Equilibrium payoffs
a) The reward system changes payoffs for Player A, but does not change the equilibrium strategies in the game. Player A still takes the money at the first opportunity and payoffs are (10, 0).
(b) Round 2 of this game leads to the familiar “take immediately” equilibrium. Given that outcome, there are no credible promises or deals that could be made in round 1, so that round stands on its own. Some of the payoffs in round 1 differ from those in the standard version of the game (e.g., once the pile has seven dimes and A takes the pile, the payoffs are (50, 0) instead of (70, 0)), but the equilibrium is the same. A takes the pile on her first move; payoffs are (10, 0).
(c) As in part b, the second round equilibrium is “take immediately” and the first round stands alone al-though some of the payoffs differ from the standard version of the game. None of the changes affects the equilibrium outcome. Player A takes the pile immediately and the payoffs are (10, 0).