The Coke vs. Pepsi Battle

A common approach to simulate how opinions evolve is to use opinion dynamic models. In these models, everyone starts with their own personal preference: maybe they are a die-hard Coke fan, completely neutral, or already loyal to Pepsi. However, these opinions are not fixed; they constantly shift based on the influence of those around us and the commercials we receive. For example, when someone is repeatedly exposed to Pepsi commercials, their preferences naturally start to shift in Pepsi’s favor. Or, if all your close friends are raving about Coke, chances are you will start leaning that way too. The real power of advertising lies in how interconnected people are. Since everyone’s opinion is impacted by their friends, a change in one person’s opinion can ripple through the entire social network. This effect becomes even more powerful when the person targeted is an “influencer” - someone whose opinion strongly affects many others.

Therefore, we want to identify the most influential individuals who are also receptive to our advertisement. Then we focus the Pepsi commercials on these key people. The challenge? We do not have direct knowledge of the social network (who is friends with whom), how well people react to commercials, or even their current opinions. Therefore, we need to come up with strategies to figure out who the best people are to target based only on observable data, like who clicks on our ads. It is assumed that people are more likely to interact with a commercial if it aligns with their opinion closely. With this assumption and the measured clicks, we are uncovering hidden network structures with the help of mathematical approximations and filtering techniques like Kalman Filters. This allows us to determine the influencers to target, getting the highest possible approval for Pepsi while only spending a limited budget on advertising.