Networked Digital Public Goods Games with Heterogeneous Players and Convex Costs

Yukun Cheng, Xiaotie Deng, Yunxuan Ma

Track: Economics, online markets and human computation

Keywords: Public Good Games; Networks; Nash Equilibrium; Social Welfare; Pseudo-Gradient Dynamics; Comparative Statics.

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 across the Internet. However, the inherent non-exclusivity and non-competitiveness of these public goods frequently result in under-provision, a dilemma exacerbated by individuals' tendency to free-ride. This scenario fosters both cooperation and competition among users, leading to the emergence of public goods games.

This paper investigates networked public goods games involving heterogeneous players and convex costs to explore solutions of Nash Equilibrium (NE) for this problem. In these games, each player can choose her own effort level, representing the contributions to public goods.
We employ network structures to depict the interactions among participants.
Each player's utility is composed of a \emph{concave} value component, influenced by collective efforts, and a \emph{convex} cost component, determined solely by individual effort.
To the best of our knowledge, this study is the first to explore a 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. Additionally, we introduce the concept of game equivalence, which expands the range of public goods games that can support a unique NE.
We also delve into \emph{comparative statics}, an essential tool in economics, to evaluate how slight modifications in the model—interpreted as monetary redistribution—impact player utilities. In addition, we analyze a particular scenario with a predefined game structure, illustrating the practical relevance of our theoretical insights.
Consequently, 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.

Submission Number: 501