Quantum Strategies Win in a Defector-Dominated Population

TL;DR

This study demonstrates that quantum strategies can successfully invade and dominate in various networked populations engaged in classic evolutionary games, even when initially rare and in defector-dominated environments.

Contribution

It introduces quantum strategies into evolutionary game theory on different networks and analyzes their invasion success and conditions across multiple game types.

Findings

Quantum strategies invade successfully across all tested networks and games.

Regular lattice networks are most susceptible to quantum strategy invasion.

In scale-free networks, invasion depends on hubs adopting quantum strategies or higher quantum strategy fractions.

Abstract

Quantum strategies are introduced into evolutionary games. The agents using quantum strategies are regarded as invaders whose fraction generally is 1% of a population in contrast to the 50% defectors. In this paper, the evolution of strategies on networks is investigated in a defector-dominated population, when three networks (Regular Lattice, Newman-Watts small world network, scale-free network) are constructed and three games (Prisoners' Dilemma, Snowdrift, Stag-Hunt) are employed. As far as these three games are concerned, the results show that quantum strategies can always invade the population successfully. Comparing the three networks, we find that the regular lattice is most easily invaded by agents that adopt quantum strategies. However, for a scale-free network it can be invaded by agents adopting quantum strategies only if a hub is occupied by an agent with a quantum strategy or if the fraction of agents with quantum strategies in the population is significant.