## Quantum-like Representation of Extensive Form Games: Wine Testing Game

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Khrennikov, Andrei

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We consider an application of the mathematical formalism of quantum mechanics
(QM) outside physics, namely, to game theory. We present a simple game between
macroscopic players, say Alice and Bob (or in a more complex form - Alice, Bob
and Cecilia), which can be represented in the quantum-like (QL) way -- by using
a complex probability amplitude (game's ``wave function'') and noncommutative
operators. The crucial point is that games under consideration are so called
extensive form games. Here the order of actions of players is important, such a
game can be represented by the tree of actions. The QL probabilistic behavior
of players is a consequence of incomplete information which is available to
e.g. Bob about the previous action of Alice. In general one could not construct
a classical probability space underlying a QL-game. This can happen even in a
QL-game with two players. In a QL-game with three players Bell's inequality can
be violated. The most natural probabilistic description is given by so called
contextual probability theory completed by the frequency definition of
probability.

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Quantum Physics