Theory of Computing Systems

, Volume 49, Issue 1, pp 162–181 | Cite as

On the Complexity of Iterated Weak Dominance in Constant-Sum Games

  • Felix BrandtEmail author
  • Markus Brill
  • Felix Fischer
  • Paul Harrenstein


In game theory, an action is said to be weakly dominated if there exists another action of the same player that, with respect to what the other players do, is never worse and sometimes strictly better. We investigate the computational complexity of the process of iteratively eliminating weakly dominated actions (IWD) in two-player constant-sum games, i.e., games in which the interests of both players are diametrically opposed. It turns out that deciding whether an action is eliminable via IWD is feasible in polynomial time whereas deciding whether a given subgame is reachable via IWD is NP-complete. The latter result is quite surprising, as we are not aware of other natural computational problems that are intractable in constant-sum normal-form games. Furthermore, we slightly improve on a result of V. Conitzer and T. Sandholm by showing that typical problems associated with IWD in win-lose games with at most one winner are NP-complete.


Game theory Constant-sum games Solutions concepts Iterated weak dominance Computational complexity 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Felix Brandt
    • 1
    Email author
  • Markus Brill
    • 1
  • Felix Fischer
    • 2
  • Paul Harrenstein
    • 1
  1. 1.Institut für InformatikTechnische Universität MünchenGarchingGermany
  2. 2.Harvard School of Engineering and Applied SciencesCambridgeUSA

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