Continuous-Time Public Good Contribution Under Uncertainty

34 Pages Posted: 12 Jul 2013

See all articles by Giorgio Ferrari

Giorgio Ferrari

Bielefeld University - Center for Mathematical Economics

Frank Riedel

Bielefeld University - Center for Mathematical Economics

Jan-Henrik Steg

Bielefeld University - Center for Mathematical Economics

Date Written: July 10, 2013

Abstract

We study a continuous-time problem of optimal public good contribution under uncertainty for an economy with a finite number of agents. Each agent can allocate his wealth between private consumption and repeated but irreversible contributions to increase the stock of some public good. We study the corresponding social planner problem and the case of strategic interaction between the agents and we characterize the optimal investment policies by a set of necessary and sufficient stochastic Kuhn-Tucker conditions. Suitably combining arguments from Duality Theory and the General Theory of Stochastic Processes, we prove an abstract existence result for a Nash equilibrium of our public good contribution game. Also, we show that our model exhibits a dynamic free rider effect. We explicitly evaluate it in a symmetric Black-Scholes setting with Cobb-Douglas utilities and we show that uncertainty and irreversibility of public good provisions do not affect free-riding.

Keywords: irreversible investment, singular stochastic control, first order conditions for optimality, stochastic games, Nash equilibrium, free-riding

JEL Classification: C02, C61, C62, C73

Suggested Citation

Ferrari, Giorgio and Riedel, Frank and Steg, Jan-Henrik, Continuous-Time Public Good Contribution Under Uncertainty (July 10, 2013). Institute of Mathematical Economics Working Paper No. 485, Available at SSRN: https://ssrn.com/abstract=2292736 or http://dx.doi.org/10.2139/ssrn.2292736

Giorgio Ferrari (Contact Author)

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Frank Riedel

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Jan-Henrik Steg

Bielefeld University - Center for Mathematical Economics ( email )

Postfach 10 01 31
Bielefeld, D-33501
Germany

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
47
Abstract Views
664
PlumX Metrics