The Arithmetic of Mutual Help

M. Nowak, R. May and K. Sigmund

The principle of give and take pervades our society. It is older than commerce and trade. All members of a household, for example, are engaged in a ceaseless, mostly unconscious bartering of services and goods. Economists have become increasingly fascinated by these exchanges. So have biologists. Charles Darwin himself was well aware of the role of co-operation in human evolution. In Descent of Man he wrote that “the small strength and speed of man, his want of natural weapons, etc., are more than counterbalanced by his … social qualities, which lead him to give and receive aid from his fellow-men”.

Textbooks on animal behaviour are filled with examples of mutual aid: grooming, feeding, teaching, warning, helping in fights and joint hunting. In ecology symbiotic associations are increasingly seen as fundamental.

But at the same time, the ubiquity of co-operation seems to have become ever more paradoxical. What prevents mutualists from turning into parasites? Why should anyone share in a common effort rather than cheat the others? Natural selection puts a premium on individual success. How can this mechanism shape behaviour that is altruistic in the sense that it benefits others at the expense of one’s own progeny?

Kin Selection and Reciprocal Aid

There are two main approaches to this question that go under the headings of kin selection and reciprocal aid. These concepts are not mutually exclusive, but they are sharply distinct. Kin selection is rooted in genetics [“Kin Recognition” by D.W. Pfennig and P.W. Sherman, p. 68].

If a gene helps in promoting the reproductive success of close relatives of its bearer, it helps in promoting copies of itself. Within a family, a good turn is its own reward.

But a good turn to an unrelated fellow being has to be returned in order to pay off. Reciprocal aid - the trading of altruistic acts - is essentially an economic exchange. It works less directly than kin selection and is therefore more vulnerable to abuse.

Two parties can strike a mutually profitable bargain, but each could gain still more by withholding its contribution. In modern society an enormous apparatus of law and enforcement makes the temptation to cheat resistible. But how can reciprocal altruism work in the absence of those authoritarian institutions?

Prisoner's Dilemma

To demonstrate the conundrum, Robert L. Trivers, a sociobiologist (and, fittingly, a former lawyer), now at the University of California in Santa Cruz, borrowed a metaphor from game theory known as the Prisoner’s Dilemma. As originally conceived in the early 1950-s, each of two prisoners is asked whether the other committed a crime; their level of punishment depends on whether one, both or neither indicates the other’s guilt.

This situation can be viewed as a simple game. The two players engaged in it have only to decide whether they wish to co-operate with each other or not. If they both want to co-operate, they get a reward of three points each. If both defect (by not co-operating), they get only one point each. But if one player defects and the other co-operates, the defector receives five points, whereas the player who chose to co-operate receives nothing.

Will they co-operate? The reward for mutual co-operation is higher than the punishment for mutual defection, but a one-sided defection yields a greater reward. This temptation endangers almost every form of co-operation, including trade and mutual aid, and implies that the best move is always to defect, irrespective of the opposing player’s move. The logic leads inexorably to mutual defection.

Most people feel uneasy with this conclusion. They do often co-operate, in fact, motivated by feelings of solidarity or selflessness. In business dealings, defection is also relatively rare, perhaps from the pressure of society.

Co-operative populations are sometimes dominated by a strategy called Generous Tit-for-Tat, a strategy named Pavlov by the mathematicians David and Vivien Kraines. After experiencing a reward for mutual co-operation, a Pavlov player repeats the former co-operative move. After getting away with unilateral defection, it similarly repeats its last move. But after being punished for mutual defection, Pavlov switches to co-operation. This principle of “win-stay, lose-shift” seems to work well in many situations. In animal psychology it is viewed as fundamental: a rat is ready to repeat an action that brings reward, whereas it will tend to drop behaviour that has painful consequences. The same crude application of carrot-and-stick underlies most attempts of bringing up children.

Fixed in Flatland

It should come as no surprise that co-operation is easier to maintain in a sedentary population: defectors can thrive in an anonymous crowd, but mutual aid is frequent among neighbours.

Consider a spatially constrained version of the tournament, with each member of the population sitting on a square of an extended chessboard. Each player is either a pure co-operator or a pure defector and interacts only with eight immediate neighbours, playing one round of the Prisoner's Dilemma with each.

A lone co-operator will be exploited by the surrounding defectors and succumb. But four co-operators in a block can conceivably hold their own, because each interacts with three co-operators. Conversely, lone defectors will always do well, because they will be surrounded by exploitable co-operators. But by spreading, defectors surround themselves with their like and so diminish their own returns.

It is certainly possible that co-operators are wiped off the board. But we frequently find various shifting mosaics, with both strategies being maintained. Mixtures of pure co-operators and pure defectors can coexist indefinitely. The important requirement is that each player should not interact with too many neighbours.

That's Life

Throughout the evolutionary history of life, co-operation among smaller units led to the emergence of multicellular creatures from single-celled organisms. In this sense, co-operation becomes as essential for evolution as competition.

Sophisticated creatures may be drawn to follow strategies that encourage co-operation because of repeated interactions among individuals who can recognise and remember one another.

In the course of evolution, there appears to have been ample opportunity for co-operation to have assisted everything from humans to molecules. In a sense, co-operation could be older than life itself.

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