# Absence-proofness: Group stability beyond the core

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## Abstract

We introduce a new cooperative stability concept, *absence-proofness *(AP). Given a TU game \(\left( {N,v} \right) \), and a solution well defined for all subsocieties, a group of people \(S\subseteq N\) may benefit by partially seceding from cooperation. \(T\subseteq S\) stays out, and collects its stands alone benefits while \(S\backslash T\) receives its allocation specified by the solution at the reduced problem where only \(N\backslash T\) is present. We call a solution manipulable if \(S\) can improve upon its allocation in the original problem by such a maneuver, and solutions that are immune to such manipulations are called absence-proof. We show that population monotonicity (PM) implies AP, and AP implies separability. In minimum cost spanning tree problems, by replacing PM with AP, we propose a family of solutions that are easy to compute and more responsive than the well-known Folk solution to the asymmetries in the cost data, keeping all its fairness properties.

## Keywords

Core Absence-proofness Population monotonicity## Notes

### Acknowledgments

An extended version of this work is completed under the supervision of my PhD thesis advisor, Hervé Moulin. I am immensely indebted to him for all the inspiring discussions. I am grateful to Barış Esmerok, Uğur Özdemir, William Thomson, Vladimir Unkovski-Korica and three anonymous referees for their valuable comments, and also Javier Arín for the argument showing the nucleolus is separable on convex games. The previous version of this work is completed during my PhD studies at Rice University, and this version at National Research University Higher School of Economics. I thank both institutions for supporting my work.

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