Extensions to Tiered Coalition Formation Games

In 2017, Siler introduced Tiered Coalition Formation Games (TCFGs), inspired by the tiered organization of Pokémon characters on a fan-based website, Smogon. Siler showed that, for a natural notion of agent preferences, the Nash table tier lists were precisely the core stable tier lists, and provided a polynomial-time algorithm to find a Nash stable tier list. However, the tiers in that list had size one, which eliminated the intra-tier competitions that make tier lists meaningful. We extend Siler’s definition to allow for win probabilities, examine k-tier TCFGs, and provide a heuristic algorithm for finding good k-tier partitions that allow intra-tier competition.