ICI: An Invitation-Aware Diffusion Model for Private Social Networks

Background

In the contemporary digital era, where social networks are integral to daily human interaction, the dynamics of information dissemination within these networks represent a critical area of inquiry. The concept of Invitation-Aware Diffusion (IAD) delineates the process wherein information is transmitted from one entity to another via an explicit invitation mechanism, encompassing the nuanced behaviors of user invitations and acceptances. This phenomenon is ubiquitously observed across a myriad of social platforms in the real world, including but not limited to WeChat, LinkedIn, and various online gaming environments. Distinct from passive engagements such as liking or commenting on content from unfamiliar sources, invitation actions predominantly transpire among interconnected individuals within private social networks, leveraging pre-established social bonds for propagation.

An illustrative case is seen in Tencent's gaming platforms, which frequently orchestrate events aimed at reinforcing bonds among acquaintances by incentivizing users to invite peers to participate in gaming activities. Accepting these invitations enables individuals to further extend invitations, engendering a cascading chain of engagement. Furthermore, a comprehensive understanding of IAD's underlying mechanisms significantly contributes to the advancement of several ancillary applications, including but not limited to, influence maximization, rumor detection, diffusion prediction, and influencer pricing.

Related Work and Challenges

Current research on Invitation-Aware Diffusion (IAD) primarily focuses on exploring its macroscopic attributes, such as the size and depth of the diffusion tree originating from selected users, and the role of homophily in IAD. However, these studies have not succeeded in developing a diffusion model that accounts for invitation behaviors.

Moreover, despite the plethora of diffusion models proposed over recent decades, adapting them to the invitation mechanism poses significant challenges. A primary obstacle is the ambiguity surrounding the social influence process within IAD, that is, how individuals are notified or activated by others. To address this, the social influence processes in existing models are mostly derived from two conventional frameworks: the Independent Cascade (IC) and the Linear Threshold (LT) models. The former assumes that each individual is independently influenced by their active friends, while the latter suggests that a user is influenced only when a sufficient number of friends are activated.

This raises a crucial question: does the social influence process in IAD align with the IC model, the LT model, or neither? Furthermore, the transition of invitation and acceptance behaviors adds complexity to the IAD's diffusion process, making it challenging for existing models to capture accurately.

Figure 1: User Behavior Conversion Funnel, depicted from top to bottom, represents the stages of Awareness, Interest, Adoption, and Action.

Main Contributions and Innovations

In this work, we introduce for the first time a diffusion model that accounts for invitation behaviors: the Independent Cascade with Invitation (ICI). ICI adapts the influence process of the traditional Independent Cascade (IC) model to depict the invitation behavior among friends. It also incorporates the multi-level user behavior transformation inherent in the invitation mechanism, such as users becoming new inviters after accepting an invitation (as illustrated in Figure 1). Moreover, we validate our design through empirical studies on IAD within gaming contexts. Notably, our proposed ICI algorithm can also be applied to other propagation scenarios that involve conversion funnels.

In terms of application, we integrate ICI into four key tasks: cascade estimation, diffusion prediction, acquaintance recommendation, and influence maximization. For each application, we provide detailed analysis regarding accuracy and computational complexity, underscoring the adaptability of ICI across a range of scenarios. In offline experiments, our solution demonstrated the ability to outperform the best competitors by up to 5 times in cascade estimation and to improve diffusion prediction by 40.3%.

We deployed ICI and its applications within Tencent's online gaming environment for friend ranking and key opinion leader (KOL) selection scenarios, achieving improvements of up to 20.3% and 170%, respectively.

Model Overview

At the core of the Independent Cascade with Invitation (ICI) model lies the simulation and understanding of invitation behaviors through social connections and their impact on information dissemination. This model accomplishes its objectives by incorporating several key technical concepts and steps:

1. User Role Categorization: The ICI model identifies three user roles: Inviter, Invitee, and Acceptor. This classification reflects the complexity of invitation behaviors within social networks, where each user can play different roles at various times.

2. Independent Invitation Process: The model assumes that each Inviter has the opportunity to independently invite their friends to become new Invitees. This process is probabilistic, meaning the success of an Inviter inviting a friend depends on a predefined invitation probability.

3. Multi-Stage Behavior Transition: Beyond just the occurrence of an invitation, the ICI model further simulates the probability of users transitioning from Invitee to Acceptor, and from Acceptor to a new Inviter. These transition processes are controlled by specific probability parameters, reflecting the various actions a user might take upon accepting an invitation.

Figure 2 illustrates a simulation instance of the ICI model. The process persists until no new Inviters are generated, at which point the instance concludes.

Figure 2: Illustration of the ICI Model Simulation (Unaware Users: Light Grey; Invitees: Yellow; Acceptors: Orange; Inviters: Yellow).

Application Scenario: Friend Ranking

These activities are all-encompassing, offering each player a personalized list of friends of a limited length. Players can earn rewards by clicking on friends in the list and inviting them to convert. Rewards can be items that promote activity, such as team score bonus cards, event tokens, or commercial resources like cash envelopes from purchases/lotteries, discount coupons, etc. In the absence of algorithmic intervention, lists are typically generated based on the intimacy between friends. While this method may aid click-through rates, it overlooks the propagative effect of the activity, i.e., a user clicking on another user during the activity leads to the latter's conversion, thereby influencing and driving more users to convert within the activity.

To incorporate the propagative influence of player friends into this scenario, we calculate the influence spread of each player's friend based on the ICI model and recommend a group of friends with the highest individual ICI influence as a heuristic indicator to the player. Specifically, the influence spread of each user represents the number of users that he/she can, directly and indirectly, influence to become acceptors under the ICI model.

We applied the proposed algorithm to a social lottery activity in a popular Tencent RPG game during August and September 2022. As shown in Tables 1 and 2, in terms of invitation rate, the ICI model achieved a 20.3% increase in August and a 10.8% increase in September compared to the intimacy strategy. These figures indicate that the ICI model performs better in enhancing the willingness of users to send invitations, meaning it more effectively identifies target individuals that users are likely to be interested in and willing to share. In terms of the pay rate, the ICI model outperformed the intimacy strategy by 31.6% in August and 3.7% in September. The improvement in pay rate suggests that the target users recommended by the ICI model have the potential to drive deeper conversions, reflecting the potential of the ICI model to increase platform revenue.

Application Scenario: KOL Selection

This type of activity involves the platform pre-selecting a batch of seed users to easily obtain activity rewards, such as scorecards, skins, or increased chances of winning prizes. Other players can unlock rewards by teaming up with qualified players and can also continue to "infect" their friends with eligibility. The rule of the activity is that the more friends you team up with, the more rewards you get. Compared to traditional activities (directly giving all players activity eligibility without transmission logic), seed propagation not only allows for more precise control of resource allocation but also stimulates spontaneous competition among players and community discussions due to the scarcity of activity eligibility, combined with effective exposure from KOLs, significantly improving activity engagement.

In such propagation activities, selecting high-quality seeds from the social network to maximize the spread range becomes crucial for the success of the activity. To address this, we utilize the proposed ICI model to solve the Influence Maximization (IM) problem in social networks. The Influence Maximization problem is defined as:

Given a social network, the budget number of seed users, and a diffusion model, find a seed set within the budget to maximize the overall influence starting from the seed set under this model.

Since such problems are NP-Hard, we adopt a classical greedy algorithm here to obtain the seed set. We applied the proposed algorithm and the baseline algorithm selected based on degree centrality to a seed propagation activity in a popular Tencent FPS game, selecting 5000 seed players for each. The experimental results show that seed users selected using the ICI model achieved significant effects in information dissemination and activity participation compared to those selected using the baseline algorithm. Specifically, compared to the seed set selected by the baseline algorithm, the seed users selected using the ICI model increased the spread increment by 170% and achieved a 37.5% increase in the user invitation rate. This result indicates that the ICI model can effectively identify users with higher social influence and propagation potential, thereby maximizing the influence of social network marketing activities.

Summary

The Independent Cascade Invitation (ICI) model jointly developed by Tencent IEG CDP Platform and PyroWis AI has demonstrated its outstanding ability in predicting and optimizing information dissemination. The model has been applied in multiple Tencent games, significantly enhancing the performance of friend ranking and KOL selection systems. Looking ahead, we will continue to focus on further deepening the model's learning and parameter optimization to better meet users' personalized needs. At the same time, we also look forward to exploring the application potential of the ICI model in a wider range of social network scenarios, to promote continuous innovation and development in social network information dissemination strategies.

Reference

Shiqi Zhang, Jiachen Sun, Wenqing Lin, Xiaokui Xiao, Yiqian Huang, and Bo Tang. 2024. Information Diffusion Meets Invitation Mechanism. In Proceedings of the ACM Web Conference 2024 (WWW ’24). https://doi.org/10.1145/3589335.3648337.

See the Chinese version of this blog from Tencent's official account: https://mp.weixin.qq.com/s/MxmyNQLPjtT7rnNG36m1Tg.

See the source code in: https://github.com/jeremyzhangsq/ICI.