SITUATION: A COORDINATION GAME—DRIVING CONVENTIONS
We next look at an example of a coordination game, which has the property that players have a common interest in coordinating their actions. A coordi- nation game that most adults engage in every day is the choice of the side of the road upon which to drive. It’s not really that important whether everyone drives on the left (as in England and Japan) or on the right (as in the United States and Chile), but just that we agree to a standard.
The game between two drivers is represented in FIGURE 4.6. It is easy to verify that there are two Nash equilibria. One has both Thelma and Louise driving on the left, and the other has both driving on the right. If Louise drives on the left, then Thelma’s payoff from doing the same is 1, while it is �1 from driving on the right. Thus, left is indeed best for Thelma, given that Louise is choosing left. The same argument verifies that Louise’s
driving on the left is best, given that Thelma drives on the left. In fact, since this is a symmetric game, I can invoke the magic words—“by symmetry”—to conclude that Louise’s strategy of left is optimal as well. This makes (left, left) a Nash equilibrium. An analogous argument allows us to conclude that (right, right) is a Nash equilibrium.
In contrast, (left, right) is not a Nash equilibrium. Given that Louise is driv- ing on the right, Thelma’s payoff from driving on the left is �1, while she can do better by driving on the right and getting a payoff of 1. It is straightforward also to argue that (right, left) is not a Nash equilibrium.
Nash equilibrium doesn’t tell us which standard a population of drivers will settle upon; instead, it tells us only that they will settle upon some standard. History shows that societies do settle upon a driving convention, and which side of the road it is can vary across time and space. It is estimated that about 75% of all roads have the custom of driving on the right.3 Although today everyone con- forms to a driving convention because it’s the law, conventions developed long before they were legislated (and, indeed, long before automobiles came on the scene). Generally, the law just codified a custom that had developed on its own.
Suppose an American driver and an English driver are driving towards each other on neutral ground. Each is driving a car from her own country. All of this is common knowledge. On which side of the road will each drive? Will it turn into a game of Chicken? Is Nash equilibrium a good predictor?