Quantum games and quaternionic strategies

Quantum games and quaternionic strategies It is well-known that the phenomenon of entanglement plays a fundamental role in quantum game theory. Occasionally, games constructed via maximally entangled initial states (MEIS) will have new Nash equilibria yielding to the players higher payoffs than the ones they receive in the classical version of the game. When examining these new games for Nash equilibrium payoffs, a fundamental question arises; does a suitable choice of an MEIS improve the lot of the players? In this paper, we show that the answer to this question is yes for at least the case of a variant of the well-known two player, two strategy game of Chicken. To that end, we generalize Landsburg’s quaternionic representation of the payoff function of two player, two strategy maximally entangled states to games where the initial state is chosen arbitrarily from a circle of maximally entangled initial states and for the corresponding quantized games show the existence of superior Nash equilibrium payoffs when an MEIS is appropriately chosen. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Quantum games and quaternionic strategies

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Publisher
Springer US
Copyright
Copyright © 2013 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-013-0553-5
Publisher site
See Article on Publisher Site

Abstract

It is well-known that the phenomenon of entanglement plays a fundamental role in quantum game theory. Occasionally, games constructed via maximally entangled initial states (MEIS) will have new Nash equilibria yielding to the players higher payoffs than the ones they receive in the classical version of the game. When examining these new games for Nash equilibrium payoffs, a fundamental question arises; does a suitable choice of an MEIS improve the lot of the players? In this paper, we show that the answer to this question is yes for at least the case of a variant of the well-known two player, two strategy game of Chicken. To that end, we generalize Landsburg’s quaternionic representation of the payoff function of two player, two strategy maximally entangled states to games where the initial state is chosen arbitrarily from a circle of maximally entangled initial states and for the corresponding quantized games show the existence of superior Nash equilibrium payoffs when an MEIS is appropriately chosen.

Journal

Quantum Information ProcessingSpringer Journals

Published: Mar 10, 2013

References

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