Jeopardy!

I'm a big fan of strategy, and economics satiates a good deal of my desire for it. Poker does too. Nonetheless, I've yet to encounter a diminishing marginal return to more competition in my life, so I enjoy as much of it as I can get.

Betting in final Jeopardy fascinates me. Some ideas I've been tossing around (and I'm sure this has been written about somewhere else many times; feel free to link it up):

- If you're in the lead, do you worry at all about the person in third place? I'm leaning now towards no, but I could be convinced otherwise. I think it may involve all three people being pretty close.

- If you're in third, obviously you want to two people ahead of you to be close, as presumably they both bet large amounts trying to beat each other and, if they both miss, the first person can slide in for the win (which happened tonight...on a final Jeopardy question category of "Military men" and having an enlisted serviceman in third place. Rigged? You decide.). But couldn't the top two people recognize this and mutually lower the stakes to effectively eliminate the lower player regardless of outcome? I know, there's no communication, it's a one time game, and even if both of those weren't true, it's not a stable equilibrium...nonetheless, I'm surprised this hasn't caught on in small bits here and there.

- I would think that if you're confident in your ability to answer one question-- and given the selection bias in people that can actually get on this show, I'd sense this is probably more true than not-- you'd find the top person always betting such that if they get it right and the second person bets it all and gets it right, they win by a dollar. Of course, knowing this, the second place person has an optimal betting strategy themselves, and then the third person too. We don't witness these respective strategies every single night, so where does this break down?

- I could be wrong, but in the past, if contestants tied, they brought them both back the next night. Why wouldn't people go for this? It's a chance to build trust with another contestant and make Jeopardy a repeated game. I suppose there's the fear of having someone approximately your equal back in the next game with you, but if you build the trust, they're not trying to get rid of you-- they could also go for the tie. Shirking is always a possibility...I'm surprised people haven't at least attempted the tie and move on in attempt to make friendly with another contestant. All you lose is one dollar for the chance to be playing the game with someone else. Maybe they don't let ties move on together anymore...in which case, strike all of this.

- Has the pattern of betting in final Jeopardy evolved over the years? There's totally a paper there. I'd suspect people learn and refine betting strategies; we may not be at the optimal betting solution, but given the path we took, I'd bet we're pretty near a locally optimal solution. Along the same lines, did Ken Jennings change his betting strategy throughout his run?