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.
Quantum games extend classical game theory into the quantum realm by incorporating quantum players and quantum strategies. Two-player quantum games have been widely studied and applied, among other areas, in optimization and decision-making. In this work, we introduce, formalize and analyze a novel class of three-player quantum games, referred to as Proxy Quantum Games (PQGs). In this setting, one player, the Controller, influences or governs the strategic operations executed by a second player, the Proxy, who, in turn, competes directly against a third player, the Opponent. The strategic influence is implemented via controlled unitary operations, whereby the Proxy’s available strategies are conditioned on the Controller’s quantum state. We further generalize the PQG framework by incorporating multiple Controllers acting on a common Proxy, thereby enabling the study of higher-order strategic interactions and multi-agent influence structures. The objective under consideration is the maximization of the Controller’s expected payoff, under various configurations of strategic control and entanglement. Comparative analyses are conducted between the PQG formulation and conventional multiplayer quantum games, highlighting key differences in strategic behavior and payoff distributions.
Game theory studies strategic decision-making among rational agents, and many classical games can be mapped onto interaction models such as the Ising model. Quantum game theory extends this framework by allowing players to exploit quantum superposition and entanglement. In this work, we study quantum games using an operator-based formulation derived from the transverse-field quantum Ising model. We show that the Hamiltonian-driven dynamics naturally generate entangling operator which resolve the dilemma in the game settings. This leads to a clear quantum advantage over classical outcomes. Unlike standard quantization schemes based on fixed entangling gates, the present approach enables tunable entanglement, controlled directly by physical Hamiltonian parameters, providing a hardware-relevant perspective on quantum game design.
As quantum processors advance, the emergence of large-scale decentralized systems involving interacting quantum-enabled agents is on the horizon. Recent research efforts have explored quantum versions of Nash and correlated equilibria as solution concepts of strategic quantum interactions, but these approaches did not directly connect to decentralized adaptive setups where agents possess limited information. This paper delves into the dynamics of quantum-enabled agents within decentralized systems that employ no-regret algorithms to update their behaviors over time. Specifically, we investigate two-player quantum zero-sum games and polymatrix quantum zero-sum games, showing that no-regret algorithms converge to separable quantum Nash equilibria in time-average. In the case of general multi-player quantum games, our work leads to a novel solution concept, that of the separable quantum coarse correlated equilibria (QCCE), as the convergent outcome of the time-averaged behavior no-regret algorithms, offering a natural solution concept for decentralized quantum systems. Finally, we show that computing QCCEs can be formulated as a semidefinite program and establish the existence of entangled (i.e., non-separable) QCCEs, which are unlearnable via the current paradigm of no-regret learning.
Classical game theory is a powerful tool focusing on optimized resource distribution, allocation, and sharing in classical wired and wireless networks. As quantum networks are emerging as a means of providing true connectivity between quantum computers, it is imperative and crucial to exploit game theory for addressing challenges such as entanglement distribution and access, routing, topology extraction, and inference. Quantum networks provide the promising opportunity of employing quantum games owing to their inherent capability of generating and sharing quantum states. In addition, quantum games offer enhanced payoffs and winning probabilities, new strategies, and equilibria, which are unimaginable in classical games. Employing quantum game theory to solve fundamental challenges in quantum networks opens a new fundamental research direction necessitating inter-disciplinary efforts. In this article, we introduce a novel game-the-oretical framework for exploiting quantum strategies to solve – as an archetypal example – one of the key functionalities of a quantum network, namely, entanglement distribution. We compare quantum strategies with classical ones by showing the quantum advantages in terms of link fidelity improvement and latency decrease in communication. In the future, we will generalize our game framework to optimize entanglement distribution and access over any quantum network topology. We will also explore how quantum games can be leveraged to address other challenges like routing, optimization of quantum operations, and topology design.
Strategic decision-making among many agents under incomplete information is central to economics, security, and multi-agent artificial intelligence (AI). Computing equilibria in such settings is challenging because the joint type-action space grows exponentially with the number of players. In binary-type, binary-action Bayesian games with
n players, an explicit representation over type-action profiles requires
O(22n) entries, making direct linear-programming (LP) formulations increasingly costly as
n grows. We propose a hybrid quantum-classical framework for approximating Bayes correlated equilibrium (BCE) using a parameterized quantum circuit (PQC). The PQC represents the conditional distribution over joint actions using
O(nL) trainable parameters, where
L denotes the circuit depth; for the largest trained setting,
n=8 and
L=2, this corresponds to
48 trainable angles. Each player count is trained independently by maximizing expected social welfare with a penalty on positive aggregated BCE obedience violations. On a strategically coupled Bayesian congestion game with
n=2,4,6,8 players, feasible PQC solutions attain higher welfare than MCCFR and DCFR product-strategy baselines while satisfying
εmax≤10−3, where
εmax denotes the maximum positive aggregated BCE obedience violation. Across five independent runs per setting, all runs are feasible for
n=2,4,6, while four of five are feasible for
n=8. PQC welfare remains below the exact LP optimum, with the absolute gap increasing with
n, while classical state-vector simulation prevents PQC training beyond eight players. These results demonstrate the use of a compact PQC parameterization for approximate equilibrium computation and quantify its welfare, feasibility, and classical simulation scaling on the studied benchmark.