The Theory of Public Good Provision: The Nash Equilibrium Approach

The Nash Equilibrium Approach of Private Provision

The prior section investigated the normative analysis of the provision of public goods. This section investigates the positive theoretical analysis of the private provision of public goods. When the government does not provide public goods optimally, how do private agents behave? They may have an incentive to provide the public goods privately. The standard approach with the private provision of public goods is called the Nash equilibrium approach, whereby each agent optimizes the provision of public goods at a given level of public goods provided by other agents.

A public good can be provided by the private sector. Households may contribute to the provision of public goods if the initial level of public goods is too low. For example, we have already considered the provision of streetlights in front of houses. Suppose the government does not provide streetlights at all. Then, each agent may decide how many streetlights, which are pure public goods, she or he would like to have in front of her or his house.

Alternatively, if we consider the provision of an international public good, each country may be regarded as a private contributor since it determines its provision of the international public good based on its own interest. For example, the total emissions of CO2 could be reduced by the abatement activities of countries; thus, the provision of abatement spending by each country may be regarded as a private provision of public goods. Then, the Nash equilibrium approach becomes relevant since each country behaves non-cooperatively to maximize its own welfare. Appendix of this Chapter deals with this case.

Alternatively, one could consider intergovernmental finance. Suppose local governments can provide nationwide public goods, the benefit of which spills over the country. If central government does not provide these goods, each local government has an incentive to provide them.

 
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