Differential Equation Approximations for Population Games using Elementary Probability

TL;DR

This paper introduces a simplified method using undergraduate probability to derive differential equation approximations for population games, making the mean-field approach more accessible for analyzing strategic interactions among large agent populations.

Contribution

It provides a more accessible derivation of differential equation approximations for population games, reducing reliance on advanced mathematical techniques.

Findings

Simplified derivation using undergraduate probability

Effective mean-field approximation for population games

Enhanced accessibility for analyzing large-scale strategic interactions

Abstract

Population games model the evolution of strategic interactions among a large number of uniform agents. Due to the agents' uniformity and quantity, their aggregate strategic choices can be approximated by the solutions of a class of ordinary differential equations. This mean-field approach has found to be an effective tool of analysis. However its current proofs rely on advanced mathematical techniques, making them less accessible. In this article, we present a simpler derivation, using only undergraduate-level probability.