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Quantum correlations and Nash equilibria of a bi-matrix game
Playing a symmetric bi-matrix game is usually physically implemented by
sharing pairs of 'objects' between two players. A new setting is proposed that
explicitly shows effects of quantum correlations between the pairs on the
structure of payoff relations and the 'solutions' of the game. The setting
allows a re-expression of the game such that the players play the classical
game when their moves are performed on pairs of objects having correlations
that satisfy the Bell's inequalities. If players receive pairs having quantum
correlations the resulting game cannot be considered another classical
symmetric bi-matrix game. Also the Nash equilibria of the game are found to be
decided by the nature of the correlations.Comment: minor correction
Exact Algorithms for Solving Stochastic Games
Shapley's discounted stochastic games, Everett's recursive games and
Gillette's undiscounted stochastic games are classical models of game theory
describing two-player zero-sum games of potentially infinite duration. We
describe algorithms for exactly solving these games
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