I like the show Cutthroat Kitchen, and I’m wondering if there’s a name for the type of prize setup that they have. In the show, contestants each get handed $25,000 to start off with. During the game, they can spend this money bidding on sabotages against the other contestants. A contestant gets eliminated each round and gives up their money as they leave. The one who remains at the end of the final round gets whatever money he didn’t spend during the game as a prize (this has ranged from $100 to all $25,000).
It seems to me that there should be a word for a game where you start with money, can use the money during the game, and at the end win whatever you haven’t used as a prize, but I don’t know what it is.
It’s a version of The Prisoner’s Dilemma. The optimal strategy would be for the contestants to agree in advance that no one will spend any money to try to gain an edge over the others. That guarantees the maximum payout to the winner.
The problem of course is that there is strong pressure on the contestants to defect. But if everyone spends $1000 to gain an edge, then the expenditures cancel each other out.
It’s not the Prisoner’s Dilemma at all - in the Prisoner’s Dilemma, if both people don’t defect, then they both come out better, if one defects the one who doesn’t comes out worse while the one who does comes out better, and if they both defect they both come out worse. In this game, only one person comes out with any money, everyone else comes out with zero regardless of whether they ‘defect’ or not. The bit about spending money cancelling out is also completely wrong, since it’s not actually possible for everyone to spend $1000 and cancel each other out. There are only 1-3 sabotages up for bid in a round, they’re all different, some of them will affect some contestants worse than others, and the cumulative effect of multiple sabotages is generally worse than just getting one.
Your strategy guarantees that whoever wins gets as much money as possible, but I can’t see why anyone (much less all contestants) would consider maximizing someone else’s prize a worthwhile goal. In the Prisoner’s Dilemma, ‘spend the least amount of time in jail’ is a clear and obvious goal. But here, ‘be the winner regardless of amount won’ is reasonable, as is ‘maximize my chance of walking away with a decent prize’, while ‘make sure that whoever wins gets as much as possible’ is not a big deal. And it gets worse in the real-world analysis, since if you theoretically did collude to remove all of the sabotages, you would end up with the producers not wanting to work with any of you again, on this show or any other games that are supposed to be entertaining, since you worked to remove the main draw of the show.
If all else is equal, everyone has the same chance at winning the prize, and so they all have the same expected return. It’s Prisoner’s Dilemma with a gambling component thrown in.
Just to get an answer to my original question without all of the Prisoner’s Dilemma stuff, lets assume that the game has a rule that if no one bids on a sabotage, then one person at random is forced to make a minimum bid on it, so that collusion to avoid playing the sabotage portion of the game isn’t possible, and someone will always have a variance in the amount of prize money. Or we can assume that collusion is against the contract that people sign before going on the show. (Either one of these could actually be true, AFAIK) Is there a name for the type of game where you can use prize money for advantage in the game but it reduces your eventual payout to do so? It seems to me that there should be a term for this, which is why I posted it in GQ originally.
I’m not really sure how a game with multiple elimination rounds and four contestants instead of two can even be called a variant of Prisoner’s Dilemma. There isn’t any mechanism that produces the ‘if two people ‘defect’, they are both worse off’ effect that is a key feature of the traditional PD.
And I don’t think it’s valid to analyze a real life game that involves player choice and skill by assuming that everyone has the exact same skillset and levels and makes the exact same choices in all situations, especially when the game is set up explicitly to give the players different situations to deal with. There’s also the problem that playing the game with the allegedly optimal strategy will guarantee that you don’t get to make multiple plays of the game (since the producers don’t want people who won’t participate in the draw of the show), and expected value isn’t a very useful evaluation tool if you don’t get multiple tries at the game.