When quantum games can be played classically: in support of van Enk-Pike's assertion

Abstract

N. Vyas and C. Benjamin (arXiv:1701.08573[quant-ph]) propose a new mixed strategy for the (quantum) Hawk-Dove and Prisoners' Dilemma games and argue that this strategy yields payoffs, which cannot be obtained in the corresponding classical games. They conclude that this refutes the earlier assertion by S.J. van Enk and R. Pike that the quantum equilibrium solution is present in a corresponding extended classical game. This paper argues that the scheme suggested by N. Vyas and C. Benjamin changes the rules of the original game, and hence it does not refute the argument put forward by van Enk and Pike.