Kelvin Wong

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Using a Game Show to Teach Game Theory [Draft]

by Kelvin Wong

Kelvin Wong is a Ph.D. candidate in economics at the University of Minnesota and the winner of multiple teaching awards, including the 2013 Economist Educators Best in Class Award and the Walter W. Heller Outstanding Teaching Award.


Game theory is often one of the most intriguing and exciting topics in an introductory microeconomics course. However, the way that it is delivered is usually nothing to be excited about. If theories of classic games such as the Prisoner’s Dilemma or Battle of the Sexes are all the students are seeing, then they may fail to see the power of game theory as a social tool. To elevate interest in class, as well as make game theory something that the students can “own” for themselves, a game show can be played during lecture.

How to Incorporate the Game Show into Lecture

It is recommended that basic game theory tools be taught already, prior to playing the game show. In the previous class, games such as the Prisoner’s Dilemma and Battle of the Sexes should be introduced, along with how to find Nash Equilibrium, dominant, strategy, and first-mover’s advantage. Alternatively, perhaps the game show can be played to motivate and introduce game theory. Instructors should determine whether this activity will be used as motivation or reinforcement.

Start off by introducing the game: There was a British game show called Golden Balls, where four contestants go through a series of rounds to build up the amount of money that the winner could take home. Two contestants are also eliminated throughout the game, leaving two for the final activity, called “Split or Steal.” In Split or Steal, each contestant has two balls in front of them. Inside one ball is the word “Split,” and inside the other is the word “Steal.” A contestant would know which one of his balls is “Split” or “Steal” because he can look inside the balls before the round starts. Then, the two contestants can talk with each other for about a minute, at the end of which they must pick a ball to play. If both players picked their “Split” ball, then they split the winnings and each goes home with half the winnings. However, if one person picks “Split” and the other “Steal,” then the person who picked “Steal” will get all the winnings. Lastly, if both pick “Steal,” then both go home with nothing.

The above setup can be depicted in the following simple 2 player, 2 action simultaneous game:

Kwgame1.png

After introducing the game, it is recommended to have students come up to play the game, with money on the line. Having students participate is a great way to teach the class something, as classmates are much more likely to pay attention when their peers are up front. After allowing the two students to talk and pick either split or steal, analyze whether the students’ decisions were in line with what they were expected to do, based on game theory. To make things line up with the framework that is discussed in an introductory class where only strict Nash Equilibria are discussed, it should also be assumed that there is a negative payout from picking “Split” when someone picks “Steal.” The reasoning is simple - on top of making no money, there is a psychological hurt of being cheated on, as it is very likely that both parties agreed to pick “Split” while talking. The edited game will look something like this, such that the Nash Equilibrium is now a strict one.

Kwgame2.png

Further Discussion by Watching the Game Show Played by Actual Contestants

Following the games with students, show portions of the actual game show (videos can be easily found on YouTube by searching for “Split or Steal”), go through the payouts, and have the class predict what will happen. Turns out there are some interesting twists that the class does not expect in these shows! For example, in one video, a man tells the other contestant that he will pick “Steal” no matter what, and will split the winnings with him after the show (instead of simply splitting by both picking “Split”). Thus, he was trying to get the other person to pick “Split,” because if “Steal” was picked, both would steal and both would end up with nothing. In the end, they both picked “Split.” The first-mover always had in mind to pick “Split” from the start, and only wanted to guarantee that the other person will also pick “Split.” This is somewhat like the “first mover’s advantage” concept, except that the first-mover ended up picking something other than what he promised. The idea of “cheap talk” can thus be introduced here as well.

Limitations of Only Using Monetary Payouts

It is important to make a statement about the difference between only looking at monetary payouts rather than utility payouts. Most videos that are found online show Split/Steal or Split/Split as the result, which doesn’t seem to make sense based on the above analysis, but that is because only monetary payouts were used (aside from the minor assumption of psychological negative payout). In reality, some contestants will find it harder to pick “Steal” when facing a poor old lady compared with when facing a young businessman. This would then be a great place to make a statement that one’s beliefs and morals also matter very much, even if we simplify the analysis to just look at monetary payouts.