3.

4.   For an Ultimatum game with counter-offers from a declining pool of money, suppose we start with $100 and $19 is removed from the pool after each offer is rejected, and no counter-offer  can be made if the pool drops to $1 or less. Assume: players reject any offer where they expect a tie or where they expect to be able to receive at least as much money from a counter-offer that they project will be accepted; players are rational; all offers must be in increments of an even $1. Express all offers in terms of (x,y) where x is the money player 1 will keep if accepted and y is the money player 2 will keep if accepted. So, if the initial offer is (100,0) it will be rejected, and player 2 could counter with (0,81) or (1,80) or another pair of positive integers that sum to 81 (100 – 19 = 81).

For the SPNE solution, what is the initial offer?

(You may want to also find the solution with each specific number of possible counter-offers, but that is not part of the homework set)

5.   Similar to Q4 above, begin with $300 and the pool of money declines by $35 each round. What is the SPNE of the initial offer?