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On Iterated Dominance, Matrix Elimination, and Matched Paths

Authors Felix Brandt, Felix Fischer, Markus Holzer



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LIPIcs.STACS.2010.2448.pdf
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Felix Brandt
Felix Fischer
Markus Holzer

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Felix Brandt, Felix Fischer, and Markus Holzer. On Iterated Dominance, Matrix Elimination, and Matched Paths. In 27th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 5, pp. 107-118, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)
https://doi.org/10.4230/LIPIcs.STACS.2010.2448

Abstract

We study computational problems arising from the iterated removal of weakly dominated actions in anonymous games. Our main result shows that it is NP-complete to decide whether an anonymous game with three actions can be solved via iterated weak dominance. The two-action case can be reformulated as a natural elimination problem on a matrix, the complexity of which turns out to be surprisingly difficult to characterize and ultimately remains open. We however establish connections to a matching problem along paths in a directed graph, which is computationally hard in general but can also be used to identify tractable cases of matrix elimination. We finally identify different classes of anonymous games where iterated dominance is in P and NP-complete, respectively.
Keywords
  • Algorithmic Game Theory
  • Computational Complexity
  • Iterated Dominance
  • Matching

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