Native quantum games from interacting discrete-time quantum walks

TL;DR

This paper introduces a new class of quantum games based on interacting discrete-time quantum walks, demonstrating how strategic behavior and equilibria emerge from physical quantum interactions.

Contribution

It presents a novel framework where quantum interactions define strategic behavior, with analytical and numerical analysis of equilibrium states in quantum walk-based games.

Findings

Stable stationary strategies exist with interaction but not without

Interaction-induced interference creates strategic coupling

Payoff functions become non-separable at first order in interaction strength

Abstract

We study how strategic interaction can arise from controlled quantum dynamics rather than being imposed as an external mathematical structure. We introduce a class of interaction-defined quantum games in which players are represented by distinguishable quantum walkers, strategies correspond to local coin operations, and payoffs are defined as expectation values of physical observables. Using interacting discrete-time quantum walks as a concrete platform, we demonstrate numerically that competitive, cooperative, and asymmetric games admit stable stationary strategy profiles when the walkers are coupled, while no non-trivial equilibria exist in the absence of interaction. To clarify the game-theoretic structure, we derive an analytic perturbative decomposition of the payoff function in the weak-interaction regime, showing explicitly that strategic coupling originates from interaction-induced interference terms in the joint probability distribution. For a collision-based phase interaction, the payoff becomes non-separable at first order in the interaction strength and generically admits stationary points satisfying the Nash conditions. Our results provide a physically explicit realization of strategic interdependence in quantum transport processes and establish interacting quantum walks as a minimal platform for studying game-theoretic behavior emerging from unitary dynamics.