Examine the following game tree. Fred and Sally are planning on running competing restaurants. Each must decide whether to rent space or buy space. Fred goes first at decision node F. Sally goes second at either decision node S1 or decision node S2 (depending on what Fred chose to do at decision node F). Note that the payoff to Sally at terminal node A is X. a. If X < 12, what terminal node will the subgame perfect Nash equilibrium path lead to? b. If X > 12, what terminal node will the subgame perfect Nash Equilibrium path lead to? c. Suppose that X = 11 and that it is now possible for Fred to make a side payment of value V to Sally that will boost her payout at terminal node A from X = 11 to X = 11 + V. What is the minimum amount that V can be such that the subgame perfect Nash equilibrium path will lead to terminal node A? Assume that V can take on only discrete units (0, 1, 2, 3,…).
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