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Strategies in competing subset selection

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  • Claudia Marini
  • Gaia Nicosia
  • Andrea Pacifici
  • Ulrich Pferschy

Abstract

We address an optimization problem in which two agents, each with a set of weighted items, compete in order to minimize the total weight of their solution sets. The latter are built according to a sequential procedure consisting in a fixed number of rounds. In every round each agent submits one item that may be included in its solution set. We study two natural rules to decide which item between the two will be included. We address the problem from a strategic point of view, that is finding the best moves for one agent against the opponent, in two distinct scenarios. We consider preventive or minimax strategies, optimizing the objective of the agent in the worst case, and best-response strategies, where the items submitted by the opponent are known in advance in each round. Copyright Springer Science+Business Media, LLC 2013

Suggested Citation

  • Claudia Marini & Gaia Nicosia & Andrea Pacifici & Ulrich Pferschy, 2013. "Strategies in competing subset selection," Annals of Operations Research, Springer, vol. 207(1), pages 181-200, August.
    • Handle: RePEc:spr:annopr:v:207:y:2013:i:1:p:181-200:10.1007/s10479-011-1057-2
    DOI: 10.1007/s10479-011-1057-2
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    References listed on IDEAS

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    1. Schlag, Karl H. & Sela, Aner, 1998. "You play (an action) only once," Economics Letters, Elsevier, vol. 59(3), pages 299-303, June.
    2. Joseph Y.-T. Leung & Michael Pinedo & Guohua Wan, 2010. "Competitive Two-Agent Scheduling and Its Applications," Operations Research, INFORMS, vol. 58(2), pages 458-469, April.
    3. Kahn, J & Lagarias, J C & Witsenhausen, H S, 1987. "Single-Suit Two-Person Card Play," International Journal of Game Theory, Springer;Game Theory Society, vol. 16(4), pages 291-320.
    4. Fujimoto, Masako & Yamada, Takeo, 2006. "An exact algorithm for the knapsack sharing problem with common items," European Journal of Operational Research, Elsevier, vol. 171(2), pages 693-707, June.
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    Cited by:

    1. Darmann, Andreas & Nicosia, Gaia & Pferschy, Ulrich & Schauer, Joachim, 2014. "The Subset Sum game," European Journal of Operational Research, Elsevier, vol. 233(3), pages 539-549.
    2. Gaia Nicosia & Andrea Pacifici & Ulrich Pferschy, 2018. "Competitive multi-agent scheduling with an iterative selection rule," 4OR, Springer, vol. 16(1), pages 15-29, March.

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