Peer-to-peer (P2P) services such as mobile P2P transmissions and resource sharing, provide efficient methods to deliver data without the deployment of any central server. Nevertheless, the free-riding phenomenon inherit in such services presses a need for incentive mechanisms to stimulate contributions of data transmissions or sharing. As a result, it is imperative to answer the following questions: whether, and if so to what extent, an incentive mechanism can invoke such contributions? To answerthese questions, we employ an n-player continuous quantum game model to analyze the general extrinsic incentive mechanisms as well as the reputation-based incentive mechanisms, a typical class of extrinsic incentive mechanisms. We focus on studying the extrinsic incentive mechanisms in this paper due to their wide scope of applications stemming from the fact that they promote cooperative behaviors by offering rewards rather than depending on the internal bounds (e.g., social ties) among peers, which may not always exist between any pair of peers. To the best of our knowledge, we are the first to analyze the extrinsic incentive mechanisms for P2P services from a quantum game perspective. Such a perspective is adopted because the extended strategy space in the quantum game broadens the range for searching optimal strategies and the introduction of entanglement makes the proposed analytical frameworks more practical due to the consideration of the peers' relationships imposed by the rewards in extrinsic incentive mechanisms. Our quantum game-based analytical framework is generic because it is compatible with classic game-based schemes. The analytical results can provide a straightforward insight on evaluating the potential of the extrinsic incentive mechanisms and can serve as important references for designing new extrinsic incentive mechanisms.
Peer-to-peer (P2P) services such as mobile P2P transmissions and resource sharing, provide efficient methods to deliver data without the deployment of any central server. Nevertheless, the free-riding phenomenon inherit in such services presses a need for incentive mechanisms to stimulate contributions of data transmissions or sharing. As a result, it is imperative to answer the following questions: whether, and if so to what extent, an incentive mechanism can invoke such contributions? To answerthese questions, we employ an n-player continuous quantum game model to analyze the general extrinsic incentive mechanisms as well as the reputation-based incentive mechanisms, a typical class of extrinsic incentive mechanisms. We focus on studying the extrinsic incentive mechanisms in this paper due to their wide scope of applications stemming from the fact that they promote cooperative behaviors by offering rewards rather than depending on the internal bounds (e.g., social ties) among peers, which may not always exist between any pair of peers. To the best of our knowledge, we are the first to analyze the extrinsic incentive mechanisms for P2P services from a quantum game perspective. Such a perspective is adopted because the extended strategy space in the quantum game broadens the range for searching optimal strategies and the introduction of entanglement makes the proposed analytical frameworks more practical due to the consideration of the peers' relationships imposed by the rewards in extrinsic incentive mechanisms. Our quantum game-based analytical framework is generic because it is compatible with classic game-based schemes. The analytical results can provide a straightforward insight on evaluating the potential of the extrinsic incentive mechanisms and can serve as important references for designing new extrinsic incentive mechanisms.
The peer-to-peer transmission is a mainstream in challenged network environments. Yet, the free rider phenomenon in peer-to peer transmissions presses a need for incentive mechanisms to stimulate contributions of data transmission. As a result, it is imperative to answer the questions: whether and to what extent an incentive mechanism can invoke such contributions? To answer these questions, we employ an n-player continuous quantum game model to analyze extrinsic incentive mechanisms (promoting cooperative behaviors by offering rewards), and use the quantum prisoner's dilemma model to analyze intrinsic incentive mechanisms (encouraging reciprocal cooperation by exploiting internal bounds). To the best of our knowledge, we are the first to analyze incentive mechanisms for peer-to-peer transmissions from a quantum game perspective. Such a perspective is adopted because the extended strategy space in the quantum game broadens the range for searching optimal strategies and the introduction of entanglement makes the proposed analytical frameworks more practical due to the consideration of the peers' relationships in decision-making. Our proposed quantum game-based analytical frameworks are generic because they are compatible with classic game-based schemes. Our analytical results can provide straightforward insights on evaluating the potential of incentive mechanisms and can serve as important references for designing new incentive mechanisms.
Quantum teleportation is a fundamental protocol enabling the transfer of quantum states between remote nodes without physical transmission. As the Quantum Internet evolves, optimizing quantum teleportation becomes crucial due to entanglement degradation, resource constraints, and network efficiency. This paper proposes a game-theoretic framework for managing quantum teleportation by modeling quantum nodes as rational agents competing or cooperating to maximize teleportation fidelity and entanglement utility. We introduce cooperative and non-cooperative game models, analyze Nash equilibrium strategies for teleportation efficiency, and propose a Shapley-value-based entanglement allocation for fair resource distribution. Our system model incorporates graph-theoretic representations of quantum networks, utility functions, and incentive mechanisms to encourage efficient teleportation strategies. A Qiskit-based simulation evaluates teleportation fidelity and resource efficiency, comparing game-theoretic strategies with classical resource allocation methods. Our findings demonstrate that game-theoretic approaches significantly enhance teleportation efficiency, entanglement utilization, and robustness in a dynamic Quantum Internet environment.
Quantum generalizations of conventional games broaden the range of available strategies, which can help improve outcomes for the participants. With many players, such quantum games can involve entanglement among many states which is difficult to implement, especially if the states must be communicated over some distance. This paper describes a quantum mechanism for the economically significant n-player public goods game that requires only two-particle entanglement and is thus much easier to implement than more general quantum mechanisms. In spite of the large temptation to free ride on the efforts of others in this game, two-particle entanglement is sufficient to give near optimal expected payoff when players use a simple mixed strategy for which no player can benefit by making different choices. This mechanism can also address some heterogeneous preferences among the players.
This work concentrates on simultaneous move non-cooperating quantum games. Part of it is evidently not new, but it is included for the sake self consistence, as it is devoted to introduction of the mathematical and physical grounds of the pertinent topics, and the way in which a simple classical game is modified to become a quantum game (a procedure referred to as a quantization of a classical game). The connection between game theory and information science is briefly stressed, and the role of quantum entanglement (that plays a central role in the theory of quantum games), is exposed. Armed with these tools, we investigate some basic concepts like the existence (or absence) of a pure strategy and mixed strategy Nash equilibrium and its relation with the degree of entanglement. The main results of this work are as follows: 1) Construction of a numerical algorithm based on the method of best response functions, designed to search for pure strategy Nash equilibrium in quantum games. The formalism is based on the discretization of a continuous variable into a mesh of points, and can be applied to quantum games that are built upon two-players two-strategies classical games, based on the method of best response functions. 2) Application of this algorithm to study the question of how the existence of pure strategy Nash equilibrium is related to the degree of entanglement (specified by a continuous parameter γ ). It is shown that when the classical game GC has a pure strategy Nash equilibrium that is not Pareto efficient, then the quantum game GQ with maximal entanglement (γ = π/2) has no pure strategy Nash equilibrium. By studying a non-symmetric prisoner dilemma game, it is found that there is a critical value 0γc such that for γγc there is a pure strategy Nash equilibrium and for γ≥γc there is no pure strategy Nash equilibrium. The behavior of the two payoffs as function of γ starts at that of the classical ones at (D, D) and approaches the cooperative classical ones at (C, C) (C = confess, D = don’t confess). 3) We then study Bayesian quantum games and show that under certain conditions, there is a pure strategy Nash equilibrium in such games even when entanglement is maximal. 4) We define the basic ingredients of a quantum game based on a two-player three strategies classical game. This requires the introduction of trits (instead of bits) and quantum trits (instead of quantum bits). It is proved that in this quantum game, there is no classical commensurability in the sense that the classical strategies are not obtained as a special case of the quantum strategies.
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.
Emergent cooperation in classical Multi-Agent Reinforcement Learning has gained significant attention, particularly in the context of Sequential Social Dilemmas (SSDs). While classical reinforcement learning approaches have demonstrated capability for emergent cooperation, research on extending these methods to Quantum Multi-Agent Reinforcement Learning remains limited, particularly through communication. In this paper, we apply communication approaches to quantum Q-Learning agents: the Mutual Acknowledgment Token Exchange (MATE) protocol, its extension Mutually Endorsed Distributed Incentive Acknowledgment Token Exchange (MEDIATE), the peer rewarding mechanism Gifting, and Reinforced Inter-Agent Learning (RIAL). We evaluate these approaches in three SSDs: the Iterated Prisoner's Dilemma, Iterated Stag Hunt, and Iterated Game of Chicken. Our experimental results show that approaches using MATE with temporal-difference measure (MATE\textsubscript{TD}), AutoMATE, MEDIATE-I, and MEDIATE-S achieved high cooperation levels across all dilemmas, demonstrating that communication is a viable mechanism for fostering emergent cooperation in Quantum Multi-Agent Reinforcement Learning.