dorsal/arxiv
View SchemaQuantum strategies
| Authors | David A. Meyer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9804010 |
| URL | https://arxiv.org/abs/quant-ph/9804010 |
| DOI | 10.1103/PhysRevLett.82.1052 |
| Journal | Phys.Rev.Lett. 82 (1999) 1052-1055 |
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.
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"abstract": "We consider game theory from the perspective of quantum algorithms.\nStrategies in classical game theory are either pure (deterministic) or mixed\n(probabilistic). We introduce these basic ideas in the context of a simple\nexample, closely related to the traditional Matching Pennies game. While not\nevery two-person zero-sum finite game has an equilibrium in the set of pure\nstrategies, von Neumann showed that there is always an equilibrium at which\neach player follows a mixed strategy. A mixed strategy deviating from the\nequilibrium strategy cannot increase a player\u0027s expected payoff. We show,\nhowever, that in our example a player who implements a quantum strategy can\nincrease his expected payoff, and explain the relation to efficient quantum\nalgorithms. We prove that in general a quantum strategy is always at least as\ngood as a classical one, and furthermore that when both players use quantum\nstrategies there need not be any equilibrium, but if both are allowed mixed\nquantum strategies there must be.",
"arxiv_id": "quant-ph/9804010",
"authors": [
"David A. Meyer"
],
"categories": [
"quant-ph"
],
"doi": "10.1103/PhysRevLett.82.1052",
"journal_ref": "Phys.Rev.Lett. 82 (1999) 1052-1055",
"title": "Quantum strategies",
"url": "https://arxiv.org/abs/quant-ph/9804010"
},
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