I’ve been interested in learning more about Game TheoryÂ (wikipedia)Â lately and in particular The Prisoner’s Dilemma. One very interesting example happened on the Jeopardy show last Friday (March 16th 2007)—for the first time in 23 years, Jeopardy had a three way tie.
The tie was an anomaly in large part because one player didn’t play the game to win. Going into Final Jeopardy!, here’s how the totals stood…
- Scott: $13,400
- James: $8,000
- Anders: $8,000
So if you were playing the game, how much would you have bet? If you’re James or Anders, you can’t win by betting nothing and hoping for Scott to wager more than $5,400 and then get the question wrong because he won’t risk that much. In order for either James or Anders to win, you would have to bet everything, get the answer right and have Scott answer incorrectly.
If you’re Scott you have to wager at least $2,601 to win. It’s unlikely that you would get the question wrong and the other two get it right, so even with a really difficult question, chances are you’d still be left with between $10,799 or $8,001 depending on how aggressive you were—either way enough to beat either of your opponents who didn’t bet anything.
Scott probably assumed that one or both of his opponents would wind up with $16,000. What Scott did next is kind of like The Prisoner’s DilemmaÂ (wikipedia)Â except that Scott was safe from either James or Anders “defecting”.
Scott decided to wager exactly $2,600 creating a three-way tie. He didn’t really lose anything because now he will return on Monday with the same two opponents that he’s already beaten and by not taking the extra $1 (or extra $2399 the most additional money he could have won with a “safe” wager) he allowed both James and Anders to also collect $1600 in winnings.
Scott has a Livejournal entry about the game:
Oh, you want to know about the Final Jeopardy! wager? It was an intentional bet. I counted on Anders and Jamey betting rationally and wagering everything. I thought it would be really cool to be a part of Jeopardy history. I knew that meant I’d be playing seasoned opponents, but it didn’t matter to me. I had already won a couple of games myself, and I thought it would be neat to share the money. (See my post about Jennifer from a couple of days; that’s what the literary people call foreshadowing. :-)). Now there’ll be a notation next to one of my games in the J! Archive. How cool is that?