Incentive Compatible Influence Maximization in Social Networks and Application to Viral Marketing

Information diffusion and influence maximization are important and extensively studied problems in social networks. Various models and algorithms have been proposed in the literature in the context of the influence maximization problem. A crucial assumption in all these studies is that the influence probabilities are known to the social planner. This assumption is unrealistic since the influence probabilities are usually private information of the individual agents and strategic agents may not reveal them truthfully. Moreover, the influence probabilities could vary significantly with the type of the information flowing in the network and the time at which the information is propagating in the network. In this paper, we use a mechanism design approach to elicit influence probabilities truthfully from the agents. We first work with a simple model, the influencer model, where we assume that each user knows the level of influence she has on her neighbors but this is private information. In the second model, the influencer-influencee model, which is more realistic, we determine influence probabilities by combining the probability values reported by the influencers and influencees. In the context of the first model, we present how VCG (Vickrey-Clarke-Groves) mechanisms could be used for truthfully eliciting the influence probabilities. Our main contribution is to design a scoring rule based mechanism in the context of the influencer-influencee model. In particular, we show the incentive compatibility of the mechanisms when the scoring rules are proper and propose a reverse weighted scoring rule based mechanism as an appropriate mechanism to use. We also discuss briefly the implementation of such a mechanism in viral marketing applications.

💡 Research Summary

The paper tackles a fundamental yet overlooked assumption in the influence‑maximization literature: that the edge‑level influence probabilities are known to the planner. In real social networks these probabilities are private information held by individual users and can be strategically misreported. To obtain truthful reports the authors adopt a mechanism‑design perspective and propose two distinct models.

1. Influencer Model – Only the influencer of each directed edge knows the probability of activating the neighbor. Users are asked to report their outgoing influence vectors. Even if the planner runs an optimal influence‑maximization algorithm on the reported data, agents may benefit by lying, because the chosen seed set directly affects their chance of being selected. The authors show that without monetary incentives the algorithm is not incentive compatible. They then apply a Vickrey‑Clarke‑Groves (VCG) mechanism: the planner still selects the seed set that maximizes expected spread (the efficient allocation) but each agent receives a Clarke payment equal to the externality she imposes on the rest of the system. This payment scheme makes truthful reporting a dominant strategy, guarantees allocative efficiency, and preserves individual rationality.

2. Influencer‑Influencee Model – A more realistic setting where both endpoints of an edge (the influencer and the influencee) possess information about the activation probability. Each side reports its own estimate, and the planner aggregates the two reports into a single probability. To incentivize truthful reporting the authors employ proper scoring rules, which reward agents based on the accuracy of their reported probability distribution relative to the true (but unknown) distribution. They introduce a novel “reverse weighted scoring rule” derived from the classic weighted rule. This rule penalizes under‑estimation more heavily than over‑estimation, thereby discouraging agents from inflating their influence to be selected while still rewarding accurate reports.

The paper proves that under the reverse weighted scoring rule the reporting game has a Nash equilibrium in which every agent reports her true influence probability. Moreover, the mechanism satisfies:

• Efficiency – the seed set chosen maximizes expected spread given the truthful probabilities;
• Individual Rationality – each participant’s expected utility (spread contribution plus payment) is non‑negative;
• Incentive Compatibility – truthful reporting maximizes each agent’s expected payoff.

The authors also discuss practical implementation for viral marketing campaigns. A platform could collect influence estimates via in‑app surveys or API calls, compute payments (e.g., coupons, loyalty points) according to the scoring rule, and then run any standard influence‑maximization algorithm (greedy, CELF, etc.) on the aggregated probabilities. The mechanism thus bridges the gap between theoretical diffusion models and the noisy, strategic data encountered in real‑world marketing.

Key contributions are:

1. Formalizing influence maximization under incomplete information as a game‑theoretic problem;
2. Demonstrating the inadequacy of naïve reporting and providing a VCG‑based solution for the single‑reporter (influencer) case;
3. Designing a scoring‑rule‑based payment scheme for the dual‑reporter (influencer‑influencee) case, including the novel reverse weighted scoring rule;
4. Proving incentive compatibility, efficiency, and individual rationality of both mechanisms;
5. Outlining a feasible deployment pathway for viral marketing platforms.

Overall, the work extends the influence‑maximization framework to realistic settings where agents act strategically, offering concrete mechanisms that can be integrated into existing social‑media marketing pipelines to obtain more reliable diffusion parameters and achieve higher campaign ROI.