Utility Theory and Deal or No Deal
Michael A. Jones
American Mathematical Society
Deal or No Deal was a prime time game show on the National Broadcasting Corporation network in which a Contestant selects one of 26 suitcases. Inside each suitcase is a different dollar amount; all 26 dollar amounts are known beforehand. In a series of rounds, the Contestant is asked to "deal" (in which she accepts a monetary offer from a Banker) or to "no deal" (in which she has to open a specified number of suitcases, thereby revealing the dollar amounts inside the suitcases). The game ends when either she accepts an offer or, after opening all of the suitcases except the one she selected at the outset, she receives the monetary amount in her selected suitcase.
Because each suitcase may contain any of the fixed monetary amounts, selecting a suitcase is analogous to a lottery in which each value has an equal likelihood of being selected. Assuming the Banker's offer is based on a utility function that describes the Contestant's utility or value for money and incorporates the Contestant's view toward the risk of participating in the lottery, the Banker makes an offer so that the Contestant is indifferent between accepting the Banker's offer and continuing to play the game.
In this talk, I will introduce the basics of utility theory and will explain how the Banker could use a utility function to determine an offer. I will demonstrate how data from televised episodes may be used to recover the utility function. Further, I will examine a paradoxical offer from NBC's online version of the game.
A forthcoming paper of the same name is co-authored with Jennifer Wilson, New School University, New York.