Spontaneous order


Jason Collins


January 29, 2013

Another interesting old paper off my reading pile has been Robert Sugden’s Spontaneous Order.

Sugden asks us to picture a scenario where you are travelling down a road towards another car. You have two alternatives - move to the left or right. The other car has the same choice. If you pick the same, you pass safely. A game theoretic analysis tells us that there are three Nash equilibria – that is, three sets of strategies that neither driver would have incentive to deviate from (or put yet another way, each driver’s strategy is a best response to the other driver’s strategy). The three are: both cars move left; both cars move right; or each car moves left or right with 50 per cent probability.

But which strategy do they choose? Sugden writes:

[T]he ultimate objective of game theory is to show that rational analysis uniquely prescribes a particular strategy for each player in a game. It is as if each player sits in a room by himself, knowing nothing about the other player except his utility function and that he is rational, and knowing nothing about how the game may have been played by other people. Each player must decide what to do, applying unlimited powers of rationality to this severely restricted information and to nothing else. …

One of the major achievements of Thomas Schelling … has been to show that games like Chicken cannot be “solved” in this way. The ideally rational but completely inexperienced players of classical game theory would find they had insufficient data to determine what they should do. In contrast, ordinary people with limited rationality but some degree of experience and imagination might have no difficulty in coordinating their behavior. On this view, the program of classical game theory is a blind alley: it requires us to throw away the information that players need if they are to work out what it is rational for them to do. …

If we are to coordinate our behavior, as we both wish to do, we must rely on some shared notion of prominence. Our common experience of English driving provides the clue we need. Steering left is prominent because it is common knowledge that this is what people generally do: we have each observed this, we can each assume the other has observed it, and so on.

But this raises a new question. Where does this experience come from? Why steering to the left?

If we are to explain why one convention is found rather than another, it is not very useful to start from a comparison between a world in which everyone follows one convention and a world in which everyone follows the other: either of these worlds, once achieved, would be self-perpetuating. Instead we must consider the process by which conventions evolve. More particularly, we must look at how they start to evolve. Once a convention has started to evolve - once significantly more people are following it than are following any other convention - a self-reinforcing process is in motion. The conventions that establish themselves will be the ones that can take root (biological metaphors are almost unavoidable) most quickly in a convention-free world.

I have always been a fan of arguments that recognise the path dependent nature of evolution. There are many possible outcomes, but various historical contingencies shape the result.

A convention can start to evolve as soon as some people believe that other people are following it. But what gives rise to this initial belief? One possibility is that the same forces are at work as enable people to coordinate their actions without communication in unrepeated games. Some forms of coordination are more prominent than others, and people have a prior expectation of finding the most prominent ones. But, I have argued, prominence is largely a matter of common experience. The implication is that conventions may spread by analogy from one context to another. If it is a matter of common knowledge that a particular convention is followed in one situation, then that convention acquires prominence for other, analogous situations. For example: on my journey to work there is a narrow bridge, not wide enough for two vehicles to pass. If two drivers approach from opposite directions, which of them should give way? Coming on this problem for the first time, my prior expectation was when the drivers came into view of one another, whoever was closer to the bridge would be given the right of way. This expectation-which proved correct-was based on an analogy with the “first come, first served” principle.

This line of reasoning has some relevance to arguments about the evolution of cooperation.  In A Cooperative Species, Bowles and Gintis note that where there are repeated interactions between people, there can be infinitely many equilibria. This concept is known as the folk theorem. Due to this possibility, Bowles and Gintis suggest that it is unlikely that cooperation could evolve in such a situation purely by self-interested rationality. How would the parties reach equilibrium, and why would it be the cooperative one? But as Sugden’s argument suggests, if certain equilibria have prominence, possibly by historical accident and the shared experience of the actors, there may be more scope for cooperation. Humans are not perfectly rational beings solving a problem from scratch. We are evolved creatures with a history and experience.