The Implications of an Ultimatum
On September 23 we discussed the prospect of an ultimatum experiment. I found it particularly interesting because of the power one holds merely in being lucky enough to make the first (and only) offer.
In class, we looked at a game between two people, A and B. A proposes a split and B can accept or reject. If B accepts, B gets the payoff A offered, otherwise B gets nothing. When A and B are splitting $100, it makes the most sense for A to offer $1 to B. In this case B should accept because $1 is better than $0. A chooses this amount because it yields the highest payoff for himself while assuring that he will still get the payoff.
As we discussed in class though, experimental tests of this scenario rarely see the $99-$1 transaction ever get carried out. It was concluded that this must be because the value of B accepting $1 is less than the value of accepting $0. Clearly, there must be an added value for B to not accept the $1. This is intriguing.
From the experiments it can be concluded that the payoff for B is not merely $1 or $0 but instead something more like $1 or $0 + some function of A’s payoff. It would be interesting to try and lock down this “function of A’s payoff” so as to see exactly what offer A should make to best his own share.
In class, we took an iClicker poll to see what students would offer if they were in this situation. Unfortunately I was not able to take a picture of the graph that arose from the question, but I can recreate the general look of it here:
From the graph, we can do some pseudo math. If we only look at instances other than the 99 – 1 offering, we can attempt to model the “function of A’s payoff” assuming that every other offer would be accepted. In my simulated graph, there were 30 people offering $10, 50 people offering $20, 70 people offering $30, and 90 people offering $50. This is equivalent to saying 30/240 offered $10, 50/240 offered $20, 70/240 offered $30, and 90/240 offered $50. This implies the expected value of an accepted offer (if all of these offers were accepted) would be 1/8*$10+5/24*$20+7/24*$30+3/8*$50 = $32.92.
Does this mean that the “function of A’s payoff” equals 32.92/100 ~ 30% of A’s payoff? I am not sure, but I definitely think one could find the function if they were able to run this experiment many times over.