Question (20 points) P1 and P2 are bargaining over one dollar. Players alternate in making offers as illustrated in the figure. Step 1 Step 2 Step 3 Stage 1: P1 proposes to take a share s leaving 1 s; to P2. P2 either accepts the offer in which case the game ends and payoffs (s;, 1 s1) are immediately received or rejects the offer in which case play continues to second stage Stage 2: P2 proposes that P1 gets a share s, leaving 1 s to P2. P1 either accepts the offer in which case game ends, payoffs (s;,1 s2) are received or rejects the offer in which case the play continues to third period. Stage 3: An arbitrator decides that P1 gets 1 s, and allocates s; to P2. In other words, the arbitrator gives P2 what P2 offered to P1 in Stage 2. See the Figure. The players are impatient, they discount payoffs received in later stages by a factor = 0.5 per period. Solve the game backwards and find the SPE by following the sequence described below. Find P1's optimal response to P2's offer s, in Stage 2. Find P2's optimal offer s3 in Stage 2. Find P2's optimal response to P1's offer s; in Stage 1. Step 4 Find P1's optimal offer s] in Stage 1. State how the dollar is divided in the SPE. P1 $1 P2 YES NO P2 (s1. 1- s1 ) 52 P1 YES NO Arbitrator (S2; 1-52) (1-$2; $2)