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Existence of the weak and strong core in a sharing model with arbitrary graph structures

Author

Listed:
  • Jay Sethuraman

    (Columbia University)

  • Sonal Yadav

    (University of Liverpool Management School)

Abstract

We consider a model where agents are nodes on a graph and two agents are potential partners if they are connected by an edge in the graph. Agents have to be matched in pairs, and each pair must complete a task that requires one unit of effort. Each agent has symmetric preferences around an ideal effort level. An allocation consists of pairs of agents and a sharing arrangement of the effort for each pair. We associate three natural optimization problems—integer matching, fractional matching, and fractional covering—with any given instance of our problem. We show that a strong core allocation exists if and only if the optimal values of the associated integer matching, fractional matching, and fractional covering problems coincide. A weak core allocation is shown to exist if the optimal values of the integer and fractional matching problems coincide, and always exists for bipartite and complete graphs.

Suggested Citation

  • Jay Sethuraman & Sonal Yadav, 2025. "Existence of the weak and strong core in a sharing model with arbitrary graph structures," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 80(3), pages 659-683, November.
    • Handle: RePEc:spr:joecth:v:80:y:2025:i:3:d:10.1007_s00199-025-01636-6
    DOI: 10.1007/s00199-025-01636-6
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    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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