$10

Today a friend of mine was telling me about an experiment she was a part of. Imagine that you are given $10 and told to split it between you and another person, John. The catch is: you make an offer to John, if he rejects it, neither of you get any money. If he accepts it, you both get the agreed upon amount. What is the optimal strategy? Split it 50/50, right? ...Right?!? Well, maybe...

Perhaps the simplest way to look at this is to say that splitting the money in half between you and John is the optimal solution.  The problem is that that assumes that John knows 1) that you have money that you are supposed to split between the two of you and 2) how much money that is.  If John doesn't know about the money, you could get away with offering him $0.01 (assuming you have to offer something) and still get to keep the $9.99.  Assuming John knows about the money but not the amount of money, you could still get away with $0.01... at least presumably.  But let's throw these assumptions out the window and say that John knows both that you have money to split with him and how much money you have to split with him.  So 50/50, right?

Well, before we answer that question, let's look at a very simple and a very simplistic evaluation of the situation.  It could be argued that if you offer $4.99 or less to John, you are being greedy and he should reject.  Alternatively, it could be argued that if you offer John $5.01 or more, you are being unnecessarily generous.  So, 50/50 then is viewed as a 'fair' amount.  .....But we still have a couple problems with this line of reasoning.  

The first big problem here is that we are assuming that John has as much right to the money as you do.  Only under this assumption would we say that anything less than $5 exemplifies you being greedy and anything more than $5 exemplifies you being generous.  Of course you could be told that you are acting as the CEO of a publicly traded company in which case the earnings you are to distribute really do belong to John.  Even still, you can probably come up with a legitimate way to spend the entire $10, thus justifying not giving anything to John for expected higher stock prices.  But what if you aren't the CEO of a publicly traded company?  What if you are just a person randomly picked off the street to participate in this experiment?  Under these circumstances, does John really have any right to the money?  It is in your possession to begin with... And anything you offer will make him better off than he previously was.  So if we operate under the assumption that John has no legitimate claim to the money, you can get away with offering him $0.01, right?  Maybe...

This greatly depends on how John and you are valuing the transaction.  In many economic theories, wealth is valued in the absolute.  So according to these theories, John should accept any offer of $0.01 or greater because it increases his wealth.  So the answer is $0.01.  Similarly, you should be comfortable giving John $9.99 because you would increase your wealth by $0.01 with 100% certainty.  So are either of these answers the right answer???

Well, we still can't say that with any certainty.  The problem with this method of transaction valuation is that it doesn't take into consideration one of the most fundamental human characteristics: emotion.  Okay, before we go any farther, let us just remember the situation: 1) you have been given $10 to split between yourself and John, 2) John knows that you have $10 to split between yourself and him, and 3) if John rejects your proposal, you both get nothing.

Okay, so you are probably thinking that the penultimate sentence in the paragraph before last is kind of fishy, but that requires you actually having possession of the money before divvying it up...  If you should split the money in the form of two checks, one for you and one for John, things may very well be valued differently because there are externality costs associated with a check as opposed to cash.  For instance, John now needs to go to a bank to either cash the check or to deposit it into his account; this money is not immediately available to him.  This simple fact may cause John to value the potential transaction differently than if it was cash.  If it is cash, John may prefer $9.95 to $9.99 because it would be fewer coins to carry and no pennies (presumably). 

As I said, the amount you offer depends greatly on how both you and John are valuing the transaction.  Many theories claim that people value transactions in a relative sense, not an absolute one.  If this is true, then John should accept $5 or higher only, right?

We still can’t say that, unfortunately, because of emotion.  At the most basic level, John would be indifferent on an offer of $5, so theoretically he would reject it 50% of the time.  By increasing the offer by a single penny, the probability that John will accept increases greatly, but not to 100%. 

So if we assume that you want to maximize the amount of money you would get from this transaction, there are a couple of factors to take into consideration: how John is valuing the transaction, how entitled John feels to the money, and how much information about the transaction does John really have? 

In general, my advice would be that if you are dividing cash, offer half plus a nickel; if you are dividing a check, offer half plus a penny.