Finding all solutions of affine generalized Nash equilibrium problems with one-dimensional strategy sets |
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Authors: | Axel Dreves |
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Institution: | 1. Department of Aerospace Engineering, Universit?t der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577?, Neubiberg/Munich, Germany
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Abstract: | We consider a class of generalized Nash equilibrium problems with quadratic cost functions and common linear constraints for all players. Further we focus on the case where every player has a single strategy variable within a bounded set. For this problem class we present an algorithm that is able to compute all solutions and that terminates finitely. Our method is based on a representation of the solution set as a finite union of polyhedral sets using sign conditions for the derivatives of the cost and constraint functions. The effectiveness of the algorithm is shown in various examples from literature. |
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