Exploration and Exhaustibility in Dynamic Cournot Games

26 Pages Posted: 13 Feb 2011 Last revised: 18 Aug 2011

See all articles by Michael Ludkovski

Michael Ludkovski

University of California, Santa Barbara

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Date Written: August 17, 2011

Abstract

We study the stochastic effect of resource exploration in dynamic Cournot models of exhaustible resources, such as oil. We first treat the case of a monopolist who may undertake costly exploration to replenish his diminishing reserves. We then consider a stochastic game between such an exhaustible producer and a "green'' producer that has access to an inexhaustible but relatively expensive source, such as solar power. The effort control variable is taken to be either continuous or discrete (switching control). In both settings, we assume that new discoveries occur according to a jump process with intensity given by the exploration effort. This leads to a study of systems of nonlinear first order delay ODEs. We derive asymptotic expansions for the case of a small exploration success rate and present some numerical investigations.

Keywords: Cournot games, exploration control, stochastic differential games, exhaustible resources

JEL Classification: C73, L13, L71

Suggested Citation

Ludkovski, Mike and Sircar, Ronnie, Exploration and Exhaustibility in Dynamic Cournot Games (August 17, 2011). Available at SSRN: https://ssrn.com/abstract=1759031 or http://dx.doi.org/10.2139/ssrn.1759031

Mike Ludkovski (Contact Author)

University of California, Santa Barbara ( email )

Santa Barbara, CA 93106
United States

HOME PAGE: http://www.pstat.ucsb.edu/faculty/ludkovski

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

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