Abstract
The stand alone core conditions have played a key role in the fair allocation literature for decades and has been successfully applied in many types of models where agents share a common cost or revenue. Yet, the stand-alone core conditions are not indispensable when looking for fair ways to share. The present note provides a few examples of network models where the relevance of the stand-alone core is questionable and fairness seems to require a different approach. In a networked future, design of allocation mechanisms is therefore likely to move beyond the stand alone core.
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Notes
- 1.
In case of surplus sharing the stand-alone conditions become lower bounds: no coalition of agents should get less surplus than what they could obtain standing alone.
- 2.
See e.g., Peleg and Sudhölter (2007) for various properties of cooperative games as well as solution concepts.
- 3.
An allocation rule \(\phi \) satisfies cost additivity if, for any two cost vectors c and \(c'\), that \(\phi (c+c') = \phi (c) + \phi (c').\)
- 4.
Several algorithms exists for finding a max-flow in a given graph with given capacity constraints, see e.g., Kozen (1992).
- 5.
In the related context of network formation games, Jackson (2005) points at similar types of problems because a cooperative game cannot account for the fact that the same group of agents may connect in different network configurations, and these may have different value for the group.
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Constructive comments from Justin Leroux and Christian Trudeau are gratefully acknowledged.
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Hougaard, J.L. (2019). Beyond the Stand-Alone Core Conditions. In: Laslier, JF., Moulin, H., Sanver, M., Zwicker, W. (eds) The Future of Economic Design. Studies in Economic Design. Springer, Cham. https://doi.org/10.1007/978-3-030-18050-8_39
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