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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 sequentially 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. Assume Dave makes the first move then followed by Sue.
a) Draw the game tree for this game with the respective payoffs indicated.
b) List down all the pure strategies for each player.
c) Find the Nash equilibrium and the optimal strategy for each player
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