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

TL;DR

This paper critiques a proposed quantum game strategy, arguing it alters game rules and does not refute the claim that quantum equilibria are present in extended classical games.

Contribution

It clarifies that the new quantum strategy modifies original game rules, supporting van Enk and Pike's assertion about quantum equilibria.

Findings

The proposed strategy changes the game's fundamental rules.

It does not provide evidence that quantum payoffs cannot be replicated classically.

Supports the view that quantum solutions are extendable classical solutions.

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.