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Game Theory & Performance Measurement

by | Jan 19, 2016

This post may be a bit of a stretch, but hoping you’ll find it of interest, nonetheless. It’ll show how game theory can tie into performance measurement.

My wife and I are big fans of the television game show, Jeopardy. We watch it each night, and record it so that if I’m away, we can “binge watch” when I return home. Last night’s episode was a classic, one not to be forgotten.

Going into “Final Jeopardy, two contestants were tied for the lead with \$13,800, each, and the third was far behind with only \$6,000. In this final round, they’re first given a category (in this case, “State Capitals”), and they then decide how much to wager. After a commercial break, they’re given the question and have sixty seconds to provide the answer.

Having knowledge of a wide array of topics is critically important to succeed on this show. But knowing how to wager is also very important, and I believe too many players fail in this area.

A key thing to know: you can have two winners, meaning that if the two contestants in the lead ended with the same (non-zero) amount, they would be co-winners.

Okay, so what happened?

I’ll present what occurred, and then analyze it.

First, the question (actually, it’s the “answer,” and the contestants frame their response in the form of a question):

Note that “president” has been abbreviated,” as has “national.”

The contestants wagered as follows:

• Randi (a college professor) with only \$6,000 bet it all
• Claudia with \$16,800 wagered \$16,800
• Mike with \$16,800 wagered everything.

They all got the question wrong (I’ll provide the answer below). And so, they all ended with \$0, so there was no winner, meaning no one was able to continue to tonight’s show.

Game Theory Wagering 101

The two leaders’ situation reminded me of the game theory problem, prisoner’s dilemma (if you’re unfamiliar with it, I’ll leave it to you to do the necessary research).

The ideal bet would have been \$0 (nothing). Why? Whether they got it right or wrong, they’d have \$16,800. To the best of my knowledge the contestants are not permitted to discuss how much they will wager, so they must try to guess what the others might do.

I want to emphasize this point: to me, it’s quite obvious that Mike and Claudia should have bet zero dollars. However, they won’t know what the other is doing, and while they may be quite content to be tied with the highest amount (which they would win), they don’t want to end up in second place (and only get \$2,000, and not return for another show).

“What will the other person do?,”

they surely asked themselves. If one bet \$0 and the other a mere \$1, and both got the answer correct, the one who added a dollar to their total would win.

They may have thought “we each will benefit by betting nothing; we’re guaranteed a win. That’s what we should both do. But if do and he/she doesn’t, I may lose.” And so, they have to move into a defensive posture.

Betting it all isn’t a great idea, because if they get it wrong, they end up with zero dollars, which is exactly what happened. But do they have a choice? The topic probably didn’t sound that challenging. But they still know it’s an “all or nothing” proposition.

And so, I can understand why they chose to bet it all; sadly, they both got it wrong and had nothing in the end.

Now Randi is the interesting one.

When you come in third place, you automatically get \$1,000. Why bet it all? Why bet anything? You’re guaranteed third place!

Often the person in third place will bet everything less one dollar: she should have done this.

Her wagering was incredibly poor, in my view. Perhaps she didn’t consider what the others might do; perhaps she just ruled herself out of possibly winning, and so, to see if she could at least double her money (money she wouldn’t walk away with, as she would still only get \$1,000), she bet it all. Had she bet \$5,999, she would have ended up with only a dollar.

And would have won!

Granted, her “take” for the night would only be \$1, but she’d come back to play again! She’d be a Jeopardy champ, and go into the “record books” with the lowest possible winning amount (this wouldn’t have been the first time that the winner only had one dollar).

Fascinating, simply fascinating example of game theory

After we watched this show, I spent the next 30-45 minutes discussing it with my wife (who quickly grew tired of my analysis). If I were teaching game theory, I’d use it immediately in class. If I was writing a book on game theory, it would be an example.

My wife and I play along when we watch, attempting to get as many right as possible (while we don’t actually keep score, we do acknowledge each other when we get something correct). Well, I got this question correct, and was quite pleased with myself, especially since these three very talented and knowledgeable individuals, who know far more about many topics than I do, didn’t.

The answer: Little Rock, AR (Arkansas). The President whose library is there: William Jefferson Clinton.

Knowing that the year was 1957, and that yesterday was Martin Luther King’s birthday, I suspected that there might be a tie-in with the civil rights era. At that time, schools were forced to desegregate (i.e., forced to integrate), and I recall how there was much protest over this in Little Rock. And so, then President Dwight Eisenhower sent in troops to control the situation. I guess that the historical site refers to this event.

How does this example of game theory tie in to performance measurement?

Well, I promised it would be a bit of a stretch.

In watching the game, scores change constantly, as players try to provide the question to the answers shown. Each session before “Final Jeopardy” involves six categories, with five questions each, ranging in value from \$100 to \$500 in the first session, and \$200 to \$1,000 in the second. We see the lead change, we see people lose money and go into the red, and we see both big and little bets made at three points in the game, when the player can actually wager a variable amount of money (rather than the fixed amount shown on the board).

In reality, much of what goes on during the first 27 or so minutes of the show is just a lot of “noise,” as it’s quite difficult to try to determine who will win. If we were to track performance, we’d see three lines for the players moving in different directions, making sharp turns, throughout.

“Final Jeopardy” is often the deciding part of the game. Often, the leader is a “run away,” and can’t be caught (that is, if the players in second or third place were to double their scores, they couldn’t equal or exceed the leader’s). It’s especially interesting when it is not a “run away,” and where the person in third place, partly due to knowledge, and often due to skillful wagering, wins.

Yes, it’s interesting to see how the scores change, and yes, it’s interesting to play along. If we were measuring the players’ performance this way, it would be quite confusing.

Some in our industry call for real-time performance measurement: the ability, for example, to track, throughout the day, how a manager is doing. A tick-by-tick analysis, so to speak.

I believe this is a worthy question to discuss. My initial position is opposition, but I’m open to hearing the views of others. Perhaps you’d like to chime in!?!?!?

Hope you enjoyed this first post of 2016. I took a brief break at the end of the year, partly because I was engaged in a few projects and had little time, and partly because I took a couple weeks off.

The Journal of Performance Measurement

The Performance Measurement Resource.