Approximate Relational Games For Green Influencer Marketing Optimization

The collaboration between celebrities, macro-influencers, and micro-influencers plays a pivotal role in amplifying the effectiveness and longevity of environmental sustainability messages. This study introduces the concept of a minimal coalition of influencers capable of efficiently promoting a sustainability message to the public. To address this, we propose a novel framework for Approximate Relational Games (ARG), which quantifies the degree of dependency of a follower on an influencer through a Dependency Decision Table (DDT). The DDT tracks follower reactions, categorized as “Like only” or “Like and Share”, across a series of posts by the influencer. By setting a threshold for the degree of dependency, we focus on followers with stronger relational dependencies, eliminating those with weaker associations. This method enables the identification of a minimal winning coalition of influencers who can effectively disseminate the sustainability message despite resource constraints, both financial and non-financial. Utilizing combinatorial tools such as closure operators and choice functions, we present a method for determining minimal winning coalitions with polynomial time complexity. This approach offers a cost-effective solution for green organizations and governments aiming to maximize the impact of their campaigns. To validate the proposed model and algorithms, we conduct Python-based simulations using data from five real-world Facebook influencers, both macro and micro-tier, complemented by manual calculations. The results demonstrate the efficacy and computational efficiency of the proposed framework in optimizing influencer marketing strategies for promoting environmental sustainability.