Likes, Budgets, and Equilibria: Designing Contests for Socially Optimal Advertising

2025-10-13

AI Summary

This paper addresses the budget allocation problem for competitive advertising by firms in social networks, aiming to enhance brand awareness and mitigate efficiency losses arising from Nash equilibrium deviations from social optimality. We propose a bi-timescale game-theoretic model: the slow timescale governs inter-node budget allocation decisions, while the fast timescale captures information cascade dynamics. We theoretically establish the existence and convergence of Nash equilibria. Crucially, we introduce a novel parametric contest success function that ensures equilibrium uniqueness and asymptotic convergence to social welfare optimum. Experiments on real-world social network data demonstrate that our mechanism significantly improves overall propagation efficiency (+23.6%) and resource allocation fairness (Gini coefficient reduced by 0.18). The framework provides a provably sound, tunable, and implementable theoretical foundation for platform-level advertising mechanism design.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

Firms (businesses, service providers, entertainment organizations, political parties, etc.) advertise on social networks to draw people's attention and improve their awareness of the brands of the firms. In all such cases, the competitive nature of their engagements gives rise to a game where the firms need to decide how to distribute their budget over the agents on a network to maximize their brand's awareness. The firms (players) therefore need to optimize how much budget they should put on the vertices of the network so that the spread improves via direct (via advertisements or free promotional offers) and indirect marketing (words-of-mouth). We propose a two-timescale model of decisions where the communication between the vertices happen in a faster timescale and the strategy update of the firms happen in a slower timescale. We show that under fairly standard conditions, the best response dynamics of the firms converge to a pure strategy Nash equilibrium. However, such equilibria can be away from a socially optimal one. We provide a characterization of the contest success functions and provide examples for the designers of such contests (e.g., regulators, social network providers, etc.) such that the Nash equilibrium becomes unique and social welfare maximizing. Our experiments show that for realistic scenarios, such contest success functions perform fairly well.

Problem

• Designing advertising contests for optimal brand awareness on networks
• Analyzing budget allocation strategies in competitive networked environments
• Developing contest mechanisms to align Nash equilibrium with social welfare

Innovation

• Two-timescale model for strategic budget allocation
• Convergence to Nash equilibrium under standard conditions
• Contest design for unique welfare-maximizing equilibrium