David A. Meyer,
``Quantum strategies'',
Physical Review Letters 82 (1999) 1052-1055.

We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). While not every two-person zero-sum finite game has an equilibrium in the set of pure strategies, von Neumann showed that there is always an equilibrium at which each player follows a mixed strategy. A mixed strategy deviating from the equilibrium strategy cannot increase a player's expected payoff. We show by example, however, that a player who implements a quantum strategy can increase his expected payoff, and explain the relation to efficient quantum algorithms.

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See also my reply to a comment by S. J. van Enk on this paper, and further discussion of the relation between ``Quantum games and quantum algorithms''.