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. However, these public goods' inherent non-exclusivity and non-competitiveness 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 public goods games. 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.

On typical e-commerce platforms, a product can be displayed to users in two possible forms, as an ad item or an organic item. Usually, ad and organic items are separately selected by the advertising system and recommendation system, and then combined by a content merging mechanism. Although the design of the content merging mechanism has been extensively studied, little attention has been given to a crucial situation where there is an overlap between candidate ad and organic items. Despite its common occurrence, this situation is not correctly handled by almost all existing works, potentially leading to incentive problems for advertisers and the violation of economic constraints. To address these issues, we revisit the design of the content merging mechanism. We introduce a necessary property called form stability, and provide simplification results of the mechanism design problem. Furthermore, we design two simple mechanisms strictly ensuring desired economic properties including incentive compatibility, and demonstrate their guaranteed performance through competitive ratio analysis under certain conditions.

Recently, remarkable progress has been made by approximating Nash equilibrium (NE), correlated equilibrium (CE), and coarse correlated equilibrium (CCE) through function approximation that trains a neural network to predict equilibria from game representations. Furthermore, equivariant architectures are widely adopted in designing such equilibrium approximators in normal-form games. In this paper, we theoretically characterize the benefits and limitations of equivariant equilibrium approximators. For the benefits, we show that they enjoy better generalizability than general ones and can achieve better approximations when the payoff distribution is permutation-invariant. For the limitations, we discuss their drawbacks in terms of equilibrium selection and social welfare. Together, our results help to understand the role of equivariance in equilibrium approximators.

Learning-based ad auctions have increasingly been adopted in online advertising. However, existing approaches neglect externalities, such as the interaction between ads and organic items. In this paper, we propose a general framework, namely Score-Weighted VCG, for designing learning-based ad auctions that account for externalities. The framework decomposes the optimal auction design into two parts: designing a monotone score function and an allocation algorithm, which facilitates data-driven implementation. Theoretical results demonstrate that this framework produces the optimal incentive-compatible and individually rational ad auction under various externality-aware CTR models while being data-efficient and robust. Moreover, we present an approach to implement the proposed framework with a matching-based allocation algorithm. Experiment results on both real-world and synthetic data illustrate the effectiveness of the proposed approach.