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 agents’ 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, 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 or coordination.
Bibliographical noteKAUST Repository Item: Exported on 2022-01-25
Acknowledgements: This work was supported in part by the King Abdullah University of Science and Technology (KAUST); in part by US Office of Naval Research (ONR) under Grant N00014-19-1-2556; in part by the US Army Research Office (ARO) under Grant W911NF-18-1-0325; in part by Direcciòn
General de Asuntos del Personal Académico (DGAPA), National Autonomous University of Mexico (UNAM), through the Programa de
Apoyo a Proyectos de Investigación e Innovación Tecnológica (PAPIIT) Research under Grant IN102420; in part by the Conacyt under Grant
A1-S-10610; in part by the NSF Graduate Research Fellowship under Grant DGE-2039656; and in part by the Princeton University School
of Engineering and Applied Science through the generosity of Lydia and William Addy ’82. Recommended by Senior Editor M. Guay