Abstract
We solve an N ∈ N player general-sum differential game. The optimization problem considered here is based on the Uzawa-Lucas model of endogenous growth. Agents have logarithmic preferences and own two capital stocks. Since the number of players is an arbitrary fixed number N ∈ N, the model's solution is more general than the idealized concepts of the social planer's solution with one player or the competitive equilibrium with infinitely many players. We show that the symmetric Nash equilibrium is completely described by the solution to a single ordinary differential equation. The numerical results imply that the influence of the externality along the balanced growth path decreases rapidly as the number of players increases. Off the steady state, the externality is of great importance, even for a large number of players.
| Original language | English |
|---|---|
| Pages (from-to) | 396-414 |
| Number of pages | 19 |
| Journal | Journal of Macroeconomics |
| Volume | 30 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2008 Mar |
Bibliographical note
Funding Information:Financial support by the Collaborative Research Center 373 and the Fritz Thyssen Stiftung is gratefully acknowledged. I thank Michael C. Burda, Markus Reiß, Harald Uhlig, seminar participants at Humboldt University, and two anonymous referees for helpful comments. Thanks also go to Henry Y. Wan Jr., Elias Dinopoulos, and participants of the International Conference on Dynamics, Economic Growth and International Trade (DEGIT IX) in Reykjavik. All remaining errors are my own.
Keywords
- Nash-equilibrium
- Open-loop strategies
- Ordinary differential equation
- Value function approach
ASJC Scopus subject areas
- Economics and Econometrics