Quantum-mechanical machinery for rational decision-making in classical guessing game

TL;DR

This paper demonstrates that quantum reasoning can provide a rational player with advantages in a classical guessing game without altering the game's rules, highlighting the potential of quantum decision processes.

Contribution

It introduces a novel approach where quantum reasoning enhances decision-making in classical games without changing the game structure.

Findings

Quantum reasoning can improve strategy in classical guessing games.

Quantum reasoning may also lead to worse outcomes if preferences are misaligned.

The approach shows quantum advantages are possible without modifying classical game rules.

Abstract

In quantum game theory, one of the most intriguing and important questions is, "Is it possible to get quantum advantages without any modification of the classical game?" The answer to this question so far has largely been negative. So far, it has usually been thought that a change of the classical game setting appears to be unavoidable for getting the quantum advantages. However, we give an affirmative answer here, focusing on the decision-making process (we call 'reasoning') to generate the best strategy, which may occur internally, e.g., in the player's brain. To show this, we consider a classical guessing game. We then define a one-player reasoning problem in the context of the decision-making theory, where the machinery processes are designed to simulate classical and quantum reasoning. In such settings, we present a scenario where a rational player is able to make better use of his/her weak preferences due to quantum reasoning, without any altering or resetting of the classically defined game. We also argue in further analysis that the quantum reasoning may make the player fail, and even make the situation worse, due to any inappropriate preferences.