Samaritan versus rotten kid: Another look

We set up a two-stage game with sequential moves by one altruist and n selfish agents. The Samaritan’s dilemma (rotten kid theorem) states that the altruist can only reach her first best when the selfish agents move after (before) the altruist. We find that in general, the altruist can reach her first best when she moves first if and only if a selfish agent’s action marginally affects only his own payoff. The altruist can reach her first best when she moves last if and only if a selfish agent cannot manipulate the price of his own payoff.