Question

In this game, Ann first offers to split $15 in one of three ways: (14,1), or (8,7), or (1,14), where the first number shows Ann's share, the second shows Bob's share. After Ann makes the offer, Bob can choose to Accept it (and the offer is implemented), or Reject it (and both get 0), or grab a handful of quarters and run with it, in which case he gets $2 and Ann gets $13.

Check all the strategy combinations below that are Nash equilibria in this game. Drawing the game tree carefully will help you answer the question.

Select one or more:

a. Ann: Split (14,1)

Bob: ("Grab and run"; "Grab and run"; "Grab and run")

b. Ann: Split (8,7)

Bob: (Accept; Accept; Accept)

c. Ann: Split (8,7)

Bob: (Reject (14,1) offer; Accept (8,7) offer; Accept (1,14) offer)

d. Ann: Split (1,14)

Bob: (Reject (14,1) offer; (Reject (8,7) offer; Accept (1,14) offer)

Answer 1

Since bob gets to choose among accept, reject, and grab & run, he would definitely accept the last offer i.e, (1,14) and reject the other two since in no case his utility would be greater than in the offer (1,14). Therefore option D is the most apt.

However, if Ann makes the offer (8,7) then it would be wise for bob to reject (14,1) and accept (8,7) since that would provide him a graeter utility. But this is only when it is the case that Ann wouldn't offer the 3rd case of (1,14). If (1,14) would be offered then it would be wise to reject (8,7) as well.