Narrow Results

Service quality preference behaviors of both members are considered in service supply chain (SSC) including a service integrator and a service provider with stochastic demand. Through analysis of service quality cost and revenue, the utility functions are established on service quality effort degree and service quality preference level in integrated and decentralized SSC. Nash equilibrium and quantum game are used to optimize the models. By comparing the different solutions, the optimal strategies are obtained in SSC with quality preference. Then some numerical examples are studied and the changing trend of service quality effort is further analyzed by the influence of the entanglement operator and quality preferences.

Coopetition is defined as the existence of simultaneous competition and cooperation between the same set of players, leading to entanglement of payoffs and actions of the players. This paper provides insights into the game theoretical application of quantum games to model simultaneity and entanglement that occur in coopetition. Modeling as a quantum game also allows for a larger action space and hence new equilibrium that may not have existed earlier. The impact of the level of entanglement on the equilibrium of the game can also be studied. We demonstrate the same through an example of two players who currently compete in the domestic market and are considering cooperating simultaneously in the international market. They need to determine the equilibrium strategy to adopt under coopetition that maximizes their payoffs. We also arrive at how to ensure that the quantum strategy is the equilibrium strategy for both players, namely, how to design the quantum strategy and how to define the unitary operator.

Quantum game is an interesting field and many scientists have done a lot of innovative work in it. We give a quantum model about incomplete information. In this model we find whether the pure-strategy Bayes-Nash equilibrium exists or not is strongly dependent on the entanglement of the initial state. We also find the player Bob can always find an initial state and a pure-strategy Bayes-Nash equilibrium to get more payoff than classical game with some parameter.

Quantum game theory is a recently developing field of physical research. In this paper, we investigate quantum games in a systematic way. With the famous instance of the Prisoner's Dilemma, we present the fascinating properties of quantum games in different conditions, i.e. different number of the players, different strategic space of the players and different amount of the entanglement involved.

We analyse Selten' concept of trembling hand perfect equilibria in the context of quantum game theory. We define trembles as mixed quantum strategies by replacing discrete probabilities with probability distribution functions. Explicit examples of analysis are given.

Classical Parrondo game shows that the combination of two losing games can achieve a winning result. We investigate such an effect under quantum models, and make a complete research about the initial states that can be adapted. By the comparison of the payoffs which come from the GHZ class, W class and initial states without entanglement, we find out that entanglement plays an important role here. Moreover, we reveal that, particular initial state without entanglement can even provide us optimal payoff. Thorough discussion and exact results in this article will help us not only to make appropriate choices in quantum Parrondo game, but also have a deeper understanding about entanglement and quantum game.

In this paper, by using permutation matrices as a representation of symmetric group S_N and Fourier matrix, we investigate quantum roulette with an arbitrary N-state. This strategy, which we introduce, is a general method that allows us to solve quantum game for an arbitrary N-state. We consider the interaction between the system and its environment and study the effect of the depolarizing channel on this strategy. Finally, as an example, we employ this strategy for quantum roulette with N = 3.

We modify the concept of quantum strategic game to make it useful for extensive form games. We prove that our modification allows us to consider the normal representation of any finite extensive game using the fundamental concepts of quantum information. The Selten's Horse game and the general form of two-stage extensive game with perfect information are studied to illustrate a potential application of our idea. In both examples we use the Eisert–Wilkens–Lewenstein approach as well as the Marinatto–Weber approach to quantization of games.

Noise effects can be harmful to quantum information systems. In the present paper, we study noise effects in the context of quantum games with incomplete information, which have more complicated structure than quantum games with complete information. The effects of several paradigmatic noises on three newly proposed conflicting interest quantum games with incomplete information are studied using numerical optimization method. Intuitively noises will bring down the payoffs. However, we find that in some situations the outcome of the games under the influence of noise effects are counter-intuitive. Sometimes stronger noise may lead to higher payoffs. Some properties of the game, like quantum advantage, fairness and equilibrium, are invulnerable to some kinds of noises.

Recently, the first conflicting interest quantum game based on the nonlocality property of quantum mechanics has been introduced in A. Pappa, N. Kumar, T. Lawson, M. Santha, S. Y. Zhang, E. Diamanti and I. Kerenidis, Phys. Rev. Lett.114 (2015) 020401. Several quantum games of the same genre have also been proposed subsequently. However, these games are constructed from some well-known Bell inequalities, thus are quite abstract and lack of realistic interpretations. In the present paper, we modify the common interest land bidding game introduced in N. Brunner and N. Linden, Nat. Commun.4 (2013) 2057, which is also based on nonlocality and can be understood as two companies collaborating in developing a project. The modified game has conflicting interest and reflects the free rider problem in economics. Then we show that it has a fair quantum solution that leads to better outcome. Finally, we study how several types of paradigmatic noise affect the outcome of this game.