Quantum Prisoner's Dilemma game on hypergraph networks

TL;DR

This paper explores the impact of quantum strategies in three-player Prisoner's Dilemma games on hypergraph networks, revealing that quantum strategies are not always the most stable or advantageous option.

Contribution

It introduces the use of hypergraph networks to model multi-player quantum games and compares the stability of quantum versus classical strategies in this context.

Findings

Quantum strategies are not always stochastically stable.

Defection can be as effective as quantum strategies.

Results depend on network type and structure.

Abstract

We study the possible advantages of adopting of quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner's Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum one.