A General Approach for Solving Differential Public Goods Games and a Comparison to the Static Case

Abstract

We study a class of differential public good games and show how static public good games can naturally be embedded into this class. This allows us to compare the outcomes in the static and the dynamic case. In the dynamic case we study the feedback Nah-equilibria and compare these to the Nash equilibria of the corresponding static game. To solve for feedback the Nash equilibria in the dynamic case, we solve the Hamilton-Jacobi-Bellmann equation by using the method of characteristic functions. Analytical results are given.

Keywords: Public good games, differential games, optimal control

JEL Classification: C02;,C61, C73, D21, P51