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arXiv · 1609.08360

No fixed-point guarantee of Nash equilibrium in quantum games

Faisal Shah Khan·Travis S. Humble
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Abstract

The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we find this guarantee is not provided for quantum games. In particular, we show the conditions for Glickberg's fixed-point theorem do not apply to pure quantum games when the payoff is a physical observable. We further show that Nash equilibrium can be guaranteed when the payoff is defined with respect to state preparation.

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Faisal Shah Khan, Travis S. Humble. 2016-09-27. No fixed-point guarantee of Nash equilibrium in quantum games. https://arxiv.org/abs/1609.08360

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