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Implementation of Welfare Maximizing Networks

Author

Listed:
  • Jens Leth Hougaard

    (University of Copenhagen, DK-1958 Frederiksberg C, Denmark)

  • Mich Tvede

    (School of Economics, University of Sheffield, Sheffield S1 4DT, UK)

Abstract

We consider network formation. A set of locations can be connected in various network configurations. Every network has a cost and every agent has an individual value of every network. A planner aims at implementing a welfare maximizing network and allocating the resulting cost, but information is asymmetric: agents are fully informed and the planner is ignorant. Full implementation in Nash and strong Nash equilibria is studied. We show the correspondence consisting of welfare maximizing networks and individually rational cost allocations is implementable. We construct a minimal Nash implementable, welfare maximizing, and individually rational solution in the set of upper hemi-continuous and Nash implementable solutions. It is not possible to have full implementation single valued solutions such as the Shapley value.

Suggested Citation

  • Jens Leth Hougaard & Mich Tvede, 2025. "Implementation of Welfare Maximizing Networks," Working Papers 2025005, The University of Sheffield, Department of Economics.
    • Handle: RePEc:shf:wpaper:2025005
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    File URL: https://www.sheffield.ac.uk/economics/research/serps
    File Function: First version, May 2025
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    More about this item

    Keywords

    Networks; Welfare maximization; Nash Implementation; Strong Nash Implementation;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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