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On the Existence of Nash-stable Partition in Leader's Coalition Games

Author

Listed:
  • Vasily Gusev

    (National Research University Higher School of Economics)

  • Iakov Zhukov

    (National Research University Higher School of Economics)

Abstract

This paper investigates two approaches to determining the leader of a coalition partition: the individual and the collective. In the first approach, each coalition in the partition chooses a representative, and then the leader is chosen from among all the representatives. In the second approach, the leading coalition in the partition is chosen, and then the leader from among members of that coalition is chosen. The leader and the leading coalition are chosen with a certain probability, which is guided by the weight rule or the ranking rule. Both approaches can be encountered in contests, sports competitions, and political elections. The paper delivers results on the existence of Nash-stable partitions depending on the approach and the probability of determining the leader. Cases where the number of coalitions in the partition is fixed and arbitrary are studied. The existence of an equilibrium in weakly dominant strategies is proved for the collective approach and the weight rule, and the necessary and sufficient conditions for a Nash-stable partition to exist were found for the ranking rule. The sufficient conditions for a Nash-stable partition to exist were found for the individual approach and the corresponding probabilistic rules

Suggested Citation

  • Vasily Gusev & Iakov Zhukov, 2024. "On the Existence of Nash-stable Partition in Leader's Coalition Games," HSE Working papers WP BRP 268/EC/2024, National Research University Higher School of Economics.
    • Handle: RePEc:hig:wpaper:268/ec/2024
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    More about this item

    Keywords

    coalitionformation; leaderproblem; Nashstability;
    All these keywords.

    JEL classification:

    • Z - Other Special Topics

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