5. Consider an innite bargaining game with alternating offers. There are two players, P1 and P2, who negotiate on how to split a prot of one. P1 makes the rst bid (3:, 1 3:), where a: E [0, 1]. Then P2 gives a response, which is either yes to Pl's offer, or yes to an outside offer, or no to both Page 4 of 4 pages offers. If Pl's offer is accepted, then the payo's to the two players are (2;, 1 :32). If an outside offer is accepted by P2, then the payoffs are (U, V). If P2 rejects both offers, then the game enters the next stage, where P2 makes a counter-offer (y, l y) , and y E [0, 1]. This follows by Pl's response, which also involves an outside offer. If P2's offer is accepted, then the payoffs are (y,1 g). If P1 accepts her outside offer, then the payoffs are (V,0). The game continues on till someone accepts an o'er. Note that the players discount future with factor 6,; 6 (0,1), where i = 1, 2. Every time someone is making a counter-offer, the discount factors will be applied. (a) [5 points] Draw the game tree. (b) [10 points] List the two equations used to solve for the stationary subgame perfect equilibrium. (0) [5 points] Consider the case where for each player 1i 2 1, 2, accepting the outside offer dominates rejecting both the outside and player j's offers. Show that it requires the following for this case to hold: 61 62 ] > Vma'leal'HJg