An old lady is looking for help crossing the street. Only one person

is needed to help her; more are okay but no better than one. Dave and Sue are the two people in the vicinity who can help her; they have to choose whether to do so. Each of them will get a pleasure worth 3 from her success (no matter who helps her). But each one who goes to help will bear a cost of 1, this being the value of their time taken up helping. If neither player helps, the payoff for each player is zero.

a. If this game is asimultaneous-movegame

1. Write the payoff table.
2. Find the Nash equilibrium and all pure-strategy Nash equilibria of this game.
3. Give an interpretation of this game at optimal strategy.

15

15

1. If this game is now played as asequential-movegame and Sue moves first
2. Write the game tree with respective payoffs.
3. Find all pure-strategy for each player.
4. Use rollback equilibrium to determine the pure-strategy Nash equilibria of this game.
5. What are the optimal strategies for this game for each player?
6. Give an interpretation of this game at optimal strategy.
7. Compare this game as a simultaneous-move game (a) or sequential-move game (b). Which game provides more information? Explain and justify your argument.