Choice Paralysis in Evolutionary Games

2025-09-10

AI Summary

This paper investigates the convergence of finite-strategy approximations to infinite-strategy evolutionary games, focusing on behavioral distortion in long-term dynamics induced by “choice paralysis.” We introduce two novel concepts—*choice mobility* and *choice paralysis*—and establish that choice mobility is a necessary and sufficient condition for asymptotic equivalence between finite approximations and the original infinite-dimensional system. Under mild regularity assumptions, we rigorously prove uniform convergence of finite-strategy approximations to the true dynamics—in finite time—for canonical models including the replicator dynamic. Furthermore, we construct explicit counterexamples demonstrating that when choice paralysis occurs, the infinite-strategy system may exhibit evolutionary stasis, a phenomenon entirely missed by standard finite approximations. Our results provide both theoretical convergence guarantees and practical diagnostic criteria for numerical simulation and modeling of evolutionary games.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Machine Learning: Evolutionary Learning
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

In this paper, we consider finite-strategy approximations of infinite-strategy evolutionary games. We prove that such approximations converge to the true dynamics over finite-time intervals, under mild regularity conditions which are satisfied by classical examples, e.g., the replicator dynamics. We identify and formalize novel characteristics in evolutionary games: choice mobility, and its complement choice paralysis. Choice mobility is shown to be a key sufficient condition for the long-time limiting behavior of finite-strategy approximations to coincide with that of the true infinite-strategy game. An illustrative example is constructed to showcase how choice paralysis may lead to the infinite-strategy game getting "stuck," even though every finite approximation converges to equilibrium.

Problem

• Analyzing finite-strategy approximations of infinite-strategy evolutionary games
• Studying convergence of approximations under mild regularity conditions
• Investigating choice paralysis and mobility effects on game dynamics

Innovation

• Finite-strategy approximations of infinite-strategy games
• Convergence under mild regularity conditions
• Identified choice mobility and paralysis characteristics