Quantum strategies

DOI10.48550/ARXIV.QUANT-PH/9804010zbMATH Open0958.81007arXivquant-ph/9804010OpenAlexW3038125555WikidataQ56675305 ScholiaQ56675305MaRDI QIDQ137124

David A. Meyer, David A. Meyer

Publication date: 3 April 1998

Published in: Physical Review Letters (Search for Journal in Brave)

Abstract: We consider game theory from the perspective of quantum algorithms. Strategies in classical game theory are either pure (deterministic) or mixed (probabilistic). We introduce these basic ideas in the context of a simple example, closely related to the traditional Matching Pennies game. 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, however, that in our example a player who implements a quantum strategy can increase his expected payoff, and explain the relation to efficient quantum algorithms. We prove that in general a quantum strategy is always at least as good as a classical one, and furthermore that when both players use quantum strategies there need not be any equilibrium, but if both are allowed mixed quantum strategies there must be.

Full work available at URL: https://arxiv.org/abs/quant-ph/9804010

Mathematics Subject Classification ID

2-person games (91A05) Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.) (68Q10) Quantum computation (81P68)

Cites Work

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