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

Sayantika Mandal; Harman Agrawal; Swaprava Nath

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arXiv · 2510.11253

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

Sayantika Mandal·Harman Agrawal·Swaprava Nath

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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.

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Sayantika Mandal, Harman Agrawal, Swaprava Nath. 2025-10-13. Likes, Budgets, and Equilibria: Designing Contests for Socially Optimal Advertising. https://arxiv.org/abs/2510.11253

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