Recently I've dived into game theory by attending a course. I've always been haunted by a dilemma while serving food to my guests at my apartment and now I'd like to introduce this problem in the formal terms of game theory - just for fun :D
Let's have a grill party G(N, f), where N is the set of hungry participants (|N| is the number of them), and f is the amount of food available that is divided among p1, p2, ... p|N| plates. Let h ∈ N be the host of the party, g1, g2, ..., g|N|-1 ∈ N the guests. h serves the food for all the participants including h, as well as divides the f amount among the plates while, being a kind host, lets the guests to choose which plate they want to take. In the end h takes the last one left. Actions of the players' are as follows (a1, a2, ..., an ∈ Ax denotes the set of actions player x is able to take):
