Rioting as a coordination game

There are many situations that require decision-makers to coordinate their decisions. These include situations where we are better off doing the same as everyone else, or better off doing something different to everyone else. Economists refer to these situations as coordination games (such as in this post about the panic buying of toilet paper). Earlier this week, the Scholar's Stage blog had a post about rioting that demonstrates a coordination game at work:

Let us say you are a man inclined towards a riot...

Yet you and all those like you have a problem. The man inclined towards a riot cannot simply wake up one day and begin one. The lone rioter is not a rioter at all. He is simply a common vandal. The system can handle that problem with ease. This is the sorrow of the would-be rioter: he cannot begin his riot until he is sure all the other would-be rioters will pound the streets besides him.

Up front I want to point out that people may have good reason to be angry (and in the case of recent events, justifiably so), and have good cause to have their voices heard. However, there is a difference between protest and rioting (which as the Scholar's Stage blog post notes, explains why riots have also occurred after good news like sports team victories). So, the analysis of rioting need not rely on consideration of any underlying anger.

Now, let's consider this situation using some simple game theory. To keep things simple, let's assume that there are just two potential rioters, Person A and Person B. There are two strategies: riot, and not riot. Assuming that this is a simultaneous game (both players' decisions about strategy are revealed at the same time), then we can lay out the game as a payoff table, like this:

The payoffs are measured in utility (satisfaction, or happiness), for the two players. If both players riot, they get to release their angry and smash some stuff up, and both players receive positive utility (utility = +5). If one player riots and the other doesn't, then the rioter is easily singled out by police as a vandal and subject to punishment (utility = -5), but the player not rioting is no better or worse off than before (utility = 0). If neither player riots, then both are no better or worse off than before (utility = 0).

Now, to find the Nash equilibriums in our game, we can use the 'best response method'. To do this, we track: for each player, for each strategy, what is the best response of the other player. Where both players are selecting a best response, they are doing the best they can, given the choice of the other player (this is the textbook definition of Nash equilibrium). In this game, the best responses are:

1. If Person B chooses to riot, Person A's best response is to riot (since +5 is a better payoff than 0) [we track the best responses with ticks, and not-best-responses with crosses; Note: I'm also tracking which payoffs I am comparing with numbers corresponding to the numbers in this list];
2. If Person B chooses not to riot, Person A's best response is not to riot (since 0 is a better payoff than -5);
3. If Person A chooses to riot, Person B's best response is to riot (since +5 is a better payoff than 0); and
4. If Person A chooses not to riot, Person B's best response is not to riot (since 0 is a better payoff than -5).

Notice that there are two Nash equilibriums in this game: (1) where both players choose to riot; and (2) where both players choose not to riot. Which of these two equilibriums will obtain depends on what each player thinks the other player will do. So, if there is good reason to believe that the other player is not going to riot, your best response is also not to riot (and vice versa for the other player). But, if there is good reason to believe that the other player is going to riot, your best response is to riot too (and vice versa for the other player).

How does each player work out what to do? Notice that both players in this game prefer to riot (they are better off both rioting, than both not rioting). However, you wouldn't riot if you couldn't be sure that the other player was going to as well. If one of the players can send a credible signal about their strategy to riot, then everyone knows that rioting is on the cards, and a riot develops. So, what makes a credible signal? The Scholar's Stage blog quotes David Haddock and Daniel Posby (Understanding Riots):

Certain kinds of high-profile events have become traditional “starting signals” for civil disorders. In fact, incidents can become signals simply because they have been signals before. What ignited the first English soccer riot has been lost in the mists of history; but they had become a troublesome problem sometime during the nineteenth century, as Bill Buford (1991) makes clear in quoting old newspaper accounts in his Among the Thugs. Today, there is a century’s weight of tradition behind soccer violence. People near a football ground on game day know that a certain amount of mischief, possibly of a quite violent kind, is apt to occur. Those who dislike that sort of thing had best take themselves elsewhere. Certain people, though, thrive on the action —relish getting drunk, fighting, smoking dope; enjoy the whiff of anarchy, harassing and beating respectable people and vandalizing their property. Such people—hooligans—make a point of being where the trouble is likely to start....  In Detroit in recent years, “Devils Night” (the night before Halloween) has become a springboard for multiple, independent, almost simultaneous acts of arson. These are examples, baleful ones, of how culture, habit, and tradition can overcome major organizational barriers to cooperative social endeavors and lower the cost of transacting business.

A credible signal has to be costly, and other players have to be sure that the signalling player will follow through on the strategy choice (in this case, rioting). Throwing the first stone (literally and figuratively) is a costly action, and demonstrates the willingness to riot. However, players need to know that it is 'safe' to be the person throwing that stone. Coordinating around certain 'trigger events', where rioting is 'expected' behaviour (or at least, not unexpected) provides the appearance of safety and therefore provides a way of overcoming the uncertainty inherent in this coordination game.

Based on this simple analysis, it is obvious that even something as chaotic as a riot requires some coordination.

[HT: Marginal Revolution]