Abstract
Pareto efficiency is a widely used property in solution concepts for cooperative and non--cooperative game--theoretic settings and, more generally, in multi--objective problems. However, finding or even approximating (when the objective functions are not convex) the Pareto curve is hard. Most of the literature focuses on computing concise representations to approximate the Pareto curve or on exploiting evolutionary approaches to generate approximately Pareto efficient samples of the curve. In this paper, we show that the Pareto curve of a bimatrix game can be found exactly in polynomial time and that it is composed of a polynomial number of pieces. Furthermore, each piece is a quadratic function. We use this result to provide algorithms for game-theoretic solution concepts that incorporate Pareto efficiency.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.