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Simplified group activity selection with group size constraints

Author

Listed:
  • Andreas Darmann

    (University of Graz)

  • Janosch Döcker

    (University of Tübingen)

  • Britta Dorn

    (University of Tübingen)

  • Sebastian Schneckenburger

    (University of Tübingen)

Abstract

Several real-world situations can be represented in terms of agents that have preferences over activities in which they may participate. Often, the agents can take part in at most one activity (for instance, since these take place simultaneously), and there are additional constraints on the number of agents that can participate in an activity. In such a setting, we consider the task of assigning agents to activities in a reasonable way. We introduce the simplified group activity selection problem providing a general yet simple model for a broad variety of settings, and start investigating its special case where upper and lower bounds of the groups have to be taken into account. We apply different solution concepts such as envy-freeness and core stability to our setting and provide a computational complexity study for the problem of finding such solutions.

Suggested Citation

  • Andreas Darmann & Janosch Döcker & Britta Dorn & Sebastian Schneckenburger, 2022. "Simplified group activity selection with group size constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(1), pages 169-212, March.
    • Handle: RePEc:spr:jogath:v:51:y:2022:i:1:d:10.1007_s00182-021-00789-7
    DOI: 10.1007/s00182-021-00789-7
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    References listed on IDEAS

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    1. Cechlárová, Katarína & Fleiner, Tamás, 2017. "Pareto optimal matchings with lower quotas," Mathematical Social Sciences, Elsevier, vol. 88(C), pages 3-10.
    2. Andreas Darmann & Edith Elkind & Sascha Kurz & Jérôme Lang & Joachim Schauer & Gerhard Woeginger, 2018. "Group activity selection problem with approval preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(3), pages 767-796, September.
    3. Monte, Daniel & Tumennasan, Norovsambuu, 2013. "Matching with quorums," Economics Letters, Elsevier, vol. 120(1), pages 14-17.
    4. Darmann, Andreas, 2018. "A social choice approach to ordinal group activity selection," Mathematical Social Sciences, Elsevier, vol. 93(C), pages 57-66.
    5. Monroe, Burt L., 1995. "Fully Proportional Representation," American Political Science Review, Cambridge University Press, vol. 89(4), pages 925-940, December.
    6. Chamberlin, John R. & Courant, Paul N., 1983. "Representative Deliberations and Representative Decisions: Proportional Representation and the Borda Rule," American Political Science Review, Cambridge University Press, vol. 77(3), pages 718-733, September.
    7. Andreas Darmann, 2018. "Stable and Pareto optimal group activity selection from ordinal preferences," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(4), pages 1183-1209, November.
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