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A significant aspect of the study of quantum strategies is the exploration of the game-theoretic solution concept of the Nash equilibrium in relation to the quantization of a game. Pareto optimality is a refinement on the set of Nash equilibria. A refinement on the set of Pareto optimal outcomes is known as social optimality in which the sum of players payoffs are maximized. This paper analyzes social optimality in a Bayesian game that uses the setting of generalized Einstein-Podolsky-Rosen experiments for its physical implementation. We show that for the quantum Bayesian game a direct connection appears between the violation of Bells inequality and the social optimal outcome of the game and that it attains a superior socially optimal outcome.
Quantum pseudo-telepathy games are good examples of explaining the strangeness of quantum mechanics and demonstrating the advantage of quantum resources over classical resources. Most of the quantum pseudo-telepathy games are common interest games, n
We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital process is luc
A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are defined. In
In evolutionary game theory an Evolutionarily Stable Strategy (ESS) is a refinement of the Nash equilibrium concept that is sometimes also recognized as evolutionary stability. It is a game-theoretic model, well known to mathematical biologists, that
We consider two aspects of quantum game theory: the extent to which the quantum solution solves the original classical game, and to what extent the new solution can be obtained in a classical model.