Related papers: Quantum version of the Monty Hall problem
Quantum games with incomplete information can be studied within a Bayesian framework. We analyze games quantized within the EWL framework [Eisert, Wilkens, and Lewenstein, Phys Rev. Lett. 83, 3077 (1999)]. We solve for the Nash equilibria…
The properties of the Cournot model based on the most general entanglement operator containing quadratic expressions which is symmetric with respect to the exchange of players are considered. The degree of entanglement of games dependent on…
The volunteer's dilemma is a well-known game in game theory that models the conflict players face when deciding whether to volunteer for a collective benefit, knowing that volunteering incurs a personal cost. In this work, we introduce a…
We propose a scheme for a quantum game based on performing an EPR type experiment and in which each player's spatial directional choices are considered as their strategies. A classical mixed-strategy game is recovered by restricting the…
We investigate quantum strategy in moving frames by considering Prisoner's Dilemma and propose four thresholds of $\gamma$ for two players to determine their \textit{Nash Equilibria}. Specially, an interesting phenomenon appears in…
Game theory is the mathematical framework for analyzing strategic interactions in conflict and competition situations. In recent years quantum game theory has earned the attention of physicists, and has emerged as a branch of quantum…
For any two-by-two game $\G$, we define a new two-player game $\G^Q$. The definition is motivated by a vision of players in game $\G$ communicating via quantum technology according to a certain standard protocol originally introduced by…
The two-players $N$ strategies games quantized according to the Eisert-Lewenstein-Wilkens scheme (Phys. Rev. Lett. 83 (1999), 3077) are considered. Group theoretical methods are applied to the problem of finding a general form of gate…
In the time since a merger of quantum mechanics and game theory was proposed formally in 1999, the two distinct perspectives apparent in this merger of applying quantum mechanics to game theory, referred to henceforth as the theory of…
Methods of exploring Nash equilibrium in quantum games are studied. Analytical conditions of the existence, the uniqueness or the multiplicity of the equilibria are found.
The $N$-player quantum game is analyzed in the context of an Einstein-Podolsky-Rosen (EPR) experiment. In this setting, a player's strategies are not unitary transformations as in alternate quantum game-theoretic frameworks, but a classical…
The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we…
We study a general $2 \times 2$ symmetric, entangled, quantum game. When one player has access only to classical strategies while the other can use the full range of quantum strategies, there are ``miracle'' moves available to the quantum…
We present a novel formulation of quantum game theory based on the Schmidt decomposition, which has the merit that the entanglement of quantum strategies is manifestly quantified. We apply this formulation to 2-player, 2-strategy symmetric…
We consider a coalitional game with the same payoff for all players. To maximize the payoff, the players need to use one collective strategy, if all players are in certain states, and the other strategy otherwise. The current state of each…
We define generalized quantum games by introducing the coherent payoff operators and propose a simple scheme to illustrate it. The scheme is implemented with a single spin qubit system and two entangled qubit system. The Nash Equilibrium…
We study the effect of decoherence on quantum Monty Hall problem under the influence of amplitude damping, depolarizing and dephasing channels. It is shown that under the effect of decoherence, there is a Nash equilibrium of the game in…
Both classical and quantum version of two models of price competition in duopoly market, the one is realistic and the other is idealized, are investigated. The pure strategy Nash equilibria of the realistic model exists under stricter…
Effects of quantum and classical correlations on game theory are studied to clarify the new aspects brought into game theory by the quantum mechanical toolbox. In this study, we compare quantum correlation represented by a maximally…
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…