IDEAS home Printed from https://ideas.repec.org/p/sce/scecf4/104.html
   My bibliography  Save this paper

A Stochastic Lake Game

Author

Listed:
  • Sharon I. O'Donnell
  • W. Davis Dechert

Abstract

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.

Suggested Citation

  • Sharon I. O'Donnell & W. Davis Dechert, 2004. "A Stochastic Lake Game," Computing in Economics and Finance 2004 104, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:104
    as

    Download full text from publisher

    File URL: http://panda.econ.uh.edu/research/stochastic.lake.ps
    File Function: main text
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    stochastic dynamic programming; dynamic game; potential function;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:sce:scecf4:104. See general information about how to correct material in RePEc.

    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.

    We have no bibliographic references for this item. You can help adding them by using 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/sceeeea.html .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.