Tonight’s Jeopardy had a big high and a big low for game theorists.
For most of the game, challenger Matthew LaMagna held a large lead. During Double Jeopardy, other challenger Angela Chuang hit a Daily Double in the “I Have a Theory” category. At only ~$4000 and facing Matthew at ~$18,000, Angela had only one option: make it a true Daily Double. She did. That part was sweet.
So was the clue (paraphrasing):
Beautiful Mind John Nash is credited with launching this field in economics.
Obviously, the correct response was “What is game theory?” Angela nailed it. Again, sweet. Maybe she knows game theory!
Now the sour part. Despite her best efforts, Matthew pulled away. The scores entering Final Jeopardy were $20,800 for Matthew, $8400 for Angela, and $1200 for the returning champion. Wagers are trivial at this point. Matthew has first place locked. Angela has second place locked as well because she doubles up the third place’s dollar figure. It does not take a game theorist to see this, but it helps.
(Critically, the end dollar figures are irrelevant for second and third place. Second receives a fixed $2000; third place, $1000.)
However, despite Angela’s familiarity with game theory, she wagers $8300. The returning champion wagers nothing. Final Jeopardy’s clue is triple stumper. Angela drops to $100 and third place, when all she had to do was write $0 and guarantee herself $2000. Instead, she went home with a check for $1000.
To be fair, there might be reason to not wager $0 here even though you can guarantee second place by doing so. Everyone’s favorite love-to-hate champion Arthur Chu famously wagered enough so that he would draw with second place if second place wagered everything. But Angela wasn’t even going for that. The $8300 wager could do nothing but harm her. That was sour.