The Panini collector’s problem: Optimal strategy and trading analysis

The choice of the Panini stickers for the main topic of my thesis comes from an interest to investigate a popular event repeating every four year. At the beginning of each FIFA World Cup, a large number of passionate collectors rush the nearest bookstore to buy a Panini Album and some packets of stickers, starting a long-lasting process of collection. The completion of this collection is obviously biased towards generating profit for Panini. For collector, the obtaining of new stickers is comparable to a lottery and duplicates soon start to pile up for them. Fortunately, collectors are free to exchange duplicates with each other in order to obtain those coveted missing stickers. This leads collectors to organise themselves in groups or on online platforms to reduce the cost of a collection. Regarding this repeating development, my goal was to provide a comprehensive set of metrics on what a collector should expect to spend to complete the 2018 World Cup Panini collection. Interest was also given to strategies that a collector could apply to reduce his expected cost, or limit the risk around it. Additionally, I investigated how could Panini generate more benefits by adjusting the characteristics of its collection, and I inspected the profitability of a “sticker-swapping” platform (a platform where collectors can trade stickers). In the literature, the completion of an album of stickers is called the “Coupon Collector’s Problem”. The literature is the first step of my work and I review the formulas that can be used in the analysis of the Panini collection. However, the results from the literature are insufficient to perform a proper analysis. This leads me to base my research on a numerical method, through Monte Carlo algorithms. By repeating multiple times the opening of a packet containing 5 random stickers, I was able to fully replicate the behaviour of collectors completing the 2018 World Cup Panini album. Among the results found during this research, it can be outlined that the cooperation between collectors, through trades and swaps of stickers, drastically reduces their expected cost to complete the collection. This expected cost can be reduced further by taking advantage of the fact that Panini allows collectors to order a number of specific stickers from their website, which is especially convenient to obtain the last missing stickers. It was also found that Panini could increase its profit by slightly altering the pricing model of stickers. Finally, I explored an alternative to the usual way swaps between collectors are modelled in the literature and proposed to consider relations between collectors in the form of networks. The network approach show important differences from the classical assumption, which leads to think that the popular modelling of swaps in the literature strongly underestimate the variance of the collectors’ costs.