Popularity and Strict Popularity in Altruistic Hedonic Games and Minimum-Based Altruistic Hedonic Games

We consider average-based and min-based altruistic hedonic games and study the problem of verifying popular and strictly popular coalition structures. While strict popularity verification has been shown to be coNP-complete in min-based altruistic hedonic games, this problem has been open for equal-treatment and altruistictreatment average-based altruistic hedonic games. We solve these two open cases of strict popularity verification and then provide the first complexity results for popularity verification in (both averageand min-based) altruistic hedonic games, where we cover all three degrees of altruism.