The Price Identity of Replicator(–Mutator) Dynamics on Graphs with Quantum Strategies in a Public Goods Game

Our research explores the influence of quantum strategies on the Price identity of replicator(–mutator) dynamics in networked systems. We specifically focus on potential solutions to social dilemmas through a quantum interpretation of the public goods game. The outcomes of our investigation defy the expected simplicity, suggesting that quantum strategies do not invariably induce cooperative behavior. Within the framework of replicator dynamics, based on a stratified interaction mechanism and a composite strategy update rule, complete entanglement could lead to super-cooperators dominating, given the cooperation and defection probabilities exceed zero. In replicator–mutator dynamics, super-cooperators reach their peak density when mutation leaning toward cooperation is certain. Numerical simulations corroborate our theoretical propositions, shedding light on the roles of various subpopulations as either complementary or substitutive entities. Our research underscores how quantum strategies accentuate observed patterns compared to non-entangled scenarios, and how the assuredness of mutation markedly impacts the behavior of super-cooperators.