Misspecified learning and evolutionary stability

2025-09-19

AI Summary

This paper investigates the evolutionary stability of correctly specified learning models under misspecified beliefs within an indirect evolutionary framework: specifically, when agents form beliefs via misspecified models (e.g., misestimated demand elasticity or analogy-based reasoning) and optimize accordingly, under what conditions can such misspecified models—admitting multiple feasible beliefs—invade a population adhering to a correctly specified resident model? We identify an endogenous scale dependence for successful invasion: invasion succeeds only when the invading group exceeds a critical size, enabling its multiplicity of beliefs to overcome initial fitness disadvantages and achieve stable coexistence. Methodologically, we integrate game-theoretic equilibrium analysis, belief-fitting dynamics, and best-response learning models. Theoretical analysis establishes that several canonical misspecified models constitute evolutionarily stable strategies in Cournot duopoly and the centipede game, demonstrating the nontrivial robustness and adaptive persistence of “wrong yet resilient” belief structures.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Reasoning with Beliefs

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

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.

Problem

• Extending evolutionary approach to model selection with misspecification
• Analyzing stability conditions between resident and entrant models
• Examining endogenous belief formation in strategic interactions

Innovation

• Extends indirect evolutionary approach model selection
• Defines stability by comparing resident entrant payoffs
• Shows entrants succeed with large population size