Who Pays for a Connected Public Good?
Abstract
Connectivity can turn separate contributions into a public good that benefits participants and nonparticipants alike. Yet only participants pay for it, and each can avoid her charge by withdrawing while enjoying whatever public output survives. How do network connections constrain who can or must pay, and how large a cost can the group bear? We study a participation game in which public output equals the size of the largest connected group of active players, whose members divide a fixed operating cost. The output a participant destroys by withdrawing is her withdrawal responsibility and bounds her payment. These bounds determine the group's cost-bearing capacity and, whenever the group can be kept active, which participants must pay. We prove that among connected networks with at least five players, the path uniquely maximizes the cost-bearing capacity of a group, yet minimizes the expected surviving output after a uniformly selected participant withdraws. As the group grows, the ratio of maximal capacity to gross social benefit under full participation converges to one quarter. Fragility can therefore strengthen voluntary finance, but even the most financeable network cannot close the gap between the value it creates and what its participants will pay to sustain it.
Related
- The Last Iterate of the Projected Stochastic Subgradient Method Pays a Logarithm, Even in Dimension One
- Who pays for urban environment management? The role of the third-party service provider
- Persistence Pays: Square-root condition-number dependence for Metropolis-adjusted kinetic Langevin Monte Carlo with a non-reversibly updated accept/reject uniform
- Spread and Scale: What Determines Whether Test-Time Budget Allocation Pays
- Explicit and asymptotically good constructions of Algebraic Geometry codes in the sum-rank metric
BibTeX
@misc{angulo2026pays,
title = {{Who Pays for a Connected Public Good?}},
author = {Marco Tulio Angulo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10565},
eprint = {2609.10565},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10565},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Who Pays for a Connected Public Good?
AU - Marco Tulio Angulo
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.10565
UR - https://arxiv.org/abs/2609.10565
AB - Connectivity can turn separate contributions into a public good that benefits participants and nonparticipants alike. Yet only participants pay for it, and each can avoid her charge by withdrawing while enjoying whatever public output survives. How do network connections constrain who can or must pay, and how large a cost can the group bear? We study a participation game in which public output equals the size of the largest connected group of active players, whose members divide a fixed operating cost. The output a participant destroys by withdrawing is her withdrawal responsibility and bounds her payment. These bounds determine the group's cost-bearing capacity and, whenever the group can be kept active, which participants must pay. We prove that among connected networks with at least five players, the path uniquely maximizes the cost-bearing capacity of a group, yet minimizes the expected surviving output after a uniformly selected participant withdraws. As the group grows, the ratio of maximal capacity to gross social benefit under full participation converges to one quarter. Fragility can therefore strengthen voluntary finance, but even the most financeable network cannot close the gap between the value it creates and what its participants will pay to sustain it.
ER -