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Emergence of cooperation promoted by higher-order strategy updates

Fig 5

Intuitions from a viewpoint of defectors.

Each individual (node) plays as a cooperator (pink) or a defector (blue) and participates in public goods games (PGGs) within the groups they belong to. After a game round, both the groups and the individuals receive payoffs, based on which the focal individual (a defector) updates its strategy by selecting an individual for imitation or comparison through two-stage selection. For simplicity, the group payoff is assumed to be the average of its individuals’ payoffs and the individual payoff is the game outcome within a specific group. a, Group selection can be either group-biased or group-neutral. The focal player favors group due to its higher payoff under group-biased selection, whereas it randomly chooses among neighboring hyperedges under group-neutral selection. b, Individual selection can be individual-biased or individual-neutral. The focal player prefers the defector, as defectors generally outperform cooperators in individual payoffs within a group under individual-biased selection, while it randomly picks a member within the group under individual-neutral selection. c, Strategy updates occur based on imitation or comparison. Imitation involves copying a preferential individual’s strategy, whereas comparison tends to reinforce the original defector strategy due to the higher payoff itself.

doi: https://doi.org/10.1371/journal.pcbi.1012891.g005