On the parameterized complexity of dominant strategies

V. Estivill-Castro, M. Parsa

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

Abstract

In game theory, a strategy for a player is dominant if, regardless of what any other player does, the strategy earns a better payoff than any other. If the payoff is strictly better, the strategy is named strictly dominant, but if it is simply not worse, then it is called weakly dominant. We investigate the parameterized complexity of two problems relevant to the notion of domination among strategies. First, we study the parameterized complexity of the MINIMUM MIXED DOMINATING STRATEGY SET problem, the problem of deciding whether there exists a mixed strategy of size at most k that dominates a given strategy of a player. We show that the problem can be solved in polynomial time on win-lose games. Also, we show that it is a fixed-parameter tractable problem on r-sparse games, games where the payoff matrices of players have at most r nonzero entries in each row and each column. Second, we study the parameterized complexity of the ITERATED WEAK DOMINANCE problem. This problem asks whether there exists a path of at most k-steps of iterated weak dominance that eliminates a given pure strategy. We show that this problem is W [2]-hard, therefore, it is unlikely to be a fixed-parameter tractable problem.
Original languageEnglish
Title of host publicationProceedings of Computer Science 2012 (ACSC 2012)
EditorsM. Reynolds, B Thomas
Place of PublicationMelbourne, Australia
Pages21-26
Number of pages6
Volume122
Publication statusPublished - 2012

Publication series

NameConferences in Research and Practice in Information Technology
PublisherAustralian Computer Society Inc.

Keywords

  • algorithms
  • computational game theory
  • dominant strategies
  • parameterized complexity theory

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  • Prizes

    Best Paper Award

    Mahdi Parsa (Recipient), 2012

    Prize: Prize (including medals and awards)

    Cite this

    Estivill-Castro, V., & Parsa, M. (2012). On the parameterized complexity of dominant strategies. In M. Reynolds, & B. Thomas (Eds.), Proceedings of Computer Science 2012 (ACSC 2012) (Vol. 122, pp. 21-26). (Conferences in Research and Practice in Information Technology)..