An economic excuse to cancel your date tonight

5 game theory ideas to change the way you think

My mom told me the other night that I should write another post about strategy. This spring, I took a class called Games and Information, an extension of the introductory Game Theory class (that is open for you to take online!). Both are taught by Ben Polak, one of the leading behavioral economists and most amazing professors at Yale.

Here are my favorite concepts I learned in class, with applications to the real world (online dating, Ubers, job applications). Most of them use backward induction, which is a strategy that is exactly what it sounds like: starting from an imagined/ideal outcome, and working backward to see what you should do at the very beginning.

Ok, let’s get into it! I hope you find these ideas as exciting and useful as I do.

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1. The Winner’s Curse and Overpaying Soccer Stars

In an auction where everyone has their own estimate of the true value of the good, there’s an easy trick to fall for. In class, my professor “auctioned off” a jar of pennies. We all wrote down a sealed bid, and understood that the highest bidder would win the jar. The problem was that the intrinsic value of the jar was around $5, and the winning bid far exceeded that. We all had our guess about how many pennies were in the jar, but to actually win, yours had to be the highest one.

The winner’s curse is that the winner of the auction ultimately pays too much.

There is a cure! Your bid is based off of only one piece of information—your estimate of how much the object is worth. But if you were to win, you would have much more information—that everyone else’s estimations were less than yours. You only care about the value in the event that you win. So you should bid as if you know you’re going to win.

Sometimes people chase the feeling of winning. The winner’s curse isn’t limited to a jar of pennies. It also applies to oil fields, IPOs, and sports stars. 36-year-old soccer player Lionel Messi signed a 2.5 year contract with Inter Miami that is worth up to $150 million from his salary, signing bonus, and equity. I just watched Moneyball on the plane, so I’m of the opinion that no single player can be worth that much.

Takeaway: Winning isn’t everything. It may even be worse than losing.

2. The Optimal Stopping Rule and Modern Dating

We search for things all the time: where to eat, what to buy, whom to date. Intuitively, searching for more options is appealing—we want to find the best food, house, partner. But search is also costly: it takes time, money, energy, and attention. The optimal stopping rule tells you when to stop searching and to just take the best option you’ve found so far. It’s guided by cost-benefit analysis: the expected benefit from sampling more options versus the additional search cost.

Let’s use the example of dating. If you want to find a long term partner, you can go on as many dates as you want to search for the right person. You might feel that maximizing the number of dates you go on will increase the likelihood of finding “the one.” But each additional person you search for has a cost: the energy put into meeting them (in real life or on an app), the taxi fare downtown, the bill at the bar/restaurant (if you’re the one paying), and the time you spend on the actual date. If this additional dinner turns out to introduce you to the person you end up with, that’s great. Otherwise, it’s a waste of time.

The factors that affect the optimal stopping rule are the cost of search, how likely it is that an extra date will be with your soulmate, and how impatient you are about finding a partner. Dating is also an example of search with no recall. Once you reject someone, you usually can’t go back and retrieve them if you change your mind.

Takeaway: Looking for more options isn’t always better. You’ll probably be happier making peace with what you’ve already found!

3. Incentive Compatibility and Uber Rides

Collusion happens all the time. Uber and Lyft charge similar amounts for car rides in New York City. It’s around $40 to get from the Upper West Side to SoHo, and you won’t get a huge discount from switching from Uber to Lyft, or vice versa. But if Lyft decided to deviate from these high prices and charge $30 per ride, then everyone would convert. Lyft would capture all of the rides today, and benefit in the short term. But then tomorrow, Uber would also lower its prices in order to regain its share of the taxi market. Then both companies will equally split the customers again, but making $10 less per ride. This is the “punishment” phase. Since Lyft cheated, Uber will “punish” them forever. Both companies are worse off.

When Lyft is deciding whether they want to deviate, there’s an important incentive constraint that will tell them whether it’s worth it:

The temptation to cheat today must be less than the reward of continuing the relationship (getting $40 forever) minus the punishment after cheating (getting $30 forever) for Lyft to cooperate. The values on the right side are also discounted by δ, which we can think of as the probability the relationship between Uber and Lyft still exists tomorrow.

In reality, Uber makes roughly 9x the revenue of Lyft. But we learned in class that if two parties share the prize unequally, the party with the smaller share has more incentive to deviate. Let’s say Uber and Lyft share profits 90/10. Lyft has more to gain by cheating and capturing 100% of the profits.

In equilibrium, collusion is a self fulfilling tacit agreement. We (the riders) pay more, and Uber and Lyft enjoy the inflated prices.

Takeaway: Collusion does not need a written contract, but the agreement needs to be attractive enough to maintain long term stability.

4. Using Information to Persuade and Guilty Verdicts

Let’s say there are two players in a game: a prosecutor and a judge. The judge’s goal is to determine whether a defendant is innocent or guilty correctly. The prosecutor’s goal is to maximize convictions, regardless of guilt.

The prosecutor is able to search for and provide information to the judge. If she wants to influence the verdict, she cannot lie or hide evidence she finds (assuming she abides by the law), but she can control the investigation. She decides what evidence to look for: whom to interview, what to ask, which tests to run. The prosecutor can either look for evidence that would prove the defendant guilty—a smoking gun—or evidence that would prove them innocent—an alibi.

Which one should she look for?

My first instinct was that the obvious choice is to look for smoking guns—obvious declarations of guilt. But the prosecutor should actually look for alibis. An alibi is proof of innocence, but a lack of an alibi does not prove that someone is guilty. Not all innocent people have alibis, so there could be false indications of guilt, which are the prosecutor’s friend. Looking for alibis increases the likelihood of guilty verdicts. More innocent people will go to jail.

The ability to be the provider of information is extremely powerful, even if you cannot lie or conceal results. You may want to look for imperfect information to manipulate the actions of the recipients.

Takeaway: If there is information in finding something, then there is information in not finding it. Sometimes it suits you to look for alibis if you want to persuade people of guilt!

5. Social Learning and Information Cascades

Groups of people often face similar decisions: where should I send my kids to school? Should I invest in this company? Should I adopt a new technology?

In these cases, we often see imitation. We trust that other people might know more and have better judgment, feel social pressure to conform, or see a network effect where the outcome is better when more people make the same choice (like investing in a stock).

Social learning refers to a context where people cannot directly communicate the private information they hold to others, but the choices they make are publicly observable to their successors. Let’s say I’m a parent, and I don’t tell other parents that I know school X has great teachers. But they can see that I’m sending my kid there. An information cascade happens when people ignore their own private information and simply follow earlier players’ choices. All the parents send their kids to X without doing their own research.

Following the crowd is individually rational, but it can be collectively wrong. The decisions of early movers are much more important in social learning. The outcome heavily relies on their luck.

I think there are two interesting scenarios to consider.

1. When I’m applying to a job, the employer has no idea how many other jobs I’ve applied to and been rejected from. But if they saw that 10 other firms had rejected me, they might also reject me without considering my resume at all.

2. In a professional round table discussion, if senior members speak first, the rest of the people at the meeting might be more likely to agree with them. So it might be helpful to let the interns/junior members go first, if you want them to be honest.

Takeaway: Following the crowd is individually rational, but it can be collectively wrong. Watch others, but remember your own instincts. 

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I’m not planning on becoming an economist, but the two game theory classes I’ve taken have been some of my favorites at Yale. There’s something so satisfying about watching the theory play out in real life. Of course, the real world is messy and complicated and deviates from the math, but the principles are there. And now that you know them, you’ll see them everywhere.

I’ll be around in the comments, have a great week!