Tuning Rate of Strategy Revision in Population Games

TL;DR

This paper studies how time delays in strategy updates affect population game dynamics and proposes an algorithm to tune revision rates, ensuring convergence to Nash equilibrium despite delays.

Contribution

It introduces a novel algorithm for tuning strategy revision rates in population games with delays, guaranteeing convergence to Nash equilibrium.

Findings

Large delays cause oscillations and prevent equilibrium attainment.

The proposed tuning algorithm ensures convergence despite delays.

Simulations validate the theoretical convergence results.

Abstract

We investigate a multi-agent decision problem in population games where each agent in a population makes a decision on strategy selection and revision to engage in repeated games with others. The strategy revision is subject to time delays which represent the time it takes for an agent revising its strategy needs to spend before it can adopt a new strategy and return back to the game. We discuss the effect of the time delays on long-term behavior of the agents' strategy revision. In particular, when the time delays are large, the strategy revision would exhibit oscillation and the agents spend substantial time in "transitioning" between different strategies, which prevents the agents from attaining the Nash equilibrium of the game. As a main contribution of the paper, we propose an algorithm that tunes the rate of the agents' strategy revision and show such tuning approach ensures convergence to the Nash equilibrium. We validate our analytical results using simulations.