Implementation of welfare maximizing networks

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Abstract

We consider network formation, where some locations can be connected. 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 implement solutions such as the Shapley value unless we settle for partial implementation.

Metadata

Item Type:	Article
Authors/Creators:	Hougaard, J.L. Tvede, M. https://orcid.org/0000-0003-0566-7026
Copyright, Publisher and Additional Information:	© 2025 The Author(s). Open Access: This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Keywords:	Networks; Welfare maximization; Nash Implementation; Strong Nash Implementation
Dates:	Accepted: 23 May 2025 Published (online): 16 June 2025 Published: 16 June 2025
Institution:	The University of Sheffield
Academic Units:	The University of Sheffield > Faculty of Social Sciences (Sheffield) > Department of Economics (Sheffield)
Depositing User:	Symplectic Sheffield
Date Deposited:	06 Jun 2025 09:49
Last Modified:	23 Jun 2025 08:44
Status:	Published online
Publisher:	Springer
Refereed:	Yes
Identification Number:	10.1007/s00355-025-01611-z
Open Archives Initiative ID (OAI ID):	oai:eprints.whiterose.ac.uk:227284

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Implementation of welfare maximizing networks. (deposited 09 May 2025 08:22)
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