Jun-Ichi Itaya: Existence, Uniqueness, and Algorithm for Identifying Free Riders in Multiple Public Good Games

Replacement Function Approach

This study shows the uniqueness of Nash equilibrium in the model of multiple voluntarily supplied public goods with potential contributors possessing different Cobb-Douglas preferences. This study provides a sufficient condition for uniqueness using graph theory. This sufficient condition allows us to use the replacement function approach of Cornes and Hartley (2007) not only to develop an algorithm for identifying free riders, but also to provide an alternative proof for the uniqueness of a Nash equilibrium in multiple public goods models.

Keywords: public good, voluntary provision, uniqueness, aggregate game, Nash equilibrium, algorithm