Abstract
We consider average- 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- and altruistic-treatment 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 (average- and min-based) altruistic hedonic games, where we cover all three degrees of altruism.
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