2025/12/29 by Jingmin Huang, Huang, Jingmin, Yang Sun +5
Decision Sciences · Economics, Econometrics and Finance · Social Sciences · #Evolutionary Game Theory and Cooperation #FOS: Economics and business #Game Theory and Applications #Game Theory and Voting Systems #Theoretical Economics (econ.TH)
paper · doi:10.48550/arxiv.2512.23193
openalex publication_date 2025/12/29 · openalex created_date 2025/12/31 · openalex updated_date 2026/07/28
This paper investigates the decentralized provision of public goods in directed networks. We establish a correspondence between kernels in graph theory and specialized equilibria in which players either contribute a fixed threshold amount or free-ride entirely. Leveraging this relationship, we derive sufficient conditions for the existence and uniqueness of specialized equilibria in deterministic networks and prove that specialized equilibria exist almost surely in large random networks. We further demonstrate that enhancing network reciprocity weakly expands the set of specialized equilibria without destroying existing ones. Moreover, we propose an iterative elimination algorithm that simplifies the network while preserving equilibrium properties. Finally, we show that a Nash equilibrium is stable only if it is specialized, thereby providing dynamic justification for our focus on this equilibrium class.