  Consider a very simple class of (finite) games: after an initial move by
nature, each player makes one move. Moreover, the players have common
interests: at each node, all the players get the same payoff. We show that the
problem of determining whether there exists a joint strategy where each player
has an expected payoff of at least r is NP-complete as a function of the number
of nodes in the extensive-form representation of the game.
