Arbiter as the Third Man in Classical and Quantum Games

Author: Pykacz Jarosław   Frackiewicz Piotr  

Publisher: Springer Publishing Company

ISSN: 0020-7748

Source: International Journal of Theoretical Physics, Vol.49, Iss.12, 2010-12, pp. : 3243-3249

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Abstract

We study the possible influence of a not necessarily sincere arbiter on the course of classical and quantum 2×2 games and we show that this influence in the quantum case is much bigger than in the classical case. Extreme sensitivity of quantum games on initial states of quantum objects used as carriers of information in a game shows that a quantum game, contrary to a classical game, is not defined by a payoff matrix alone but also by an initial state of objects used to play a game. Therefore, two quantum games that have the same payoff matrices but begin with different initial states should be considered as different games.