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This paper studies the provision of a public good between two agents under lack of commitment and applies it to the problem of children's consumption in separated couples, where children are considered to be public goods. The custodial mother controls the child's consumption, whereas the father can contribute indirectly by making monetary transfers to the mother, but has no control over how the mother spends them. Using minmax punishments, the author looks for the Pareto frontier of the Subgame Perfect Equilibrium payoffs, and characterizes the equilibrium and long term implications of the model.
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