TLS: Logic at bay

by Philip Pettit

THE STAG HUNT AND THE EVOLUTION OF SOCIAL STRUCTURE.
By Brian Skyrms. 149pp.

Cambridge University Press. £40 (paperback, £15.99).
US $55 (paperback, $20.99). - 0 521 82651 9

T. S. Schelling, the recent Nobel Laureate in Economics, once presented an attractive model of how segregated housing could come about. Distribute an even number of black-and-white draughts pieces on a board in a more or less random pattern. Take the pieces to represent households of two different religious or ethnic backgrounds, and suppose that while no household is strongly segregationist in mentality, each wants to have at least one third of its neighbours to be of its own kind in the eight squares or plots that surround its own, four on the sides and the four on the corners. And now begin to move those pieces as if they each had a strategy of moving from an undesirable to a desirable neighbourhood.


When you have moved the initially unhappy pieces, other pieces will become unhappy and you will have to move them also, in a second round; and for the same reasons you may have to go to a third and fourth and further round as well. The intuitively very surprising thing, however, as Schelling pointed out, is that from any more or less random starting distribution on the board, these rounds will almost invariably take you to a highly segregationist pattern, with black pieces clustering with black, and white with white. A not very segregationist strategy on the part of each household in the community will lead under an "evolutionary dynamic" to a more or less totally segregated outcome.


Schelling's toy model of segregation offers a good way of presenting the topics covered in this dense but exciting book. Where Schelling focuses on the specific problem of avoiding segregation, Brian Skyrms attends to the problem of dealing with a much more general predicament that he describes, after a story from Rousseau, as the stag hunt. And where Schelling's model uncovers the effects of one particular strategy under one set of assumptions, Skyrms explores many different strategies, under many different sets of assumptions.

The Stag Hunt and the Evolution of Social Structure is comprehensive and ambitious in scope. It is informed by an evolving body of theory that spans biology, economics and mathematics, and it is developed on the basis of experiments in behavioural economics as well as on the basis of the vast computer simulations that are now possible. These simulations play a role analogous to that of Schelling's simple draughtboard.

The opening claim of Skyrms's book is that whereas many social theorists have tried to model a range of social predicaments as instances of the "prisoner's dilemma", most fit the stag hunt better. In the classic prisoner's dilemma, two conspirators are separately offered a deal designed to make each confess (ie, defect on the other). Each is given a deal under which he will do better by confessing to the joint crime no matter what the other does.

If the other refuses to confess (cooperates), the other will go to prison for twelve years, whereas he, by confessing (defecting), will go free. If the other also confesses (defects) they will both get ten years, but were he to refuse to confess (were he to cooperate) he would get twelve. If neither confesses (if they cooperate with one another) they will be put away on some trumped-up charge for two years, so that joint cooperation is attractive. But in this scenario, joint cooperation is unlikely. The worst pay-off of all attaches to cooperating while the other defects, so that cooperation is hazardous, and the best pay-off attaches to defecting while the other cooperates, so that defecting is tempting. Lone defection is more attractive than joint cooperation, joint cooperation is more attractive than joint defection, and joint defection is more attractive than lone cooperation.

The change in the stag hunt game is that while lone cooperation remains the worst outcome, joint cooperation becomes more attractive than lone or joint defection. Thus while no one is tempted to defect on others, they will each want an assurance that others are going to cooperate before cooperating themselves; there is still a danger or risk of ending up in the worst position, as the lone cooperator.

Rousseau's story casts the members of a team that is hunting a stag as the cooperators and defection as the act of leaving the team in order to chase a hare on one's own, where this may make the team too small to catch the stag.

Getting a hare for sure is better than chasing a deer in a team that may not catch it; but being part of a team that successfully hunts a stag is better than managing to get a hare.

Skyrms is certainly right that this sort of predicament is pretty typical of social life. Getting together in successful compacts with others is often better for each of us individually than refusing contracts or reneging on contractual arrangements, since such "defection" will mean that we are marginalized. But entering a compact is a hazardous business, if the worst outcome of all is to be the only one doing his or her cooperative bit. What Skyrms does in this book is to explore a variety of factors that can make it easier or harder for players in a stag hunt game to achieve a cooperative outcome. In particular, he looks at effective factors within an evolutionary framework akin to Schelling's, where the aim is to track the outcomes that are likely to emerge over a number of rounds.

The field to which the work belongs is that of evolutionary game theory, rather than game theory applied only at a particular time.

The factors that are likely to affect success or failure include: the different strategies adopted by participants at the beginning of the evolution; the rule followed by players in revising their strategies at any later round; the proportions of those strategies in the population; the clustering or lack of clustering among players with similar strategies; the ability of players to select those with whom they wish to associate; and their capacity to communicate with each other, even in a situation where cheating is possible.

Skyrms concentrates in particular on how the prospects for an increase in cooperation, and in the resistance of a group of cooperators to invasion by defectors, are affected by clustering, communication and the capacity to associate with whoever you want.

The book is a treasure trove of interesting and intriguing results on the relevance of such factors for the solution of the stag hunt game, and so for the achievement of a certain social order. Readers may find it hard to put the results together into a single general lesson or set of lessons but no one will fail to be surprised as Skyrms shows, case after case, just how counter-intuitively things can work out. If you were surprised to hear of Schelling's result, be warned: you ain't heard nothing yet.

The only respect in which I found the book disappointing is that it never stretches beyond the confines of a progress report on where work in this area has been going. It is terse to the point of sometimes being telegraphic and it doesn't give any sense of where the approach fits with other approaches, or what its particular limitations are. One limitation that strikes me, for example, is that I do not see how the stag hunt applies to the "free-riding" type of predicament that is central to so much social life. It is characteristic of this predicament that, short of coercive law, or perhaps the sanction of disesteem, no defector can expect to be punished by a large mass of others if their individual defection makes no discernible difference. Those listeners who fail to contribute to public radio in the US, for example, will not expect to be punished by contributors, even if their cover is blown. Lone defection remains more egoistically attractive in this scenario than cooperation, since one will be able to enjoy the cooperative good without paying the cooperative cost. In this respect the situation resembles the prisoner's dilemma more than it does the stag hunt.

Such shortcomings in the book are inevitable, given that it is condensed into a volume of not much more than a hundred pages. Experts may be grateful for the way in which it cuts to the chase, but most others would benefit from a more extensive, more leisurely treatment of these wonderful topics. Inside this thin book there is a fat tome waiting to get out. I hope that Brian Skyrms will give us that tome one day; but in the meantime there is lots to celebrate about this rather more austere trailer.