Efficiency and formalism of quantum games

Abstract

We pursue a general theory of quantum games. We show that quantum games are more efficient than classical games, and provide a saturated upper bound for this efficiency. We demonstrate that the set of finite classical games is a strict subset of the set of finite quantum games. We also deduce the quantum version of the Minimax Theorem and the Nash Equilibrium Theorem.

10 pages. Efficiency is explicitly defined. More discussion on the connection of quantum and classical games

References in corpus (3)

• Experimental realization of quantum games on a quantum computer
• Quantum version of the Monty Hall problem
• Exploiting Randomness in Quantum Information Processing

Cited by in corpus (47)

• Toward a general theory of quantum games
• Quantum games with decoherence
• A necessary and sufficient condition to play games in quantum mechanical settings
• Experimental implementation of a four-player quantum game
• Quantum advantages in classically defined tasks
• Quantum Probabilities as Behavioral Probabilities
• Generalized Quantization Scheme for Two-Person Non-Zero-Sum Games
• Quantum Game Theory Based on the Schmidt Decomposition
• Entangled states that cannot reproduce original classical games in their quantum version
• Information Processing by Networks of Quantum Decision Makers
• Duality, Phase Structures and Dilemmas in Symmetric Quantum Games
• The next stage: quantum game theory
• Quantum Locality in Game Strategy
• Evolutionary Processes in Quantum Decision Theory
• The effect of quantum memory on quantum games
• Coalitions in the quantum Minority game: classical cheats and quantum bullies
• Constructing quantum games from a system of Bell's inequalities
• Noise effects in a three-player Prisoner's Dilemma quantum game
• Processing Information in Quantum Decision Theory
• Quantum Matching Pennies Game
• Equivalence between Bell inequalities and quantum Minority game
• Quantum Replicator Dynamics
• Game-theoretic discussion of quantum state estimation and cloning
• Preferences in Quantum Games
• Constructing quantum games from symmetric non-factorizable joint probabilities
• Conditional Quantum Walk and Iterated Quantum Games
• Non-factorizable Joint Probabilities and Evolutionarily Stable Strategies in the Quantum Prisoner's Dilemma Game
• Playing games with EPR-type experiments
• A competitive game whose maximal Nash-equilibrium payoff requires quantum resources for its achievement
• A Novel Clustering Algorithm Based on Quantum Games
• General quantum two-players games, their gate operators and Nash equilibria
• Strategic Insights From Playing the Quantum Tic-Tac-Toe
• Quantitative Predictions in Quantum Decision Theory
• Quantum entanglement, indistinguishability, and the absent-minded driver's problem
• The Generalized Quantization Schemes for Games and its Application to Quantum Information
• Pareto-optimal solution for the quantum battle of the sexes
• Communication aspects of a three-player Prisoner's Dilemma quantum game
• Quantum-mechanical machinery for rational decision-making in classical guessing game
• Classification of Quantum Symmetric Non-zero Sum 2x2 Games in the Eisert Scheme
• An Overview of Quantum Computing for Technology Managers
• Resolving game theoretical dilemmas with quantum states
• Note on maximally entangled Eisert-Lewenstein-Wilkens quantum games
• Quantum games: a survey for mathematicians
• Experimental Demonstration on Quantum Sensitivity to Available Information in Decision Making
• Role of information in decision making of social agents
• Static Quantum Games Revisited
• Coordination Games with Quantum Information