Posetal Games: Efficiency, Existence, and Refinement of Equilibria in Games with Prioritized Metrics
This work addresses the challenge of designing interpretable and efficient equilibria for autonomous systems like robots and vehicles, though it appears incremental as it builds on standard game theory with new preference structures.
The paper tackles the problem of modeling multi-agent interactions with conflicting rules by introducing Posetal Games, where players have partially ordered preferences, and demonstrates the existence of pure Nash Equilibria under certain conditions, with results applied to an autonomous driving scenario showing interpretability in terms of minimum-rank-violation.
Modern applications require robots to comply with multiple, often conflicting rules and to interact with the other agents. We present Posetal Games as a class of games in which each player expresses a preference over the outcomes via a partially ordered set of metrics. This allows one to combine hierarchical priorities of each player with the interactive nature of the environment. By contextualizing standard game theoretical notions, we provide two sufficient conditions on the preference of the players to prove existence of pure Nash Equilibria in finite action sets. Moreover, we define formal operations on the preference structures and link them to a refinement of the game solutions, showing how the set of equilibria can be systematically shrunk. The presented results are showcased in a driving game where autonomous vehicles select from a finite set of trajectories. The results demonstrate the interpretability of results in terms of minimum-rank-violation for each player.