Nonequilibrium dynamical games: A control systems perspective

Abstract

Dynamical games model interactions between agents that take place in ever-shifting environments. Due to the increasing penetration of autonomous systems to society, understanding and predicting the outcomes of these games has become crucial. In this work, we highlight the importance of nonequilibrium solutions to dynamical games through the lens of bounded rationality. We describe the principles of level-k thinking and cognitive hierarchy – concepts developed in the field of economics – via mathematical tools and formulation of control theory. We describe the main principles of bounded rationality for nonequilibrium differential games in both nonlinear non-zero-sum and linear zero-sum settings. The importance of those approaches is highlighted in problems of pursuit evasion between Unmanned Aerial Vehicles, while the core of the bounded rationality principles that we employ are extended to discrete stochastic dynamical games. The versatility of the proposed approach is complemented by rigorous mathematical guarantees that enable predictability of the games’ outcomes.