Saturday, January 11, 2014

The Economics of Cutthroat Kitchen

During the holiday season a coworker insisted I watch a new Food Network show called Cutthroat Kitchen. The show follows a standard chef game show format in which four chefs must cook a given menu item.  A guest judge then determines which chef's dish was the worst and that chef is eliminated.  The show proceeds through three rounds, eliminating one chef a round until the final chef is crowned the victor.

Here is the interesting twist meant to keep audiences coming back for more.  The chefs are given their prize ($25,000) at the start of the show and may spend that money in auctions during each round.  Auctions are generally for sabotages which can be given to other contestants to make their life more difficult.  For example, if the item to be cooked was meatloaf and mashed potatoes a sabotage might be to force another contestant to make mashed potatoes with potato peels or to make meatloaf with unground meat.  When losers are eliminated they return their prize money to the host whereas the winner keeps whatever they didn't spend over the course of the show.

As someone who cooks frequently the show has no educational value.  The techniques or tricks the chefs use aren't discussed.  Instead the focus is put on how a chef deals with the obstacles heaped upon him.  While amusing, it's unlikely your average viewer will ever need to cook a pancake on top of a tin can.  Thus, unless your cookware is stolen by the international culinary mafia you probably won't learn much.

As an economist however, the auctions are fascinating.  It's rare to see so blatantly how bad we are at making financial decisions under pressure.  Here is a fictional, but representative, example of how cutthroat kitchen often goes. Remember each contestant has $25,000 to spend in auctions. Any amount they don't spend will be their prize if they win.

Allen, Beth, Candice and Dave arrive at the set.  They're told they'll be cooking a pizza. As usual they have thirty minutes to complete the task after they grab their ingredients from the shows pantry.  Everyone scrambles to grab the items they'll need to make a crust and sauce as well as some cheese and toppings to cover the pizza with.

Shortly after cooking begins the host starts to auction off sabotages. The first auction (of an expected four) is for the ability to force another contestant to make their sauce out of unripe tomatoes. Beth and Dave are both terrified of having to use unripe tomatoes and so bid against each other until Beth wins the auction for $5500.  She awards the tomatoes to Candice.

Auction two is won by Dave who forces Allen to have to grate his own cheese from a block rather than using preshredded. Auction three is won again by Dave who forces Beth to choose from some common ice cream toppings instead of pizza toppings for his pizza. Finally auction four is won by Candice who gets revenge on Beth by making her cook her pizza on a griddle instead of in an oven.

The end result is Allen has to grate his cheese from a block. Beth has to use ice cream toppings instead of pizza toppings and cook her pizza on a griddle. Candice has to use unripe tomatoes in her sauce and Dave is unsabotaged.  Additionally, Allen has spent nothing, Beth is down $5500, Candice has spent $5000, and Dave has spent $10,000. Judging commences and Candice is eliminated as the judges felt her pizza was the least delicious.

Round two commences and Dave is eliminated. Allen and Beth remain with $22,000 and $18,000 respectively.  After the final round Beth is crowned the victor with winnings of $10,500.

Using this fictitious series of events we can point to a number of poor decisions contestants made along the way.  In the first round Beth and Dave were willing to spend a great deal in order to avoid getting the under ripe tomato sabotage.  This is a very common behavior as expressed by contestants.  They often are willing to bid on an auction just to guarantee they are not stuck with the sabotage.  However, in the first round losing an auction generally only costs a contestant a one third chance of being hit with the penalty (as the winner could award it to any of the three other contestants). Given this probability the prices contestants pay is borderline absurd. Contestants routinely bid as if losing an auction is a guarantee of receiving a penalty, a belief which is clearly incorrect.

Another oddity is that contestants are often most willing to spend during the first round of the contest.  Bids of $4000 to $6000 are not uncommon in the first round while in rounds two and three items will routinely sell for under $3000.  This is partially attributable to the fact that contestants that are loose with their money quickly deplete it or are eliminated thus leaving only more reluctant bidders with the assets needed for such lofty bids.  Still, it's difficult to understand why these big spenders expend so many resources so early, thus leaving themselves vulnerable in later rounds where they're more likely to be hit with sabotages.  A possible, if unlikely, explanation is they're attempting to put themselves in a position of weakness so that other players will award sabotages to stronger opponents.  However, putting oneself in a position of difficulty in order to avoid difficulty seems rather nonsensical.

The most bizarre behavior is when contestants spread penalties relatively evenly among the other contestants.  Each round one person is eliminated.  The logical behavior is as soon as a person receives a sabotage all other sabotages should be heaped upon them.  This eliminates animosity in later rounds (as the contestant will have been eliminated) and is the best method to ensure continuation through the rounds.

It would seem there are two possibly strong methods of bidding intelligently on the show given logical behavior (which the contestants never seem to exhibit).  Either win the first bid or do not bid at all.  If you choose to win the first bid you then award it to another player who then is signaled as weak to the remaining players. If that player does not win the second auction it should logically be awarded to them as well and they are now in a position where they are at best as weak as the next weakest player if they win the next two auctions and award them both to the same person. Thus the sabotaged player is forced into winning the second auction or having a very high probability of elimination.  This method is aggressive and potentially resource intensive if played against another player with the same strategy.  However, when facing three passive players (as described below) the resource cost is low.  The considerable downside is whoever you award the sabotage to essentially must bid against you in the second auction or risk the piled on sabotages. If they win the second auction they're most likely awarding their sabotage to the person who sabotaged them in the first auction (you).  So while you may gain a cheap sabotage to use against someone else, you also likely gain an expensive sabotage used on you. Overall it is a gain against the player you sabotaged, but a loss against the two players who are uninvolved.

The second, and likely preferable strategy is far simpler and likely superior.  Do not bid on the first auction.  The winner only has a one third chance of awarding the sabotage to you.  Two thirds of the time you will be able to keep all your money and receive no sabotage for the first round (as all sabotages should go to the first person sabotaged or very likely the person who sabotaged them). In the unfortunate event that you are chosen for the first sabotage you are put in a situation where you must make another player as weak as you, meaning you must start bidding and winning auctions to weaken them.  However, with the exception of a likely higher cost of auctions two, three and possibly four in the first round as compared to auction one you are at no particular disadvantage against the player you choose to target.  Overall your expected earnings increase a great deal as well as your position in later rounds of the contest.

It would be interesting to conduct interviews with contestants in order to establish their motivations for how they award sabotages. Certainly the tendency to spread the penalties around seems to indicate contestants think more of equity than how best to improve their odds of victory.  Still, at times I wonder if at times their consideration amounts to no more than, "I don't want to be stuck with that. I'll buy it then give it away to someone more or less at random."  Regardless of motivation, the show is an excellent demonstration of how not to think about strategic decisions.

That's it for this week. Until next time stay safe and rationale.

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