Thursday, August 13, 2009

Stephen Strasburg and the Ultimatum Game

One of the classic games in game theory is called the ultimatum game. In the game there is a stack of money, say $100 in $1 bills, and two people. Person A, let’s call him Mark, gets to make an offer of how to split the $100 with person B, let’s call him Stephen. Once Mark offers Stephen an amount of money, Stephen has two choices he can accept the offer or reject it. If he accepts Stephen keeps the amount offered and Mark keeps the rest. Now Stephen can also reject the offer in which case they both get nothing.

Economic Theory says Mark should offer Stephen $1, since Stephen will think $1 is better than nothing he we’ll accept so the result is Mark gets $99 and Stephen gets $1. But when economists do experiments they find that people in Mark’s position usually offer between $25 and $50 to people in Stephen’s position. Why because those in Stephen’s position will typically reject offers if they feel they are unfair, so even though it might better for Stephen to accept an offer of $10 he might reject it because it is unfair.

This situation in some sense is happening in real life. Mark in this story is Mark Lerner the owner of the Nationals (Washington DC’s baseball team). This year they drafted Stephen Strasburg with the #1 pick in the draft. Now suppose instead of the $100, we think of the pot as the future value of Stasburg as a baseball player. Mark will make Stephen a contract offer, which is Stephen’s share of the pot. Now there are slight differences since during contract negotiations Mark can make multiple offers. But in the end (Monday at midnight) if Stephen rejects it he gets nothing, but so does Mark.

Well not exactly, the Nationals get another pick next year to make up for their inability to reach a deal with Strasburg, while Strasburg gets to try to be drafted last year. We can model this with game theory too, but it just raises the minimum offer Strasburg will accept. A rejected offer happened in negotiations with Adam Crow the Nationals top pick last year.

The lesson is that Mark Lerner and the Nationals are playing a game with a real human, so they need to make an offer that Strasburg thinks is fair.

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