Department of Computer Science | Institute of Theoretical Computer Science | CADMO

Prof. Emo Welzl and Prof. Bernd Gärtner

Mittagsseminar Talk Information |

**Date and Time**: Thursday, April 04, 2013, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Antonis Thomas (University of Edinburgh)

We consider the complexity of *w*-PNE-GG, the problem of computing pure Nash equilibria in graphical games parameterized by the treewidth *w* of the underlying graph. It is well-known that the problem of computing such equilibria is *NP*-hard in general, but solvable in polynomial time when restricted to games of bounded treewidth. We prove that *w*-PNE-GG is *W[1]*-hard and thus a fixed-parameter algorithm is unlikely.

Furthermore, we describe a dynamic programming algorithm for *w*-PNE-GG. In contrast to the previous algorithms that rely on reductions to other problems, our algorithm treats directly the problem at hand. We show that *w*-PNE-GG is fixed-parameter tractable when the strategy sets have bounded cardinality.

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