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- Hartwig Bosse, Jaroslaw Byrka, Evangelos Markakis
- Theor. Comput. Sci.
- 2007

We consider the problem of computing additively approximate Nash equilibria in noncooperative two-player games. We provide a new polynomial time algorithm that achieves an approximation guarantee of 0.36392. We first provide a simpler algorithm, that achieves a 0.38197-approximation, which is exactly the same factor as the algorithm of Daskalakis, Mehta and… (More)

- Hartwig Bosse, Martin Grötschel, Martin Henk
- Math. Program.
- 2005

Our main result is that every ro-dimensional polytope can be described by at most (2n — 1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n — 2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities. 1. I N T R O… (More)

- H. Bosse, HARTWIG BOSSE
- 2007

This paper presents a construction for symmetric, non-negative polynomials, which are not sums of squares. It explicitly generalizes the Motzkin polynomial and the Robinson polynomials to families of non-negative polynomials, which are not sums of squares. The degrees of the resulting polynomials can be chosen in advance. 2000 Mathematics Subject… (More)

Our main result is that every n-dimensional polytope can be described by at most 2n − 1 polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n− 2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities.

- Hartwig Bosse, Christine Gärtner, Oleg Golubitsky
- J. Symb. Comput.
- 2013

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