I just checked out a lecture given by Martin Nowak at the Massachusetts Institute of Technology that was recently posted on the MIT videos site. The video was recently posted on the MIT site, but it is not entirely clear when it actually happened. I suspect it is the same lecture listed here. Nowak recently published a book called Supercooperators, and this lecture was clearly designed to promote the overview of how cooperation evolves provided by the book.
For those who want a nice overview of where this field has gone recently, Nowak delivers. For the most part the lecture assumes very little of its audience and explanations are nice and clear. Like most lectures given by prominent academics, this one mostly leads the audience to the work of Nowak and his students, in particular Corina Tarnita.
The lecture started off by defining cooperation as having a cost to a donor, who provides a benefit for a recipient. From the outset, Nowak made it clear that these costs and benefits are expressed in terms of fitness, but that this fitness could be either genetic or cultural in nature. He outlined the Prisoner’s Dilemma game as the theoretical basis for this sort of cost/benefit exchange, and quickly explained that defection (failing to provide a benefit for another player in the game) is the rational choice in a one-shot game. He pointed out that this ‘rational outcome’ is actually suboptimal and that so-called ‘irrational players’ who both cooperate achieve a higher overall payoff. In an interesting contextualization of this paradox, Nowak claimed that biologists have no need for this notion of rationality. He justified this statement by pointing out that the ‘rational predictions’ for a population of individuals playing the Prisoner’s Dilemma in fact violate Fisher’s Theorum because the fitness of the population actually decreases as the strategy to defect becomes fixed. I had never heard this sort of argument against trusting rational assumptions in game theory, and I need to consider how it relates to recent work that I have been doing that assumes superrationality.
Nowak then briefly outlined the way that cooperation has actually evolved in biological systems, leading to the question of how this evolution might have occurred. His answer — at least in this lecture — has to do with five mechanisms for the evolution of cooperation, which he has reviewed in previous publications (Nowak 2006). These five mechanisms are:
- Kin selection;
- Direct reciprocity;
- Indirect reciprocity;
- Spatial selection; and
- Group selection.
Nowak provided a review of all five of these mechanisms, although he emphasized those mechanisms with closest ties to his own work.
He started off with a discussion of kin selection by reviewing the contributions of J.B.S. Haldane, who first noted the importance of help directed at kin, and William Hamilton, who introduced the idea of inclusive fitness and formalized kin selection into a mathematical expression. This expression (“Hamilton’s Rule”) states that cooperation with related individuals can emerge whenever r > c/b, where r is the coefficient of relatedness between the donor and the recipient, c is the cost to the donor, and b is the benefit to the recipient. As anyone who has followed the recent controversy started by Nowak realizes, he is not a huge fan of inclusive fitness: in this lecture he suggested that Hamilton’s Rule is “in some sense… a heuristic”. He also suggested that Hamilton’s mathematics are “completely unnecessary” because straightforward population genetics theory can explain the emergence of cooperation without appealing to inclusive fitness theory.
Nowak’s discussion of direct reciprocity focused on the work of Robert Trivers and the repeated Prisoner’s Dilemma investigations of Robert Axelrod. He briefly mentioned the Folk Theorum, which suggests that an equilibrium can be achieved in which all players cooperate in the Iterated Prisoner’s Dilemma. He also introduced the strategy Tit-for-Tat, which he described as playing against yourself by holding up a mirror and repeating the moves of one’s opponent. While he acknowledged the initial robustness of the Tit-for-Tat strategy, he also expressed doubt about its real-world validity. In particular he pointed out that errors (noisy moves) can destroy performance of Tit-for-Tat. He alluded to two kinds of error: the “trembling hand”, which occurs when a player erroneously plays the wrong move in a particular round of the iterated game, and the “fuzzy mind”, which occurs when a player erroneously misreads the actual moves of an opponent. This led to a discussion of his early work on these error-prone systems, which showed that an oscillating system can be generated in which consistent defectors are taken over by Tit-for-Tat players, who in turn face a succession of takeovers by Generous Tit-for-Tat (a strategy that forgives minor errors), consistent cooperators, and finally consistent defectors. He also suggested that a new strategy — Win-Stay, Lose-Shift — can invade this system and consistently prevent the invasion of other strategies. Returning to the more general Iterated Prisoner’s Dilemma game, Nowak pointed out that cooperation depends on repeated interactions: in fact the probability of playing another round with an opponent must exceed the cost-to-benefit ratio, providing a direct analogy to Hamilton’s Rule.
Nowak has done a lot of work on indirect reciprocity, a topic which he illustrated using a Van Gogh painting depicting the good samaritan. Indirect reciprocity is not about a repeated game, but rather about repeated interactions within a network of individuals. Nowak explained the logic behind indirect reciprocity as “if I help you, someone else will help me”. He discussed the basis of this form of reciprocity, which is reputation: if the history of other players can be known based on a reputation formed by gossip, cooperative individuals can prosper in a networked population. One way to explain the social intelligence and language capabilities of humans is to suppose that indirect reciprocity was an important mechanism for fostering cooperation. Again creating a connection to the cost-to-benefit ratio, Nowak explained that the probability of knowing someone’s reputation must exceed c/b in order for cooperation to evolve. He also distinguished between direct and indirect reciprocity by appealing to an insightful observation made by David Haig: “For direct reciprocity you need a face, for indirect reciprocity you need a name”.
Nowak has also investigated spatial selection, which he described as the phenomenon that cooperators form clusters. Neighbors help each other, and we can consider ‘neighbors’ as either geographically related or as adjacent connections in a social network. Again, a connection can be made to the cost-to-benefit ratio, as cooperation can only evolve when 1/k > c/b, where k represents the average number of social connections maintained by each individual. This has always confused me somewhat because its description of cooperative populations — that they are composed of populations connected with relatively few links between each person — does not seem to match the pattern of human social connection. In his discussion of spatial selection, Nowak also discussed more detailed work he has completed (along with Corina Tarnita) using set theory, although I found this discussion too brief to understand based on the lecture alone.
Finally, Nowak discussed group selection, which he (like other advocates of this once-banished evolutionary mechanism) was happy to point out was first suggested by Charles Darwin. He explained that under group selection, groups die. This leads to another relationship of costs and benefits to the emergence of cooperation, wherein cooperation evolves by group selection when you have a large number of small groups. He briefly mentioned that migration makes it harder to evolve by group selection, but this aside was pretty unsatisfactory to me given how most of the objections to group selection focus strongly on the way migration can disrupt the evolution of cooperation.
At the end of the lecture there were a few interesting questions. The question session led Nowak to make a few more observations, including that gossip can itself be deceitful and is therefore itself a public goods game that could be nested within a game that allowed indirect reciprocity through reputation assessment. He again stressed that all five mechanisms could work regardless of what fitness criteria (genetic or cultural) was considered, and pointed out one of the fundamental differences between genetic and cultural evolution: there is limited intentionality in the ‘design’ of cultural traits while genetic traits emerge solely due to random events. He did not comment on what I consider a more important distinction between cultural and genetic evolution: that cultural evolution is horizontal in nature while most genetic evolution is not.
Below are the two segments of Nowak’s lecture:
Although I could not really see a place where I could shed any more light on this lecture, a cool feature of these MIT-supported lectures is the ability to make comments inline with the lecture: in other words, you can ‘have your say’ at any juncture in the lecture. This kind of technology has a lot of potential to foster active dialogue in response to podcast lectures.