Nash Equilibrium in Games on Graphs with Incomplete Preferences

TL;DR

This paper investigates the computation and characterization of Nash equilibria in two-player graph-based games with incomplete and possibly conflicting preferences, providing theoretical insights and practical applications in scenarios like drone delivery.

Contribution

It introduces a framework for analyzing Nash equilibria in games with incomplete preferences on graphs, considering various preference alignments and cooperation conditions, with a practical drone delivery example.

Findings

Nash equilibria characterized for fully, partially, and oppositely aligned preferences.

Conditions identified for when cooperation is necessary to achieve better outcomes.

Theoretical results applied to a drone delivery mechanism design problem.

Abstract

Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem of computing Nash equilibrium in a subclass of two-player games played on graphs where each player seeks to maximally satisfy their (possibly incomplete) preferences over a set of temporal goals. We characterize the Nash equilibrium and prove its existence in scenarios where player preferences are fully aligned, partially aligned, and completely opposite, in terms of the well-known solution concepts of sure winning and Pareto efficiency. When preferences are partially aligned, we derive conditions under which a player needs cooperation and demonstrate that the Nash equilibria depend not only on the preference alignment but also on whether the players need cooperation to achieve a better outcome and whether they are willing to cooperate.We illustrate the theoretical results by solving a mechanism design problem for a drone delivery scenario.