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International Conference on Genetic and Evolutionary Computing

An Introductory Review on Quantum Game Theory

Wenjie Liu, Jingfa Liu, Mengmeng Cui, Ming He

Published Dec 1, 2010• 9 citations
Publisher

Abstract

With utilizing some quantum mechanism into the game theory, quantum game theory provides us with the ability to achieve results not otherwise possible. In this paper, a brief overview of classical game theory and some game-theoretic terms are depicted. Then, an introduction to quantum theory is presented as well as some correlative works in this field. Finally, some well-known quantum games are analyzed and discussed, which shows its predominant effect on some games problems (the Prisoners' Dilemma, Parrondo's Games, etc.).

DOI
10.1109/icgec.2010.102

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With utilizing some quantum mechanism into the game theory, quantum game theory provides us with the ability to achieve results not otherwise possible. In this paper, a brief overview of classical game theory and some game-theoretic terms are depicted. Then, an introduction to quantum theory is presented as well as some correlative works in this field. Finally, some well-known quantum games are analyzed and discussed, which shows its predominant effect on some games problems (the Prisoners' Dilemma, Parrondo's Games, etc.).
We give a self contained introduction to a few quantum game protocols, starting with the quantum version of the two-player two-choice game of Prisoners dilemma, followed by a n-player generalization trough the quantum minority games, and finishing with a contribution towards a n-player m-choice generalization with a quantum version of a three-player Kolkata restaurant problem. We have omitted some technical details accompanying these protocols, and instead laid the focus on presenting some general aspects of the field as a whole. This review contains an introduction to the formalism of quantum information theory, as well as to important game theoretical concepts, and is aimed to work as an introduction suiting economists and game theorists with limited knowledge of quantum physics as well as to physicists with limited knowledge of game theory.
Purpose The current paper is a brief review of the emerging field of quantum-like modelling in game theory. This paper aims to explore several quantum games, which are superior compared to their classical counterparts, which means either they give rise to superior Nash equilibria or they make the game fairer. For example, quantum Prisoners Dilemma generates Pareto superior outcomes as compared to defection outcome in the famous classical case. Again, a quantum-like version of cards game can make the game fairer, increasing the chance of winning of players who are disadvantaged in the classical case. This paper explores all the virtues of simple quantum games, also highlighting some findings of the authors as regards Prisoners Dilemma game. Design/methodology/approach As this is a general review paper, the authors have not demonstrated any specific mathematical method, rather explored the well-known quantum probability framework, used for designing quantum games. They have a short appendix which explores basic structure of Hilbert space representation of human decision-making. Findings Along with the review of the extant literature, the authors have also highlighted some new findings for quantum Prisoners Dilemma game. Specifically, they have shown in the earlier studies (which are referred to here) that a pure quantum entanglement set up is not needed for designing better games, even a weaker condition, which is classical entanglement is sufficient for producing Pareto improved outcomes. Research limitations/implications Theoretical research, with findings and implications for future game designs, it has been argued that it is not always needed to have true quantum entanglement for superior Nash Equilibria. Originality/value The main purpose here is to raise awareness mainly in the social science community about the possible applications of quantum-like game theory paradigm. The findings related to Prisoners Dilemma game are, however, original.
Quantum game theory is an exciting new topic that combines the physical behaviour of information in quantum mechanical systems with game theory, the mathematical description of conflict and competition situations, to shed new light on the fields of quantum control and quantum information. This thesis presents quantizations of some classic game-theoretic problems, new results in existing quantization schemes for two player, two strategy non-zero sum games, and in quantum versions of Parrondo's games, where the \ncombination of two losing games can result in a winning game. In addition, quantum cellular automata and quantum walks are discussed, with a history-dependent quantum walk being presented.