A quantum extension to inspection game

Quantum game theory is a new interdisciplinary field between game theory and system engineering research. In this paper, we extend the classical inspection game into a quantum game version by quantizing the strategy space and importing entanglement between players. Our results show that the quantum inspection game has various Nash equilibria depending on the initial quantum state of the game. It is also shown that quantization can respectively help each player to increase his own payoff, yet fails to bring Pareto improvement for the collective payoff in the quantum inspection game.     

Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time,we find that when Nasli equilibrium exists the payoff function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example showing quantum game and classical game may differ.When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.     

Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time,we find that when Nash equilibrium exists the payoff function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example showing quantum game and classical game may differ.When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.     

Arbiter as the Third Man in Classical and Quantum Games

We study the possible influence of a not necessarily sincere arbiter on the course of classical and quantum 2×2 games and we show that this influence in the quantum case is much bigger than in the classical case. Extreme sensitivity of quantum games on initial states of quantum objects used as carriers of information in a game shows that a quantum game, contrary to a classical game, is not defined by a payoff matrix alone but also by an initial state of objects used to play a game. Therefore, two quantum games that have the same payoff matrices but begin with different initial states should be considered as different games.     

Quantum Parrondo game based on a quantum ratchet effect

A Parrondo game is a counterintuitive game where two losing games can be combined to form a winning game. We construct a quantum version of a Parrondo game based on a quantum ratchet effect for a delta-kicked model, which can be realized in optical lattices. A game set is presented and a quantum anti-Parrondo game is also investigated.     

Quantum Parrondo’s Games Under Decoherence

We study the effect of quantum noise on history dependent quantum Parrondo’s games by taking into account different noise channels. Our calculations show that entanglement can play a crucial role in quantum Parrondo’s games. It is seen that for the maximally entangled initial state in the presence of decoherence, the quantum phases strongly influence the payoffs for various sequences of the game. The effect of amplitude damping channel leads to winning payoffs. Whereas the depolarizing and phase damping channels lead to the losing payoffs. In case of amplitude damping channel, the payoffs are enhanced in the presence of decoherence for the sequence AAB. This is because the quantum phases interfere constructively which leads to the quantum enhancement of the payoffs in comparison to the undecohered case. It is also seen that the quantum phase angles damp the payoffs significantly in the presence of decoherence. Furthermore, it is seen that for multiple games of sequence AAB, under the influence of amplitude damping channel, the game still remains a winning game. However, the quantum enhancement reduces in comparison to the single game of sequence AAB because of the destructive interference of phase dependent terms. In case of depolarizing channel, the game becomes a loosing game. It is seen that for the game sequence B the game is loosing one and the behavior of sequences B and BB is similar for amplitude damping and depolarizing channels. In addition, the repeated games of A are only influenced by the amplitude damping channel and the game remains a losing game. Furthermore, it is also seen that for any sequence when played in series, the phase damping channel does not influence the game.     

Experimental implementation of a three qubit quantum game with corrupt source using nuclear magnetic resonance quantum information processor

In a three player quantum 'Dilemma' game each player takes independent decisions to maximize his/her individual gain. The optimal strategy in the quantum version of this game has a higher payoff compared to its classical counterpart. However, this advantage is lost if the initial qubits provided to the players are from a noisy source. We have experimentally implemented the three player quantum version of the 'Dilemma' game as described by Johnson, [N.F. Johnson, Phys. Rev. A 63 (2001) 020302(R)] using nuclear magnetic resonance quantum information processor and have experimentally verified that the payoff of the quantum game for various levels of corruption matches the theoretical payoff.     

Tripartite Dynamic Zero-Sum Quantum Games

The Nash equilibrium plays a crucial role in game theory. Most of results are based on classical resources. Our goal in this paper is to explore multipartite zero-sum game with quantum settings. We find that in two different settings there is no strategy for a tripartite classical game being fair. Interestingly, this is resolved by providing dynamic zero-sum quantum games using single quantum state. Moreover, the gains of some players may be changed dynamically in terms of the committed state. Both quantum games are robust against the preparation noise and measurement errors.     

第四讲 量子对策论

量子对策论是量子信息学的新兴分支,是经典对策论与量子信息学两门学科的交叉学科.由 于引入了量子力学中的量子叠加性和纠缠态,量子对策得出了与经典对策迥然不同的结果.     

Experimental realization of quantum games on a quantum computer

We generalize the quantum prisoner's dilemma to the case where the players share a nonmaximally entangled states. We show that the game exhibits an intriguing structure as a function of the amount of entanglement with two thresholds which separate a classical region, an intermediate region, and a fully quantum region. Furthermore this quantum game is experimentally realized on our nuclear magnetic resonance quantum computer.     

From Quantum State Targeting to Bell Inequalities

Quantum state targeting is a quantum game which results from combining traditional quantum state estimation with additional classical information. We consider a particular version of the game and show how it can be played with maximally entangled states. The optimal solution of the game is used to derive a Bell inequality for two entangled qutrits. We argue that the nice properties of the inequality are direct consequences of the method of construction.     

Evolutionarily stable strategies in quantum games

Evolutionarily stable strategy (ESS) in classical game theory is a refinement of Nash equilibrium concept. We investigate the consequences when a small group of mutants using quantum strategies try to invade a classical ESS in a population engaged in symmetric bimatrix game of prisoner's dilemma. Secondly we show that in an asymmetric quantum game between two players an ESS pair can be made to appear or disappear by resorting to entangled or unentangled initial states used to play the game even when the strategy pair remains a Nash equilibrium in both forms of the game.     

Quantum Version of a Generalized Monty Hall Game and Its Possible Applications to Quantum Secure Communications

In this work, the authors propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free and not fixed on its regular values. The developed quantum scheme is then used to study the expected payoff of the player, using both a separable and an entangled initial‐state. In the two cases, the classical mixed‐strategy payoff is recovered under certain conditions. Lastly, the authors extend the quantum scheme to include multiple independent players, and use this extension to sketch two possible application of the game mechanics to quantum networks, specifically, two validated, multi‐party, key‐distribution quantum protocols.     

An Invitation to Quantum Game Theory

Recent development in quantum computation and quantum information theory allows to extend the scope of game theory for the quantum world. The paper presents the history, basic ideas, and recent development in quantum game theory. In this context, a new application of the Ising chain model is proposed.     

Quantum Information Approach to the Ultimatum Game

The paper is devoted to quantization of extensive games with the use of both the Marinatto-Weber and the Eisert-Wilkens-Lewenstein concept of quantum game. We revise the current conception of quantum ultimatum game and we show why the proposal is unacceptable. To support our approach, we present a new idea of the quantum ultimatum game. Our scheme also makes a point of departure for a general protocol for quantizing extensive games.     

Non-factorizable joint probabilities and evolutionarily stable strategies in the quantum prisoner's dilemma game

The well-known refinement of the Nash Equilibrium (NE) called an Evolutionarily Stable Strategy (ESS) is investigated in the quantum Prisoner's Dilemma (PD) game that is played using an Einstein-Podolsky-Rosen type setting. Earlier results report that in this scheme the classical NE remains intact as the unique solution of the quantum PD game. In contrast, we show here that interestingly in this scheme a non-classical solution for the ESS emerges for the quantum PD.     

Proposal of Realization Restricted Quantum Game with Linear Optic Method

We present a quantum game with the restricted strategic space and its realization with linear optical system, which can be played by two players who are separated remotely. This game can also be realized on any other quantum computers. We find that the constraint brings some interesting properties that are useful for making game models.     

Constructing quantum games from symmetric non-factorizable joint probabilities

We construct quantum games from a table of non-factorizable joint probabilities, coupled with a symmetry constraint, requiring symmetrical payoffs between the players. We give the general result for a Nash equilibrium and payoff relations for a game based on non-factorizable joint probabilities, which embeds the classical game. We study a quantum version of Prisoners' Dilemma, Stag Hunt, and the Chicken game constructed from a given table of non-factorizable joint probabilities to find new outcomes in these games. We show that this approach provides a general framework for both classical and quantum games without recourse to the formalism of quantum mechanics.     

On the Effect of Quantum Noise in a Quantum-Relativistic Prisoner’s Dilemma Cellular Automaton

The disrupting effect of quantum noise on the dynamics of a spatial quantum relativistic formulation of the iterated prisoner’s dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests.     

Linear optics implementation for quantum game under quantum noise

It has recently been shown that linear optics alone would suffice to implement efficient quantum computation. Quantum computation circuits using coherent states as the logical qubits can be constructed from very simple linear networks, conditional measurements and coherent superposition resource states. We present the quantum game under quantum noise and a proposal for implementing the noisy quantum game using only linear optics.