#teachecon

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.

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?

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!