
}
Comments
This material was previously part of a larger paper titled "Evolutionarily Stable (Mis)specifications: Theory and Applications," which split into two smaller papers: "Misspecified Learning and Evolutionary Stability" and "Higher-Order Beliefs and (Mis)learning from Prices.". arXiv admin note: text overlap with arXiv:2012.15007