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Chinese Journal of Quantum Electronics

Multiplayer quantum game with continuous-variable strategies

Lei Ma

Published Jan 1, 2006• 1 citation
OpenAlex

Abstract

Quantum games has becoming a new arisen branch of the quantum information. Du etc. utilize a two mode electromagnetic fileds in discussing the continuous-variable quantum games. From the model, they realized the entanglement in the game which might lead superior consults than the coresponding classical games. A multiplayer quantum game that the players can access to a continuous set of strategies is studied. By utilizing a kind of multi-mode electromagnetic fileds and let every two mode of the fields entangled pairwise. We discovered, base on this scheme, the conclusion above could be extended to arbitrary number of participators. With the increasing of entangle parameter, The sum of the profits will also increase monotonously. When each two-mode electromagnetic fileds entangle to maximum, i.e. EPR state, they will also attain highest profits.

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•Jan 1, 2015•0 citations
Quantum games has becoming a new arisen branch of the quantum information. Du etc. utilize a two mode electromagnetic fileds in discussing the continuous-variable quantum games. From the model, they realized the entanglement in the game which might lead superior consults than the coresponding classical games. A multiplayer quantum game that the players can access to a continuous set of strategies is studied. By utilizing a kind of multi-mode electromagnetic fileds and let every two mode of the fields entangled pairwise. We discovered, base on this scheme, the conclusion above could be extended to arbitrary number of participators. With the increasing of entangle parameter, The sum of the profits will also increase monotonously. When each two-mode electromagnetic fileds entangle to maximum, i.e. EPR state, they will also attain highest profits.
Recently the concept of quantum information has been introduced into game theory. Here we present the first study of quantum games with more than two players. We discover that such games can possess an alternative form of equilibrium strategy, one which has no analog either in traditional games or even in two-player quantum games. In these ``coherent'' equilibria, entanglement shared among multiple players enables different kinds of cooperative behavior: indeed it can act as a contract, in the sense that it prevents players from successfully betraying one another.
Quantum game theory is a multidisciplinary field which combines quantum mechanics with game theory by introducing non-classical resources such as entanglement, quantum operations and quantum measurement. By transferring two-player two-strategy (2 × 2) dilemma containing classical games into the quantum realm, dilemmas can be resolved in quantum pure strategies if entanglement is distributed between the players who use quantum operations. Moreover, players receive the highest sum of payoffs available in the game, which are otherwise impossible in classical pure strategies. Encouraged by the observation of rich dynamics of physical systems with many interacting parties and the power of entanglement in quantum versions of 2 × 2 games, it became generally accepted that quantum versions can be easily extended to N -player situations by simply allowing N -partite entangled states. In this article, however, we show that this is not generally true because the reproducibility of classical tasks in the quantum domain imposes limitations on the type of entanglement and quantum operators. We propose a benchmark for the evaluation of quantum and classical versions of games, and derive the necessary and sufficient conditions for a physical realization. We give examples of entangled states that can and cannot be used, and the characteristics of quantum operators used as strategies.
A number of recent studies have focused on novel features in game theory when the games are played using quantum mechanical toolbox (entanglement, unitary operators, measurement). Researchers have concentrated in two-player-two strategy, 2x2, dilemma containing classical games, and transferred them into quantum realm showing that in quantum pure strategies dilemmas in such games can be resolved if entanglement is distributed between the players armed with quantum operations. Moreover, it became clear that the players receive the highest sum of payoffs available in the game, which are otherwise impossible in classical pure strategies. Encouraged by the observation of rich dynamics of physical systems with many interacting parties and the power of entanglement in quantum versions of 2x2 games, it became generally accepted that quantum versions can be easily extended to N-player situations by simply allowing N-partite entangled states. In this article, however, we show that this is not generally true because the reproducibility of classical tasks in quantum domain imposes limitations on the type of entanglement and quantum operators. We propose a benchmark for the evaluation of quantum and classical versions of games, and derive the necessary and sufficient conditions for a physical realization. We give examples of entangled states that can and cannot be used, and the characteristics of quantum operators used as strategies.
It has recently been realized that quantum strategies have a great advantage over classical ones in quantum games. However, quantum states are easily affected by the quantum noise, resulting in decoherence. In this paper, we investigate the effect of quantum noise on a multiplayer quantum game with a certain strategic space, with all players affected by the same quantum noise at the same time. Our results show that in a maximally entangled state, a special Nash equilibrium appears in the range of 0≤p≤0.622 (p is the quantum noise parameter), and then disappears in the range of 0.622<p≤1. Increasing the amount of quantum noise leads to the reduction of the quantum player's payoff.
Game theory is the study of strategic competition used in many branches of science. In general, a game is a match between two or more players and each wants to maximize his or her score. In a game, the player’s score depends on their strategies. The goal is to find the optimized decision, with regard to the payoff, in conformity with the rules of the game. This thesis considers the games with two players who know both their own and their rival’s payoff. However, they do not know the strategy chosen by the opponent.\nIn a classical game, the options of players are referred to as cooperation and defect. Quantum game theory is a generalization of classical game theory. In quantum games a linear combination of two options specify the strategy based on qubit. The quantum domain is characterized by entanglement. The quantum entanglement coefficient (y) varies from 0 to . The game is in the classical regime when y is smaller than a threshold. Quantum entanglement is intrinsically non-local.\nIn an iterated game tournament, 63 different strategies contest with four known strategies. Depending on the result, they are divided to a number of groups. The competition specifies which group of strategies can obtain a higher score.\nOther types of games are discussed in the thesis. They are known as incomplete information games. In these games one player has two payoff matrixes, and the rival does not know which of them is used. We discuss the advantage of using quantum strategy over the classical game, particular in avoiding the dilemma in classical games.