The Price is WRONG, Bitch!

My new apartment has both a dining table and a coffee table that is not holding up the TV, so it's much more amenable to eating a proper breakfast than my old place was. Of course, if you're up before 11 am on a school day, the only thing that can make for a truly complete breakfast is a screening of The Price is Right.

The essential contest of TPiR, for anyone who's been out of the game for a while, is a competitive bid on a random, and usually unattractive, consumer product. By placing the winning bid on this item, you get to play a minigame and put yourself in the running for the "Showcase Showdown," another bidding exercise at the end of the program where you can win a collection of fantabulous prizes.

The initial auction takes place between four contestants, who bid by shouting out some value when called on by Bob Barker. The winner is the contestant who bids the closest to the item's MSRP without going over. It doesn't take a lot of game theory to suggest that, in an auction with open bidding and a publicly-known decision rule, you want to bid last. When you're the fourth and final bidder, you have a number of options at your disposal:

1) Bid whatever your private intuition (and the screaming audience) tells you to bid; this is the only option for the contestant bidding first.
2) "Steal" someone else's bid by bidding their value + 1. The only time when this could backfire is if the rival's bid was actually greater than or equal to the item's value--meaning you've overbid--but since you have three options to choose from, hopefully you've made the educated play.
3) Bid $1, undercutting the other three in the case that they've all overbid.

Back to my breakfast: the initial auction fails because everyone's overbid, so they do it again. The previous low bid was $550.

Granny #1: bids $499. Interesting play, but hey, whatever.

Skank: bids $400. Fair enough.

Dudebro: bids $450. Now, I'd be tempted to bid $401 here, but I can see this as being a best reply if you think the item is on the range [400,499]. By bidding $401, you're inviting Granny #2 to bid $402, meaning you're fucked. By bidding $450, you force Granny #2 to bid either $1, $401 or $451.

Granny #2: bids $399. Let me repeat that, in bold: bids $399! The ONLY way she can win is if the pricetag on the item is exactly $399. I'm still pissed at her.

Granny #1 ends up winning--the price was $500. She then goes on to win the spin-the-wheel game with 40 cents, even though she moved first (Skank busted; Fat Guy finished with like 20 cents somehow).

Here's my point: you can lead a horse to an institutional incentive, but you can't make it not be retarded.