Arbiter as the Third Man in classical and quantum games

TL;DR

This paper explores how an arbiter's influence affects classical and quantum 2x2 games, revealing that quantum games are highly sensitive to initial states, making them fundamentally different even with identical payoff matrices.

Contribution

It demonstrates that in quantum games, initial states significantly alter game outcomes, unlike classical games where payoff matrices suffice to define the game.

Findings

Quantum games are more influenced by arbiter bias than classical games.

Initial states in quantum games critically determine the game's nature.

Quantum games with identical payoff matrices but different initial states are distinct.

Abstract

We study possible influence of not necessarily sincere arbiter on the course of classical and quantum 2x2 games and we show that this influence in the quantum case is much bigger than in the classical case. Extreme sensitivity of quantum games on initial states of quantum objects used as carriers of information in a game shows that a quantum game, contrary to a classical game, is not defined by a payoff matrix alone but also by an initial state of objects used to play a game. Therefore, two quantum games that have the same payoff matrices but begin with different initial states should be considered as different games.