Opinion-guided Games: Strategic Coordination Through Gradient-based Opinion Dynamics

Abstract

As the performance capabilities of autonomous agents continue to increase, being able to effectively coordinate with other agents becomes vital for deployment in real-world environments. In this thesis, I examine interaction through the lens of general-sum dynamic games, where agents are tasked with optimizing their objectives despite having potentially conflicting goals. The first contribution of this thesis is the development of an iterative linear-quadratic toolbox to efficiently compute approximate Stackelberg (leader-follower) equilibria. To navigate the ambiguity between leader-follower roles in a two-player Stackelberg game, a novel form of nonlinear opinion dynamics is used to break indecision at critical times in interaction scenarios. By using opinions as a proxy for probabilities, gradient descent over the expected payoff of the game with respect to opinions is used to populate the parameters for the nonlinear opinion dynamics. Using this nonlinear model for opinion evolution, agents are able to coordinate leader-follower roles without prior biases over the order of play. Demonstrations of the novel Stackelberg game solver are shown on hardware to illustrate its practical effectiveness in the real-world, and simulation studies validate the gradient-based nonlinear opinion dynamics. This thesis grounds the previously hand-tuned nonlinear opinion dynamics model with payoff functions associated with tangible real-world values, closing the loop between physical interaction and opinion evolution.