Abstract
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.
Highlights
IntroductionModern form of game theory can be rooted back to the seminal works by Neumann and Morgenstern (Bruza et al, 2015), which were based on the neoclassical rationality assumption
Modern form of game theory can be rooted back to the seminal works by Neumann and Morgenstern (Bruza et al, 2015), which were based on the neoclassical rationality assumption© Sudip Patra and Partha Ghose
Coming back to quantum-like game theory, we observe that here the purpose is related but fundamentally, from the perspective of probability framework, i.e. how the real moves chosen by real players, or the results of real games might be described comprehensively based on a single coherent probability or logical framework
Summary
Modern form of game theory can be rooted back to the seminal works by Neumann and Morgenstern (Bruza et al, 2015), which were based on the neoclassical rationality assumption. Coming back to quantum-like game theory, we observe that here the purpose is related but fundamentally, from the perspective of probability framework, i.e. how the real moves chosen by real players, or the results of real games might be described comprehensively based on a single coherent probability or logical framework Such a description would not be possible in standard Boolean logic or measure theory framework, which is the underlying mathematical theory for neoclassical game theory, PD being one example. In classical game theory there is not much fundamental difference between risky and uncertain contexts, decision-making under uncertainty context seems to be a fundamental contribution by quantum cognition modelling Another important work done by Khrennikov (Myerson, 2013) and Haven and Khrennikova (Kahneman et al, 1982) is construction of mental or cognitive states from the computations of phases in quantum FTP. Is pure quantum entanglement a necessary condition for designing superior than classical games? And it is in this backdrop we, current authors, present briefly our own framework
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