The injunction to behave cooperatively is inherent in our cultural understanding and is reinforced by parental, religious and legal strictures. Our fundamental predisposition to belief in the benefits of cooperative behaviour is exposed through clichés such as ‘United we stand’ or ‘Do onto others’
Surprisingly, it is only since the 1970s that economic and evolutionary theory has been able to explain the circumstances in which cooperative behaviour leads to success over non-cooperative strategies. Before this time it was axiomatic amongst social scientists that success results from pursuing one’s own self interest.
Game theory provides fruitful models for understanding the dynamics of cooperative behaviour featuring the interaction of ‘co-operators’ and ‘defectors’. In these games each player has the option of cooperating or defecting in their interactions with other players. Each player’s strategy consists of a set of rules that determine the circumstances under which they will cooperate or defect. A payoff matrix gives the rewards received by the players for all possible outcomes of each encounter.
For example Player A’s payoff matrix might be:
Player B’s matrix will be the same but with Player B and Player A changing places.
According to this trivial payoff matrix it is obvious that each player should always defect as cooperation never receives any reward.
Also leading to a trivial situation is a payoff matrix where cooperation is always rewarded and defection is never rewarded.
A more interesting matrix is one like the following:
This matrix is more interesting as it has some ambiguities and may reflect many real world situations. Although the actual payoffs vary somewhat, many two person interactions take place where each party can gain something by having the other cooperate with them. They gain if they are required to reciprocate the cooperation but they can gain even more if the other party cooperates and they don’t. Of course if they cooperate and the other party doesn’t they loose some resources and if neither cooperates it is the same as if there was no interaction.
As an example let’s suppose that A and B are bartering goods and exchange packages at each turn. Each can cooperate and have in their package the goods promised or they can defect and have a worthless substitute in their package. As in any commercial situation the goods are worth more to the person receiving them then they are to person producing them. According to our matrix, B’s goods are valued at 2 units by B and at 5 units by A. Conversely A’s goods are valued at 2 units by A and at 5 units by B.
A couple of strategic principals are clear in this situation:
The second point tells us that there is a niche in design space where all members of the population employ cooperative strategies and gain the maximum advantage. The question is: Will evolution be able to find and continue to occupy this optimum state? Prolonged occupation will not be possible if this cooperative state is vulnerable to invasion by defectors.
Clearly, if there will be only one encounter, defectors have an advantage. Even if there will be numerous encounters each player will be better off on any given turn by defecting no matter what the other player does. How can cooperative behaviour possibly evolve as a successful strategy?
Classical economist argued that it was impossible and that the only rational strategy was to defect on each play with the result that neither player makes any gains but also avoids any losses. Any yet in experiments where volunteers would play these roles cooperative behaviour would often emerge and both players would gain. The classical economists labelled these volunteer’s behaviour as naïve and irrational.
This thorny problem has been resolved by developments in evolutionary theory, specifically in the field of replicator dynamics. Replicator dynamics models the evolution of strategies within scenarios like our game. Each player has a strategy and the playoff matrix’s rewards are interpreted as units of evolutionary success. After each round of play the scores for each strategy is calculated and a strategy’s population gains or looses members according to its score. The game ends when one strategy comes to dominate the population or when a stable state of a mixed population is achieved.
In this sense a strategy is an evolutionary adaptation that can bestow success on its possessors. As a number of theorist including David Deutsche and Henry Plotkin have pointed out, all adaptations entail knowledge.[i] Evolutionary adaptations are knowledge of how to harness the possibilities in ones environment for success, how to occupy successful niches in design space. Knowledge is crucial to the success of adaptations including strategy. If there is no knowledge there can be no strategy.
Knowledge that leads to a successful strategy in our model is the knowledge that one player can have of the other’s strategy. If no knowledge of the other player were possible, no creative strategy is possible and we have little choice but to always defect. The breakthrough came with models that allowed players to retain some knowledge of the other parties. The first indication of how cooperative behaviour could evolve amongst knowledgeable parties came when models were developed using competing strategies based upon a memory of the outcome of their last encounter with each of the other parties. In contests, run on computers, with strategies developed by an array of computer scientists, evolutionary scientists and economists the ‘Tit for Tat’ strategy evolved to become dominant, driving all others to extinction. Tit for Tat was a very simple strategy that cooperates on its first encounter with any player and on subsequent encounters with that player it does whatever the other player did on the previous encounter.
Tit for Tat is a highly cooperative strategy that reciprocates cooperation and only resorts to defection when dealing with those who have defected on it. When Tit-for-Tat comes to dominate the population all interaction are cooperative, evolution has found the optimum niche in design space. It uses defection only as a method of removing its vulnerability to defectors, never as a method to gain a short term advantage from co-operators. Tit for Tat was the first example of how, even in fierce competition with the most predatory strategies, cooperation could come to dominate. Classical economists concluded that the computer models were working irrationally.
Ecologists have found some examples of the Tit-for-Tat strategy employed by animals in natural settings. But many cases of reciprocal cooperation found in nature do not fit the Tit-for-Tat model. Ants in a colony or parents with their young display high levels of cooperation but do not employ the retaliation implicit in Tit-for-Tat. In fact interactions between parents and their young usually exhibit cooperative behaviour on the part of the parent that is not reciprocated by their young.
Theorists have demonstrated that strategies based on a form of knowledge other than the memory giving Tit-for-Tat its success can also lead to the evolution of cooperation. This knowledge consists of knowing whether other parties are using the same strategy as oneself. When this knowledge is available and based on it players preferentially interact with other parties having the same strategy as them, those with cooperative strategies will come to dominate the population.[ii] This makes perfect sense as we can see from our matrix that players receive their largest average reward when both players cooperate. Players receive their greatest loss when they cooperate and the other player defects. Increasing the probability of interacting with other co-operators gives cooperative strategies a clear advantage. For defectors, like everyone else, interacting with other defectors is at best a waste of their time. Even when there is only a slightly higher frequency of interactions between like strategies, cooperative strategies will come to dominate.
Evolution is a highly competitive process that obeys no morality. An entity’s success is purely in terms of its ability to exist regardless of costs to other entities. Replication dynamics has rigorously demonstrated how cooperative strategies, strategies embodying the highest strictures of morality such as ‘Do unto others as you would have them do unto you.’ are produced and persist in this ferocious environment.
[i] Plotkin, Henry C. (1993). Darwin Machines. Harvard University Press, Cambridge
[ii] Skyrms Brian. (1996). Evolution of the Social Contract. Cambridge University Press