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Core Stability and Strategy-Proofness in Hedonic Coalition Formation Problems with Friend-Oriented Preferences

Author

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  • Bettina Klaus
  • Flip Klijn
  • Seçkin Özbilen

Abstract

We study hedonic coalition formation problems with friend-oriented preferences; that is, each agent has preferences over his coalitions based on a partition of the set of agents, except himself, into "friends" and "enemies" such that (E) adding an enemy makes him strictly worse off and (F) adding a friend together with a set of enemies makes him strictly better off. Friend-oriented preferences induce a so-called friendship graph where vertices are agents and directed edges point to friends. We show that the partition associated with the strongly connected components (SCC) of the friendship graph is in the strict core. We then prove that the SCC mechanism, which assigns the SCC partition to each hedonic coalition formation problem with friend-oriented preferences, satisfies a strong group incentive compatibility property: group strategy-proofness. Our main result is that on any "rich" subdomain of friend-oriented preferences, the SCC mechanism is the only mechanism that satisfies core stability and strategy-proofness.

Suggested Citation

  • Bettina Klaus & Flip Klijn & Seçkin Özbilen, 2023. "Core Stability and Strategy-Proofness in Hedonic Coalition Formation Problems with Friend-Oriented Preferences," Working Papers 1399, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1399
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    References listed on IDEAS

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    1. Dinko Dimitrov & Peter Borm & Ruud Hendrickx & Shao Sung, 2006. "Simple Priorities and Core Stability in Hedonic Games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(2), pages 421-433, April.
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    More about this item

    Keywords

    hedonic coalition formation; (strict) core stability; (group) strategy-proofness; strongly connected components;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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