I have this type of problem: two boys have to divide 10 playstation games. The strategy is that first one choose a game, then the second another and so on, by having a common goal to be both "the most happy they can". Obviously the two boys have different tastes about the games, so for each game they could have different utility. I want to ask if a problem like that could be solved with Game Theory, and if yes which part of Game Theory I have to look at. Since it is very long theory, and less time ahahah.
Thanks to all, have a nice week :)