If one stands back and looks at the way that research on the Prisoner’s Dilemma has developed over the years, one key development is the rise in the influence of probabilistic strategies, where the players are likely to play a certain way, and at a certain time, but it is by no means certain they will react in precisely the same way in each and every circumstance. To that we can add another element of realism in acknowledging that real life lies somewhere between playing a simultaneous and an alternating game as a result of the degree to which they alternate and the degree to which they know what the other has done.
These more realistic games also generate cycles, where strategies vary from Always Defect to Tit for Tat to Generous Tit for Tat then to indiscriminate cooperation and then, inevitably, return to square one again as defection takes over. Even though Win Stay, Lose Shift can lengthen the period of cooperation in a cycle, we find that it breaks down eventually to allow a resurgence of defectors.
The cycles that we observe in our tournaments are quite different from the findings of traditional game theory, where there is always an emphasis on stable equilibrium. Without having to go into all the details, this point can be appreciated simply by looking at the language that is used in classical evolutionary and economic game theory. References abound to evolutionarily stable strategy and Nash equilibrium, for example.
We have moved from old “evolutionary statics” and are now starting to understand the flux and change of “evolutionary dynamics.” This classical notion of life evolving to a stable and unchanging state has now been overturned by a much more fluid picture. No strategy is really stable and thus successful for eternity. There is constant turnover. Fortune does not smile forever on one person. A heaven of cooperation will always be followed by a defective hell. Cooperation’s success depends on how long it can persist and how often it reemerges to bloom once again. What a fascinating and turbulent insight into the evolution of cooperation and life.
Yet there’s still so much more left to find out. We have only explored a small subset of this extraordinary game. There are many more variants out there, huge hinterlands of games that stretch out to a receding horizon. Despite the thousands of papers written on the repeated Prisoner’s Dilemma, the mathematical possibilities in this model of direct reciprocity are open-ended, like chess, and not closed, like the strategies for playing tic-tac-toe. Our analysis of how to solve the Dilemma will never be completed. This Dilemma has no end.
Indirect Reciprocity— Power of Reputation
The moment there is suspicion about a person’s motives, everything he does becomes tainted.
—Mohandas Gandhi
“Give and it shall be given unto you.” This oft-quoted line from Luke’s Gospel story of Jesus’ birth, ministry, and resurrection seems to be just another example of direct reciprocity, which I described in the last chapter. But take a moment to think about this phrase and you will see that there is a crucial difference: it is not entirely clear who is doing the giving in response to your act of generosity. Perhaps it is a family member, friend, or workmate. But it could be a stranger too, or indeed several strangers.
Many people might interpret the quote as meaning that, if you are generous, a reward is promised in a subsequent world, a paradise or heaven. But my favorite interpretation is that the reward comes to you in the here and now. Kindness will elicit kindness. In this way, circles of humanity, tolerance, and understanding can loop through and around our society. Either way, it is a powerful form of cooperation, and its implications are huge, shaping how we behave, how we communicate, and how we think.
Even two millennia ago, in Luke’s time, one can see that this idea of “what goes around comes around” was already commonplace, certainly among the authors of the Gospels. Mark 4:24 says: “And he said unto them, Take heed what ye hear: with what measure ye mete, it shall be measured to you: and unto you that hear shall more be given.” Matthew 7:2 puts it another way: “For with what judgment ye judge, ye shall be judged: and with what measure ye mete, it shall be measured to you again.” What is remarkable is that all kinds of fascinating consequences spin out of this perspective.
In a small group, say a village, what we call indirect reciprocity bestows tremendous advantages, by allowing me to benefit from the experience that others in our clan had when dealing with you. (“Ugg has always been fair when it comes to trading tools for food. But Igg can’t be trusted.”) When dealing with you, I take into account more than just our dealings with each other.
While direct reciprocity relies on your own experience of another person, indirect reciprocity also takes into account the experience of other people. Mathematicians could say that indirect reciprocity is a broader category that includes direct reciprocity, but the two mechanisms are analyzed in quite different ways: to dissect the direct form we need to look at repeated games, as we did in the last chapter. To understand the indirect form we need to recognize the power of reputation.
Exploring the indirect form of reciprocity is important because it is critical for society. Direct reciprocity—“I’ll scratch your back and you scratch mine”—operates well within small groups of people, or in villages where there is a tight-knit community where it would be hard to get away with cheating one another. In small societies, indirect reciprocity is also at work, as people create, observe, and report the soap opera of everyday life. But by the time of Christ, Eurasia’s middle latitudes were straddled by the Roman Empire, the Parthian Empire, the Kushan Empire of Central Asia and Northern India, and the Han Empire of China and Korea. To extend and thrive, these sprawling societies had to depend on more than just direct reciprocity.
Societies could more easily evolve to become larger, more complex, and interconnected if their citizens depended on economic exchanges that relied on indirect reciprocity. Today, this is central to the way we conduct our affairs and cooperate. With the help of gossip, chat, and banter we are able to gauge the reputation of other people, sizing them up, or marking them down, to decide how to deal with them. This sheds light on both the proliferation of charity and of glossy celebrity gossip magazines.
Thanks to the power of reputation, we think nothing of paying one stranger for a gift and then waiting to receive delivery from another stranger, thanks also to the efforts of various other people whom we have never met and will never meet—from the person who packs our gift to the one who checks our credit rating. In our vast society it is a case of: “I scratch your back and someone else will scratch mine.” We all depend on third parties to ensure that those who scratch backs will have theirs scratched eventually.
Under the influence of indirect reciprocity, our society is not only larger than ever but also more intricate. The increasing size of modern communities can now support a greater subdivision of physical and cognitive labor. People can specialize when networks of indirect reciprocity enable a person to establish a reputation for being skilled at a particular job. Thanks to the power of reputation, great collections of mutually dependent people in a society can now sustain individuals who are specialized to an extraordinary degree, so that some of its denizens are able to spend much of their time thinking about how to capture the quintessence of cooperation in mathematical terms while others are paid to think about how to express mathematical terms about cooperation in plain English. It’s amazing.
This link between the size of a settlement and the specialization of its inhabitants was recorded in ancient times. Xenophon, an Athenian gentleman soldier, wrote in the fourth century BC that the bigger a settlement was, the more finely divided its labor: “In a small city the same man must make beds and chairs and ploughs and tables, and often build houses as well; and indeed he will be only too glad if he can find enough employers in all trades to keep him. Now it is impossible that a single man working at a dozen crafts can do them all well; but in the great cities, owing to the wide demand for each particular thing, a single craft will suffice