Mind Your Decisions

Multiple Equilibria in Coordination Games: Getting to Better Outcomes

Every Tuesday is a Game Theory article at Mind Your Decisions.

Some people criticize game theory (and to some extent economics as a discipline), calling it unrealistic and focusing on selfish behavior. Just check out this comment from a review of James Miller’s Game Theory at Work:

You and I both know that in reality, things simply don’t work that way between real, living, breathing people. People have feelings and emotions and many of the examples in this book do not take into account what would REALLY happen in the real world.

If that is how you view the world, then I can summarize Miller’s entire book and examples by saying “The best way to use Game Theory in real world situations is to just think of the best way you can screw other people and be an arrogant SOB”…and if that is true, then I guess Miller is the world’s greatest Game Theorist.

I don’t agree with the quote, but I guess I haven’t been doing any thing to dispute it. After all, in recent weeks, I have written about “selfish” topics like how you make your threats more credible, ways you can outguess an Indian dinner host, and the unrealistic topic of how you better survive a deadly three-way gunfight (truel) by lying about your skills. Why the focus on ruthlessness and selfishness?

Maybe game theory researchers are biased toward conflict. Or maybe those are the topics that appeal to college students who have short-attention spans. It is hard to explain, but believe me, game theory is more than just understanding selfish behavior. Game theory is useful, and one famous example is how its principles turned a previously abysmal spectrum allocation into an auction that is a multi-billion dollar operation.

For all its success, game theory has yet to change its image of selfishness. Game theory is about analyzing incentives and player interactions, which leaves plenty of room for more “wholesome” topics. In fact, there is a whole set of problems dealing with getting people to coordinate for better outcomes. Today, I discuss a few examples of how you can use game theory to get people to coordinate.

Let’s say you are introducing a new debit card and want to get people to use it. How can you convince people to use your card, and how can you get businesses to install the necessary verification hardware and software? Before you market your product, it would be a good idea to analyze the incentives of credit card users and business owners. Where would you start?

You could start by analyzing a similar problem that no doubt most of you have encountered when you shared an apartment with a friend.

Cleaning Your Apartment with Roommates

You and your friend have recently moved in together. You both care enough about hygiene that a clean apartment is desired over a dirty one. But neither of you is thrilled about cleaning the place, and you are not rich enough to hire a service. If you don’t discuss cleaning with each other, what does game theory predict will happen?

Here is how we can model this situation as a game. The players are you and your roommate, and each of you can choose either “clean” or “not clean.” If you both decide not to clean, then the apartment ends up dirty, and each of you gets a payoff of 0. If you both decide to clean, then the apartment ends up clean, and you each get a payoff of 1. If, however, one of you cleans and the other does not, the apartment is only half cleaned. The roommate that cleaned spent energy is angry about the half-cleaned place and gets a negative payoff of -1, whereas the roommate that did not clean is somewhat happy and gets a payoff of 0.5.

That last paragraph can be nicely summarized in the following table:

The black colors indicate your choices of “clean” and “not clean” as well as your payoffs. The blue colors identify your roommate’s choices and payoffs. For instance, if you choose “clean” and your roommate chooses “clean,” that corresponds to the top left box where you both get a payoff of 1. If you choose “clean” and your roommate chooses “not clean,” that is the top right corner where you get -1 and your roommate gets 0.5.

This game assumes that you and your roommate are too busy to talk to each other, so you have to guess what the other person is doing. To analyze this sort of game, you need to decide on a course of action given what you think your roommate will do. For instance, if you think your roommate will clean the apartment, you look at your payoffs in the left hand column for the actions of “clean” and “not clean.” You see that “clean” gives you 1 and “not clean” gives you 0.5 so you will decide to clean. Similarly, if you think your roommate will not clean, then you look at the right hand column to see that “not clean” gives you 0 and “clean” gives you -1. You will of course pick “not clean.” Your roommate thinks the same way and analyzes to determine the best course.

It turns out that both you and your roommate will clean if and only if the other person does so. What’s the likely outcome to the game? The “default” condition is that neither of you is cleaning, and since you cannot communicate with each other, neither of you will decide to clean. Accordingly, the apartment will remain dirty. If you could coordinate to clean and both change, then it would be possible to have the best outcome where the apartment is clean.

Now for a reality check, the model does not capture what people do in real life. We can talk to each other, so we set up cleaning schedules to coordinate, or we pay for cleaning services. Nevertheless, the model does apply for roommates who are too busy or are too passive aggressive to talk to each other. I’ve definitely seen this happen in college.

But there is a bigger lesson from the model. It is that players who want a good outcome (like a clean apartment) may unable to do coordinate because they cannot escape the “default” situation they started in.

You might ask, “Couldn’t the players just talk to each other and sort this problem out?” In the example of roommates, yes, players could talk to each other. But in many cases, it is hard for players to communicate so they will have a tough time coordinating. For instance, consider a game involving businesses and customers. Businesses have a very hard time getting feedback with customers (how many times have you answered a courtesy survey call?) to coordinate on a new idea. What happens then?

This happens to be the very situation Visa faces when it introduces a new product, like its check card. Their solution of a clever commercial suggests to me that some one in their staff understands game theory very well.

The Visa Check Card

When the Visa check card came out, both consumers and businesses had to face a decision of whether to use, or adopt, the new card.

I think about the game in the following way, where I wrote businesses’ choices and payoffs in black and customers’ choices and payoffs in blue:

Here is the logic for the payoffs: currently customers and businesses have not adopted the new card, so we’ll say they both get 0 in the status quo. If customers alone adopt, they get -1 for wasting time on getting the card which has no benefit since it cannot be used any where. If businesses alone adopt, they get a payoff of -1 for installing and paying for a service that no customers are using. Assume that if both consumers and businesses adopted, they would both be happier. Customers will get a payoff of 1 for since they can check out faster than with cash or by writing a check, and businesses, though they pay money to have the service, presumably get more customers and revenue so they also get a payoff of 1.

In this game, businesses and customers want to match each other on their action. If both adopt, they would be in the best situation. But since the card is new, the current situation is that customers and businesses pick “not adopt.” They are stuck like the roommates in a dirty apartment and neither side is able to adopt the card successfully to get to the better outcome.

How would one change that? Visa tackled this problem through a brilliant commercial (youtube).

As consumers, most of us see the commercial’s message that the check card can get us out faster than cash or a check.

The brilliance of the commercial is that it simultaneously appeals to businesses. The subtle message of the speedy lines is that the check card can help a business get more customers and generate higher revenue.

The main lesson: In coordination problems, it is not good enough that people try to change the situation. You need many people to change simultaneously or no change will occur.

And I guess this lesson brings me back to why game theory is about selfishness.

Game Theory’s Selfish Reputation

In some sense, game theory’s reputation is a coordination problem. I bet many game theorists would prefer to have a better image, but the default is that the field is about selfish behavior. It is not that convincing for me alone to write about its nicer topics, as reputation is based on what the majority writes. I can write to many people, or start a Facebook group, but it would be hard to coordinate the mass of game theorists. So we game theorists too are stuck with a bad outcome, and a selfish label, since we fail to coordinate.