Three people live on the same unpaved road

Three people live on the same unpaved road. All three people would like to have the road paved, but they cannot decide how to pay for it. Getting the road paved is worth $3 to each person and these valuations are commonly known to all players. It would cost $4 (in total) to hire a contractor to pave the road. First, suppose that people make their offers sequentially. First, person 1 states $1. Second, person 2 observes Si and then states $2. Finally, person 3 observes both si and s2 and then states $3. Predict the outcome of this game using the backward induction approach. Each player simultaneously and independently selects an integer from {0, 1, 2, 3, 4]. Let si denote the offer of player i. Hint: There is no need to draw the game tree", just think what will happen. • If si + 32 + S3 4, the road is paved and player i pays $i = 0, $2 = 1, 83 = 3 Pi = 4* S 81 +52 + 83 O O O O $i = 0, 82 = 3, S3 = 1 $i = 2, 82 = 2, S3 = 0 $i = 3, 82 = 1, 83 = 0 $i = 1, S2 = 1, s3 = 2 That is, each player i pays in proportion to her offer such that the sum of collected payments equals 4. For example, if s? = 2, 82 = 2, S3 = 4, then p1 = 1, P2 = 1, P3 = 2.