PMC

The rehabilitation games. From left to right: single-player / competitive game (which look the same), cooperative game with split field, cooperative game with shared field

A: A cooperative Nash equilibrium in which defectors play softly with cooperators and cooperators play hard with defectors when the game B is a Snow Drift game exists when the cost of cooperation is smaller than the coordination asymmetry defined as the payoff difference of hard and soft strategies in the Snow Drift game. B: A cooperative Nash equilibrium, when the game B is a Stag Hunt game, exists when the cost of cooperation is smaller than the cost of coordinating on an inferior equilibrium, defined as the payoff difference of the superior and inferior equilibria in the Stag Hunt game. These conditions can be derived by requiring the payoff of Nash strategies (shown in white) to be larger than all the other payoffs in the same column.

Cooperative phenotype positively predicts both pro-environmental behaviour (a) and belief in climate change (b). “Cooperative phenotype” is a latent variable captured by cooperative decisions in the Dictator Game, Public Goods Game, Trust Game, and Stag Hunt Game. “Climate change belief” is a latent variable captured by three self-report items measuring belief in the reality of climate change, belief that climate change is human caused, and concern about climate change. For visualisation ease, regression lines and 95% confidence interval shaded areas are predictions from least-squares regressions without covariates.

A: The probability of settling in cooperative fixed point starting from random initial conditions for different structures of game B. While for anti-coordination games, the cooperative fixed point has a large basin of attraction, for the Stag Hunt game, cooperative fixed points can occur only for special initial conditions. B to C: The probability of settling in the cooperative fixed point as a function of the initial frequency of cooperators , A, and initial frequency of soft players, , B, for different structures of game B is plotted. The replicator-mutator dynamic is solved for 10⁷ different randomly generated initial conditions to derive the probabilities.