Using a Game Show to Teach Game Theory
by Kelvin Wong
This contribution comes from Kelvin Wong, a Clinical Assistant Professor in the Department of Economics at Arizona State University 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 prior to playing the game show; in the previous class, games such as the Prisoner’s Dilemma and Battle of the Sexes can be introduced, along with how to find Nash Equilibrium, dominant strategy, and first-mover’s advantage. Alternatively, the game show can be played to motivate and introduce game theory. Instructors can determine whether this activity will be used as motivation or reinforcement.
Start off by introducing the game: In a British game show called Golden Balls, four contestants go through a series of rounds to build up the amount of money that the winner could take home. Two contestants are 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 knows 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 pick 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” gets 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:
After introducing the game, 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 are 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 can 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.
Further Discussion by Watching the Game Show Played by Actual Contestants
Following the games with students, show portions of the actual game show, go through the payouts, and have the class predict what will happen. In this clip, Richard and Carol plays a game of split or steal. This is a good introductory video, as they do what we expect them to do, and it shows how the game works.http://www.youtube.com/watch?v=wewk06udkNo
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 tries to get the other person to pick “Split,” because if “Steal” is picked both would steal and both would end up with nothing. In the end, they both pick “Split.” The first-mover always had in mind to pick “Split” from the start, and only wanted to guarantee that the other person would 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 concept of “cheap talk” could be introduced here as well. In this clip, Nick and Ibrahim play what might be the most famous game of split or steal. Nick uses “cheap talk” successfully and causes Ibrahim to choose something that Nick wanted.https://www.youtube.com/watch?v=S0qjK3TWZE8
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 are used (aside from the minor assumption of psychological negative payout). In reality, some contestants might find it harder to pick “Steal” when facing a senior citizen than when facing a young businessman. This would then be a great place to make a statement that beliefs and morals also matter very much to the decisions we observe.
Empirical Analysis of Cooperative Behavior in Golden Balls
“Split or Steal? Cooperative Behavior When the Stakes Are Large.” Martijn J. van den Assem, Dennie van Dolder and Richard H. Thaler; Management Science, 2012, 58(1), pp. 2-20. http://dx.doi.org/10.1287/mnsc.1110.1413 Abstract: We examine cooperative behavior when large sums of money are at stake, using data from the TV game show “Golden Balls.” At the end of each episode, contestants play a variant on the classic Prisoner’s Dilemma for large and widely ranging stakes averaging over $20,000. Cooperation is surprisingly high for amounts that would normally be considered consequential but look tiny in their current context, what we call a “big peanuts” phenomenon. Utilizing the prior interaction among contestants, we find evidence that people have reciprocal preferences. Surprisingly, there is little support for conditional cooperation in our sample. That is, players do not seem to be more likely to cooperate if their opponent might be expected to cooperate. Further, we replicate earlier findings that males are less cooperative than females, but this gender effect reverses for older contestants because men become increasingly cooperative as their age increases.