IDEAS home Printed from
MyIDEAS: Log in (now much improved!) to save this paper

A Stochastic Lake Game

Listed author(s):
  • Sharon I. O'Donnell
  • W. Davis Dechert

In this paper we solve a stochastic dynamic programming problem for the solution to a dynamic game in which the players select a mean level of control. The state transition dynamics are a function of the current state of the system and a multiplicative noise factor on the control variables of the players. The particular application is to lake water usage. (A deterministic version of the model was analyzed by Brock and Dechert, "The Lakegame.") The control variables are the levels of phosphorus discharged (typically by farmers) into the water shed of the lake, and the random shock is the level of rainfall that washes the phosphorus in to the lake. The state of the system is the accumulated level of phosphorus in the lake. The system dynamics are sufficiently non-linear so that there can be two Nash equilibria, and hence a Skiba point can be present in the optimal control solution. In the paper we analyze (numerically) how the dynamics and the Skiba point change as the variance of the noise (the rain) increases. The numerical analysis uses a result of Dechert (JET 1978) that allows us to construct a potential function for the dynamic game. This greatly reduces the computational burden in finding Nash equilibrium solutions for the dynamic game.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
File Function: main text
Download Restriction: no

Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 104.

in new window

Date of creation: 11 Aug 2004
Handle: RePEc:sce:scecf4:104
Contact details of provider: Web page:

More information through EDIRC

No references listed on IDEAS
You can help add them by filling out this form.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:sce:scecf4:104. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Christopher F. Baum)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.