Limit distributions of generalized St. Petersburg games

The St. Petersburg game is known as a probability model with infinite expectation, and has some extensions. Gut and Martin-Löf (2013) studied convergence in distribution along a suitable specific subsequence under their generalization. In this article, we extend their results using residue analysis investigated by Vardi (1995). We give the explicit limit distributions via characteristic functions with gamma functions which become semi-stable or strictly semi-stable.