  We introduce Q-Nash, a quantum annealing algorithm for the NP-complete
problem of Fnding pure Nash equilibria in graphical games. The algorithm
consists of two phases. The first phase determines all combinations of best
response strategies for each player using classical computation. The second
phase finds pure Nash equilibria using a quantum annealing device by mapping
the computed combinations to a quadratic unconstrained binary optimization
formulation based on the Set Cover problem. We empirically evaluate Q-Nash on
D-Wave's Quantum Annealer 2000Q using different graphical game topologies. The
results with respect to solution quality and computing time are compared to a
Brute Force algorithm and the Iterated Best Response heuristic.
