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Just Keep Playing: Repeated Games Made Easy

Interactive strategic games are both fun and engaging to students interested in learning social science subjects, and can be an ideal complement to the traditional ‘chalk and talk’ lecture. 

However, with games and with lectures in the social sciences, there is often some detachment of what is taught in classrooms to reality. For example, the classic Prisoner’s Dilemma is often used to illustrate the concept of Nash Equilibrium. Yet, students often bring up the fact that two criminals may commit many crimes together over time and they might cooperate (not rat each other out) knowing if they rat out their partner now, they may not be so lucky next time. Simulating repeated interactions like that in class, when the time is limited and where the number of students is unpredictable, can be especially difficult and may just be outright impossible with a paper and pencil based setup. To make a repeated game work in the classroom and deliver the expected learning outcomes, the following components are necessary:

Maintain Matching

Without being able to match the same players together during the course of a repeated game, it would be difficult for students to test any strategies, including the ones they developed themselves.

Provide Instant End-of-Game Feedback

Students need to know the outcome from each game so that they can learn and adjust their strategy, if necessary.

Simulate Infinitely Repeated Interactions

If students know the number of times the game will be played beforehand, they may be able to ‘solve’ the game through backwards induction. Although this can be an interesting lesson, it is different from simulating infinitely repeated games. The ability to create that uncertainty of when an interaction may end is a must for repeated games to emulate the real world.

Deliver Aggregated Results

One of most of interesting aspects of repeated games is to allow students to spot trends, if any, during the course of the game. Being able to show results by looking at the repeated games as a whole, i.e. as a super game, offers a powerful way for students to see the emergence of certain strategies and evolution of the relationships, immediately playing it themselves. MobLab has made running repeated games almost effortless. Built on top of the existing ‘Replay’ function, where an instructor can repeat a finished once at a time, an advanced set of parameters are now added to streamline and automate both finitely and infinitely repeated games. Here are some of the highlights:

We have implemented a new parameter for all games called Minimum Periods. This is a threshold where the repeated interactions would last at least the specified number of periods.

To simulate infinitely repeated interactions, instructors can set Ending Probability, so that after the Minimum Periods has been reached, this is the probability that the game will end following the next period. This creates the uncertainty that is parallel to real-world applications.

In addition to the existing per-game summary results, a few of our games have multi-period game results and aggregated statistics to track how each group progressed in the multi-period game as well as how they compare to other groups.

We are very excited about empowering instructors to create an even more immersive learning environment for their students. Students will be able to relate what they have seen and experienced using MobLab to the real world. By limiting the time and effort it would take an instructor to run a repeated game in class, we are hoping that repeated games become an integral part of the social science classroom.

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When things get boring in a chemistry class the instructor can always blow something up. Classroom experiments give economists the same ability to help their students experience the principles they are learning in class that a lab does for a chemistry instructor - minus the risk of setting the classroom on fire.

Science Education Resource Center at Carleton College

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The Ultimatum Game with Chocolates: A Classroom Experiment in AP Psychology

This is a guest post by Beilin Zhang Technical Lead at MobLab.

I am a biologist by training, and like most biologists, I spent most of my time in school thinking about experiments. Through the years, I learned to appreciate the effort involved in and the beauty of well thought out experiments. In fact, some might say I treat experiments seriously.

When my son, a high school junior, mentioned to me that he planned to conduct an Ultimatum experiment in his AP psychology class as his final project, my immediate response was “It is much harder than you think to do an experiment. How much do you know about the subject? Have you looked at what other people have done?” Deep down, I knew I was being a little harsh, but I too wanted my son to appreciate the difficulty and complexity in running an experiment.

My son explained to me that he would like to see if people will act more generously after receiving a generous offer and less so after a stingy offer. That is, if a person receives a generous offer and is about to make the proposal in the next game with a different player, will he be more generous? My son said he had read several papers and had talked to his teacher, and his teacher was actually very interested. I felt much better now since he at least did some research, and then he asked me, “Dad, can I use MobLab’s software”? “Well, of course, our software would be perfect for you. You can get your classmates in a computer lab, set up a Ultimatum game, play as many rounds as you like, matching your peers up any way you want and be done in 10 minutes, with the result to show to everyone”. “That’s great. Thanks Dad”.

A week before the experiment, he told me that the school computer lab was all booked up and he could not get it for the psychology class. The school does not have enough laptops for the whole class, and not everyone had a smartphone. He had to resort to the traditional method of paper and pencil. Our first lesson learned about doing a classroom experiment: things do not always go as planned.

For the next several days, I watched him scrounging envelopes around the house, making labels, creating a spreadsheet with macros for data recording and analysis. He also bought a few pounds of mixed candies from costco, and meticulously put each type into a separate bag and count them (26 bags of different candies ranging from twizzlers to skittles to snickers and butterfingers). These would be how the students were “paid” for their performance in the experiment, as cash was not a viable option. Lesson number two: He learned that experiment preparation is not simple.

The experiment was actually quite successful. His teacher and classmates were very interested in the experiment. It took about 30 minutes to run two rounds, giving out envelopes to half of the class with a card inside for people to write their offers, collecting them back and giving them to the other half of the class to get their responses, recording the data, then reversing the roles and repeating. He found that his classmates were much more generous, offering more than 50% on average. How could that be? It turned out that a couple of his classmates do not care much for candy and offered all of their portion to their partner. One of them also rejected an offer of 60%! Even after removing some of these outliers, the average offer was still considerably higher than 20%. My son figured that may have something to do with the classroom dynamics. He and his classmates had spent a year together and they genuinely wanted to be fair to their friends, despite being anonymous. He saw no correlation between the offer a person received and the offer he made later, but he also talked about some controls he could have done, alternative incentives he could use, and maybe even used a larger sample or different sample in the future. I am just glad he has started to appreciate the importance of proper design!

The last lesson he learned? Use the proper tool. Using the MobLab software would have made his experiment so much easier and he could have done a few more rounds in less time.

I am happy that my son carried it through, despite my initial hesitation. Now that I think back, when I first started doing experiments, I made many mistakes. I learned through my mistakes and got better. A lot of students want to do experiments, but oftentimes they get deterred by the cost or the complexity of running an experiment. We should not ask them to conceive the perfect experiments; instead, we should make experiments much more accessible so they can do them whenever they have some hypothesis or idea they want to test. This is actually why I joined MobLab, to make social science experiments more accessible.

By the way, the high schoolers really liked the chocolates. At the end of the experiment when people came to pick up their rewards, the M&M’s were gone almost instantaneously, and then Kit Kat, Twix, Crunch. All that was left for the parents back home were the Twizzlers and Lemonheads.

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Reality Classroom Storage Wars

You want to teach your students about auctions? Do your students love reality TV? Enter Storage Wars, the reality show that provides viewers with inside access to the drama of auctioning off foreclosed storage units with all of their contents. The folks at A&E know that competitive bidders not really knowing what’s inside the unit makes for good TV. 

Auction Process

In Storage Wars, interested buyers get five minutes to peer inside a storage unit that is up for sale. However, they cannot go inside and they cannot move or touch any of the unit’s contents. After the five minutes is up, an auctioneer begins an English (open outcry, first-price) auction. Bidders harass and outbid each other for a good whose value is largely speculative. Eventually, one party, the high bidder, is willing to outpay all the rest for the storage unit. Only then is s/he allowed inside the unit to begin assessing whether or not s/he can recoup the cost of the storage unit through sale of the goods inside or even earn a profit.

The Winner’s Curse

Your students might already know about auction mechanisms like the English auction or the difference between first-price and second-price but it’s always good to have a refresher. More importantly, you can use the Storage War example to teach Affiliated or Common Value Auctions (most real life auctions fall under these categories). Unlike private value auctions where bidders have different values for the good that are not related to each other, bidders’ values for the contents of the storage unit are likely positively correlated (Affiliated Value) or the same (Common Value). The five-minute inspection from outside gives every bidder a signal, that is, a clue about how much the unit might be worth, but no one knows for sure. Some bidder might think they saw a Porsche while other bidders think it’s a stack of cardboard boxes. The true value is probably somewhere in between. This accounts for the Winner’s Curse phenomenon where the “winner” ends up overpaying for the unit. The winning bidder is usually the one with the highest estimate of the unit’s value, but this “winner” neglects to take into account that others think the unit is not worth as much, often with good reason. This video shows what happens when a buyer thinks they bought something of value, only to find out otherwise, a classic case of the Winner’s Curse. 

Student Bonus

Your students might be shocked, just shocked, that this reality TV show may not be so real. Ask them how they might change their bidding strategy, now knowing that the storage units might be rigged?

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3 Ways to Spruce Up Lecturing Alternate Bargaining

Alternate Bargaining is a mainstay in Game Theory courses every year. It is a simple game that illustrates a typical negotiation and highlights the trade-off between delay costs and share of the pie. Plus, it is a great way to get students to practice writing out extensive form games. Here are 3 fun videos to engage your students when it comes to the Alternate Bargaining game. 

The Game

A sum of money (let’s say $10) is given to two students.  The money now belongs to the students and it is up to the students how to divide the amount of money between them. One student, we’ll call her Student A, will be the first to make an offer to the other student on how to divide the money.  The second student, Student B, will see the offer and will have to make a decision whether to accept or reject the offer. If the offer is accepted, both students walk away with the proposed deal. If the offer is rejected, it is Student B’s turn to make a counter-offer. However, after a rejection, the $10 will shrink by some percentage (say 10%). That means that Student B can only make an offer on how to split $9. The bargaining will continue until one of the students accepts an offer or the money runs out.

1. The Office – The Surplus Episode.

Few things can perk up a group of students like a clip or comedic example from the hit TV show The Office. You can find this episode easily on The Economics of the Office (Season 5, Episode 10), but we will briefly go through the premise: The episode starts out with the manager of the office finding a surplus of $4,300 in the company’s budget. He brings it to the attention of his employees and they start haggling over whether to use the money to buy new chairs or a new copier. The negotiations continue throughout the day when the manager realizes that if he doesn't spend the extra money, he will get 15% of the $4,300 in his next paycheck as a bonus for saving the cash. He informs his employees that if they can’t decide between the new chairs and new copier by the end of the day, he will take the bonus. Basically, he turns it into an Ultimatum Game for his employees. Now, there is a significant cost if the employees remain undecided. Soon, the employees realize they would be better off agreeing to something, rather than getting nothing and decide to get new chairs. The manager, confident in his employees’ inability to reach an agreement, shops for some extravagant personal items. And comedy ensues.

2. Robert De Niro and Ricky Gervais show you how it’s done:

Stardust is a swash-buckling adventure set in the magical kingdom of Stormhold. In this clip, Ricky Gervais, British actor & comedian, shows you how to negotiate for lightning. The seller, Robert De Niro, runs a tight ship and almost walks away with his product. Ricky Gervais may have started out with incomplete information about Robert De Niro's bargaining type, but he soon discovers just how tough De Niro is. What makes such a bargaining posture a credible threat and when is it just empty talk?

3. Negotiations can get very animated:

This charming clip makes it clear that taking your time to negotiate can lead to some very serious repercussions (like no deal at all OR no legs because the other party chopped off your legs with an exclamation point!) You can ask your students to come up with a script of a real-life economic negotiation that mirrors the disintegration in the video.

Student Homework Bonus!

Find another example of the alternate bargaining game reflecting from daily life, pop culture, or another game. Have the students write their example in extensive form and specify the strategies.