An evolutionary game model of families’ voluntary provision of public goods

Abstract

We consider a two-stage voluntary provision model where individuals in a family contribute to a pure public good and/or a household public good, and an altruistic parent makes a non-negative income transfer to his or her child. The subgame perfect equilibrium derived in the model is analyzed using two evolutionary dynamics games (i.e., replicator dynamics and best response dynamics). As a result, the equilibria with ex-post transfers and pre-committed transfers coexist, and are unstable in the settings of replicator dynamics as well as best response dynamics, whereas the monomorphic states (i.e., all families undertake either ex-post or pre-committed transfers) are stable. An income redistribution policy does not alter the real allocations in the settings of both evolutionary dynamics games, because the resulting real allocations depend on only the total income of society and not on the distribution of individual income.