Game theory

We consider a production planning problem where two competing companies are selling their items on a common market. Moreover, the raw material used in the production is a limited non-renewable resource. The revenue per item sold depends on the total amount of items produced by both players. If they collaborate they could apply a production strategy that leads to the highest combined revenue. Usually the formation of such syndicates is prohibited by law; hence we assume that one company does not know how much the other company will produce. The  problem for player A to find an optimal production plan without information on the strategy of player B can be formulated as a nonlinear mathematical optimization problem. In its naive formulation the model is too large, making its solution practically impossible. After a reformulation, it turns into a much smaller model, which is solved by spatial branch-and-cut methods and linear programming. It turns out that player A can have a production strategy which yields an income for A that player B cannot beat, no matter how he produces.


  • Social Science Research Center Berlin (WZB)
  • Zuse Institute Berlin


  • DFG, Collaborative Research Center SFB-1026.

Related publications

  • Armin Fügenschuh, Roel van Veldhuizen, Ingmar Vierhaus, Production Planning for Non-Cooperating Companies with Nonlinear Optimization , Proceedings of the 11th Global Conference on Sustainable Manufacturing, Universitätsverlag der TU Berlin, pp. 588-593, 2013. (Also available as ZIB Technical Report ZR-13-25 , 2013.)

This website uses cookies. There are two types of cookies: The first type supports the basic functionality of our website. The second allows us to improve our content for you by saving and analyzing pseudonymised user data. Since this second type is technically not required to run the website, you can withdraw your consent to those cookies at any time. For more information please visit our pages on data protection.


These cookies are needed for a smooth operation of our website.


For statistical reasons, we use the platform Matomo to analyse the user flow with the help of website users‘ pseudonymised data. This allows us to optimize website content.

Name Purpose Lifetime Type Provider
_pk_id Used to store a few details about the user such as the unique visitor ID. 13 months HTML Matomo
_pk_ref Used to store the attribution information, the referrer initially used to visit the website. 6 months HTML Matomo
_pk_ses Short lived cookie used to temporarily store data for the visit. 30 minutes HTML Matomo