Kantian equilibria in classical and quantum symmetric games

TL;DR

This paper explores Kantian equilibria in classical and quantum symmetric 2x2 games, deriving a formula for equilibrium strategies and showing quantum strategies often yield better payoffs.

Contribution

It introduces a general formula for Kantian equilibrium strategies in symmetric games and compares classical and quantum outcomes, highlighting quantum advantages.

Findings

Quantum strategies often lead to more beneficial Kantian equilibria.

Derived a universal formula for equilibrium strategies in symmetric games.

Quantum versions outperform classical in many cases.

Abstract

The aim of the paper is to examine the notion of simple Kantian equilibrium in $2 \times 2$ symmetric games and their quantum counterparts. We focus on finding the Kantian equilibrium strategies in the general form of the games. As a result, we derive a formula that determines the reasonable strategies for any payoffs in the bimatrix game. This allowed us to compare the payoff results for classical and quantum way of playing the game. We showed that a very large part of $2\times 2$ symmetric games have more beneficial Kantian equilibria when they are played with the use of quantum strategies.