Stable Partitions in Networks Under Symmetric Neighborhood-Composition Costs
- 1School of Mathematics and Statistics, Qingdao University, Qingdao 266071, China
- 2School of Business, Qingdao University, Qingdao 266071, China
Abstract
We study changes in group membership on a fixed network. Link costs are symmetric, with the larger of the two neighborhood adjustments applied to both players. A stable partition is reachable through a finite sequence of best responses and allows no player to lower their cost by moving to another group. On a star with at least two group labels, the stable structure depends on a single threshold. Above it, all players belong to one group. Below it, the center is alone and all peripheral players belong to another group. At the threshold, both forms allow no profitable move, and we identify the initial partitions from which each is reachable. On a complete network with two group labels, explicit thresholds determine the stable difference between group sizes. At threshold values, this difference also depends on the initial partition. Compared with the asymmetric model, our rule permits stable separation on a star and larger differences in group sizes on a complete network under the same conditions.
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BibTeX
@article{sun2026stable,
title = {{Stable Partitions in Networks Under Symmetric Neighborhood-Composition Costs}},
author = {Ping Sun and Haoyue Lin and Yeming Dai},
journal = {Mathematics},
year = {2026},
month = nov,
doi = {10.3390/math14214007},
url = {https://www.mdpi.com/2227-7390/14/21/4007},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Stable Partitions in Networks Under Symmetric Neighborhood-Composition Costs
AU - Ping Sun
AU - Haoyue Lin
AU - Yeming Dai
PY - 2026
DA - 2026/11/03
JO - Mathematics
DO - 10.3390/math14214007
UR - https://www.mdpi.com/2227-7390/14/21/4007
AB - We study changes in group membership on a fixed network. Link costs are symmetric, with the larger of the two neighborhood adjustments applied to both players. A stable partition is reachable through a finite sequence of best responses and allows no player to lower their cost by moving to another group. On a star with at least two group labels, the stable structure depends on a single threshold. Above it, all players belong to one group. Below it, the center is alone and all peripheral players belong to another group. At the threshold, both forms allow no profitable move, and we identify the initial partitions from which each is reachable. On a complete network with two group labels, explicit thresholds determine the stable difference between group sizes. At threshold values, this difference also depends on the initial partition. Compared with the asymmetric model, our rule permits stable separation on a star and larger differences in group sizes on a complete network under the same conditions.
SN - 2227-7390
ER -