Nash equilibria in quantum games
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- by Steven E. Landsburg
- Proc. Amer. Math. Soc. 139 (2011), 4423-4434
- DOI: https://doi.org/10.1090/S0002-9939-2011-10838-4
- Published electronically: April 19, 2011
Abstract:
For any two-by-two game $\mathbf {G}$, we define a new two-player game $\mathbf {G}^Q$. The definition is motivated by a vision of players in game $\mathbf {G}$ communicating via quantum technology according to the protocol introduced by J. Eisert and M. Wilkins.
In the game $\mathbf {G}^Q$, each player’s (mixed) strategy set consists of the set of all probability distributions on the 3-sphere $\mathbf {S}^3$. Nash equilibria in the game can be difficult to compute.
Our main theorems classify all possible mixed-strategy equilibria. First, we show that up to a suitable definition of equivalence, any strategy that arises in equilibrium is supported on at most four points; then we show that those four points must lie in one of a small number of allowable geometric configurations.
References
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Bibliographic Information
- Steven E. Landsburg
- Affiliation: Department of Economics, University of Rochester, Rochester, New York 14627
- Received by editor(s): October 24, 2009
- Received by editor(s) in revised form: October 17, 2010
- Published electronically: April 19, 2011
- Communicated by: Richard C. Bradley
- © Copyright 2011 Steven E. Landsburg
- Journal: Proc. Amer. Math. Soc. 139 (2011), 4423-4434
- MSC (2010): Primary 91A05, 81P45
- DOI: https://doi.org/10.1090/S0002-9939-2011-10838-4
- MathSciNet review: 2823088