In a simple game (see Section 2.15), every subset of players is identified as either winning or losing.

1. If there is no restriction on this identification, how many distinct simple games are there with 3 players?

There are \(2^3 = 8\) subsets. Since there are two choices for each of the subsets, there are \(2^{2^3} = 256\) distinct simple games.

2. With \(n\) players?

There are \(2^{2^n}\) distinct games.