Deal or No Deal: Risk Aversion, Loss Aversion, and Fair Odds (or lack thereof)
What I have noticed about the show -- especially last night's episode -- is that most of the deals that are offered by the 'banker' tend to be 'low-ball' offers until the later stages of the game (if the contestant lasts that long). What I mean by 'low-ball' is that the banker tends to not offer fair odds (by that I mean, in this context, what gambler's think of when they are being offered payoffs that match the statistical expected value). It is only in the latter stages of the game that the contestant is offered deals that are close to fair odds.
That is what happened to the first contestant on last night's episode. The deal that he accepted -- which I believe was for $250,000 -- exactly matched the mathematical expected value of having a 50% chance (which is the probability he was facing) of getting $500,000. It turned out to be a profitable move since the case he originally chose had some miniscule amount in it (rather than the $500,000). The contestant's final decision doesn't violate economists' ideas about risk neutral / risk averse decision making.
Up until that point, however, this particular contestant exhibited behavior that would confound both economists and common sense (a particularly strange situation since economics and common sense are often at odds with each other). If I remember correctly, prior to the final offered deal, the contestant had been offered a deal where he actually got slightly better than fair odds. If I recall correctly, he was offered a deal where he could get a sure deal for around $168,000 when he faced a 1/3rd chance of getting $500,000 (so the sure thing value exceeded the expected value of the payoff).
I'm not sure what to make of that kind of decision making under risk and time pressure. Behavioral economists often talk of 'loss aversion' as opposed to 'risk aversion'; with loss aversion, people are willing to take risks in order to minimize losses. It doesn't seem like the contestant was loss averse since he was willing to forgo a good sure thing (even passing up a better than fair odds deal) for the risky chance of getting the $500,000 (the higher amounts of $1 million and above were knocked off earlier). Neoclassical economists can't find much comfort in the contestant's decisions (at least not until the very end) since even they would have screamed for him to take the deal. Even an intellectually oriented gambler would have been baffled by the contestant's decisions. Only an irrational, compulsive gambler could have justified the decisions made by the contestant prior to the final decision point (when all but the craziest gambling addict would have approved of the decision).
It's worth noting, of course, that this was just one contestant. He may have been an anomaly. A more careful study of this show (in it's Italian version) has been done and can be downloaded from Francesco Trebbi's webpage (he was one of the co-authors).
One final thing to note, at least from a psychological perspective, is that the 'banker' may adjust his offers up or down based on the banker's perceptions of the contestant's attitude toward risk, loss, and gambling. For example, if the banker thinks that the contestant is likely to be very confident about his or her chances of winning, the banker may adjust his offer up slightly from whatever baseline the banker is using (of course, if the contestant is wrong about his/her confidence in his/her luckiness, then he/she will fall flat on his/her face). Just a thought. I'm not sure about it since I don't know the exact algorithm (if he has one; although, from what I saw from the last few offers on last night's show, it probably is based on expected value calculations) that the banker uses to come up with the dollar figure for the offer.
It may also be the case that the banker is instructed to make low-ball offers (considerably less than fair odds / expected value deals) in the early stages of the game in order to make the contestants tend to want to reject the earlier offers and spur them on to continuing on with the game. This could be done for ratings purposes. After all, NBC doesn't want to gamble on its profits by risking losing its viewers.