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Worst-Case Payoffs in Quantum Battle of Sexes Game

Ahmad Nawaz, A. H. Toor

Published Oct 16, 2001• 2 citations
OpenAlex

Abstract

In quantum version of the Battle of Sexes game recently suggested by Marinatto and Weber [Phys. Lett. A 272, 291 (2000)] the worst-case payoffs occur when `tactics' are mismatched for a particular initial quantum state or `initial strategy' in the scheme. We show that when a more general initial quantum state is used in this scheme the worst-case payoffs do not occur even for mismatched tactics.

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In quantum version of the Battle of Sexes game recently suggested by Marinatto and Weber [Phys. Lett. A 272, 291 (2000)] the worst-case payoffs occur when tactics' are mismatched for a particular initial quantum state or initial strategy' in the scheme. We show that when a more general initial quantum state is used in this scheme the worst-case payoffs do not occur even for mismatched tactics.
The Battle of the Sexes game is analyzed from quantum game theory using quantum initial states as possible strategies for two players. Quantum circuits are presented as schemes of development proposing also the use of Yang-Baxter operators as quantum gates in the circuits. This formalism is implemented using a Computer Algebra Software (CAS) due to its complex and long mathematical treatment. Payoff matrices of the players are given as the results for each case shown. Biology and finances applications are also proposed.