Networked Digital Public Goods Games with Heterogeneous Players and Convex Costs

2025-02-03

AI Summary

This paper investigates the strategic provision of digital public goods (e.g., open-source software) by heterogeneous agents on complex networks, introducing—for the first time—convex cost structures into networked public goods games. To capture the coupling between individual effort choices and nonlinear costs, we formulate a nonlinear game model and analyze it using pseudo-gradient dynamics, convex optimization, and comparative statics. We rigorously establish the universal existence of Nash equilibria and derive precise graph-theoretic and cost-parameter conditions for uniqueness. Our analysis uncovers the synergistic interplay between network topology and cost convexity in shaping contribution incentives. Furthermore, we quantitatively assess how policy interventions—such as funding reallocation—affect individual utilities and aggregate social welfare. The results provide a testable theoretical framework and principled foundations for mechanism design in internet-based common-pool resource governance.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Non-convex Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

In the digital age, resources such as open-source software and publicly accessible databases form a crucial category of digital public goods, providing extensive benefits for Internet. This paper investigates networked public goods games involving heterogeneous players and convex costs, focusing on the characterization of Nash Equilibrium (NE). In these games, each player can choose her effort level, representing her contributions to public goods. Network structures are employed to model the interactions among participants. Each player's utility consists of a concave value component, influenced by the collective efforts of all players, and a convex cost component, determined solely by the individual's own effort. To the best of our knowledge, this study is the first to explore the networked public goods game with convex costs. Our research begins by examining welfare solutions aimed at maximizing social welfare and ensuring the convergence of pseudo-gradient ascent dynamics. We establish the presence of NE in this model and provide an in-depth analysis of the conditions under which NE is unique. We also delve into comparative statics, an essential tool in economics, to evaluate how slight modifications in the model--interpreted as monetary redistribution--affect player utilities. In addition, we analyze a particular scenario with a predefined game structure, illustrating the practical relevance of our theoretical insights. Overall, our research enhances the broader understanding of strategic interactions and structural dynamics in networked public goods games, with significant implications for policy design in internet economic and social networks.

Problem

• Nash Equilibrium
• Network Public Goods Game
• Resource Cost

Innovation

• Game Theory Model
• Network Public Goods
• Nash Equilibrium