Evolutionary branching of social preferences in a public good provision game

We study the evolution of other-regarding preferences in a public goods game where the production function exhibits varying degrees of complementarity between individual efforts. Individuals are rational agents who play a Nash equilibrium, but differ in the weight they assign to others' payoffs, capturing varying degrees of prosocial or anti-social preferences. This preference trait evolves through payoff-based biased social learning, modeled within an adaptive dynamics framework. Because material payoffs induced by the equilibrium contributions may be non-concave in the preference parameter, evolutionary branching can arise. We show that monomorphic populations are evolutionarily stable only when complementarity between individual efforts is sufficiently strong, in which case preferences converge toward either prosociality or anti-sociality depending on the nature of strategic interactions between players. By contrast, when contributions are highly substitutable, monomorphic populations can become unstable, giving rise to polymorphic populations in which multiple preference types coexist. These results highlight how the structure of the public goods environment shapes the evolution and diversity of other-regarding motivations in culturally evolving populations.