Tuning Cooperative Behavior in Games with Nonlinear Opinion Dynamics

TL;DR

This paper introduces a nonlinear opinion dynamics model to analyze and tune cooperative behavior in multi-agent social dilemmas, revealing how parameters influence equilibrium stability and cooperation levels.

Contribution

It provides a systematic, analytically tractable framework for understanding and controlling cooperation in multi-agent games using nonlinear opinion dynamics.

Findings

Bifurcation analysis identifies conditions for bistability of strategies.

Model parameters affect the size of attraction regions for equilibria.

Insights into tuning cooperation in prisoner's dilemma and public goods games.

Abstract

We examine the tuning of cooperative behavior in repeated multi-agent games using an analytically tractable, continuous-time, nonlinear model of opinion dynamics. Each modeled agent updates its real-valued opinion about each available strategy in response to payoffs and other agent opinions, as observed over a network. We show how the model provides a principled and systematic means to investigate behavior of agents that select strategies using rationality and reciprocity, key features of human decision-making in social dilemmas. For two-strategy games, we use bifurcation analysis to prove conditions for the bistability of two equilibria and conditions for the first (second) equilibrium to reflect all agents favoring the first (second) strategy. We prove how model parameters, e.g., level of attention to opinions of others (reciprocity), network structure, and payoffs, influence dynamics and, notably, the size of the region of attraction to each stable equilibrium. We provide insights by examining the tuning of the bistability of mutual cooperation and mutual defection and their regions of attraction for the repeated prisoner's dilemma and the repeated multi-agent public goods game. Our results generalize to games with more strategies, heterogeneity, and additional feedback dynamics, such as those designed to elicit cooperation.