PSYC 532 (2012): Evolutionary Game Theory and Cognition

Past Thursday was my fourth time guest lecturing for Tom’s Cognitive Science course. I owe Tom and the students a big thank you. I had a great time presenting, and hope I was able to share some of my enthusiasm for evolutionary games.

I modified the presentation (pdf slides) by combining lecture and discussion. Before the lecture the students read my evolving cooperation post and watched Robert Wright’s “Evolution of compassion”. Based on this, they prepared discussion points and answers to:

  1. What is kin selection? What is green-beard effect or ethnocentrism? How do you think kin selection could be related to the green-beard effect or ethnocentrism?
  2. What does Wright say compassion is from a biological point of view? Do you think this is a reasonable definition?
  3. Can a rational agent be compassionate? Is understanding the indirect benefits (to yourself or your genes) that your actions produce essential for compassion?
  4. What simplifying assumptions does evolutionary game theory make when modeling agents? Are these assumptions reasonable?
  5. Can compassion or cooperation evolve in an inviscid environment? What about a spatially structured one?
  6. What is reciprocal altruism, direct reciprocity and indirect reciprocity?
  7. What is a zero-sum game? Does a non-zero-sum relationship guarantee that compassion will emerge?
  8. Is the Prisoner’s dilemma a zero-sum game? Can you have a competitive environment that is non-zero sum?

During the lecture, we would pause to discuss these questions. As always, the class was enthusiastic and shared many unique viewpoints on the topics. Unfortunately, I did not sufficiently reduce the material from last year and with the discussion we ran out of time. This means that we did not get to the ethnocentrism section of the slides. For students that want to understand that section, I recommend: Evolution of ethnocentrism in the Hammond and Axelrod model.

To the students: thank you for being a great audience and I encourage you to continue discussing the questions above in the comments of this post.

Remembering the dangers of nationalism

Canadian veterans and the Royal Canadian Legion at Remembrance Day ceremonies on Lower Field of McGill University (November 11th, 2012). Photographed and arranged by Adam Scotti; reproduced with permission.

Remembrance Day is a time to reflect on past conflicts and honour the men and women that did not return home from war. The day commemorates the armistice signed on the morning on November 11th, 1918 to formally end the hostilities of the First World War “at the 11th hour of the 11th day of the 11th month”. It is observed by a minute of silence to honour the fallen in all armed conflicts. It is difficult for me to trace my genealogy past the Russian Civil War and draw any personal connection to the First World War. But like many Russians, war losses are a looming memory as none of my great-grandfathers returned home from the Second World War. However, even with careful memory of past conflicts, it seems that we are not capable of avoiding new ones.

In a typical high-school history text, one will see WW1 attributed to nationalism. This is a form of tag-based ethnocentrism, where the arbitrary tag is nationality — a slippery concept for formal definitions but one for which many of us have an intuitive grasp from cultural indoctrination. Of course, nationality seems like a very high-level tag, with many arbitrary distinctions possible to separate people within a single nation (to take a recently prominent one: political party allegiance). As such, our concerns about the expansion of the moral circle apply just as well to nationality as they do to all of humanity. If we understood how the in-group expands from a family, clan, or tribe to the nation, we would be most of the way to an emphatic civilization. The only hurdle would be to understand what the permanent absence of an out-group entails. For now, I will leave the issues of connecting tribe-level ethnocentrism to nationalism at the level of analogy.

A popular approach in understanding nationalism and war is to trace it to a potential evolutionary origin. Usually, this means understanding how tribal ethnocentrism and warfare could have emerged in late Pleistocene and early Holocene humans. Choi and Bowles (2007) take this approach through an agent based group-selection model. Agents form groups (or tribes) of three generations, with each generation consisting of 26 individuals. As far as I can tell, only one of the three generations reproduces and participates in interactions. Each individual is either an altruist or not (in-group strategy), and parochial or tolerant (out-group strategy). Within the tribe, a public-goods game is played with altruists cooperating and nonaltruists defecting. Reproduction is pseudosexual (individuals don’t have sexes, but are still paired to produce offspring) and proportional to the fitness of both parents with full recombination (the in-group and out-group strategies are at two independent loci) and a small probability of mutation and a small random migration rate between groups.

Between the groups, the authors employ a very complicated mechanism. All 20 groups are paired randomly to interact, each group has a probability equal to the group’s fraction of tolerant agents to choose a non-hostile interaction. If both groups choose to be non-hostile, then each tolerant agent gets a benefit g from each tolerant agent of the other group. If either group is hostile, then there is a chance of war equal to the difference in proportion of parochial altruists (warriors) between the groups (|\Delta_{ij}| = |f^{\text{PA}}_i - f^{\text{PA}}_j|). If war does not occur, then there is still no benefit to tolerant agents, and the individual payoff is completely from the in-group game. If war occurs, then a constant fraction of parochial altruists perish (14%) regardless of if the war is a tie (with probability \frac{1}{2}(1 - |\Delta_{ij}|) or the side with more PAs is victorious. If the stronger group is victorious, then they kill a fraction of 2.5 |\Delta_{ij}| of the weaker group’s civilians. The authors do not make clear what happens when 2.5 \Delta_{ij} \geq 1 - f^{\text{PA}}_j, but presumably there is a floor effect and every member of group j is killed. The stronger group (both civilians and parochial altruists) then produces the offspring to repopulate the losing group.

In the above model there are two stable equilibria. In one there is about 15% of both in-group altruism, and out-group parochialism, and in the other there is 85% of each. In the first equilibrium there is very little war and hostility, in the second it abounds, but at levels that are not unreasonable given the archaeological data. Transitions can happen between these equilibria relatively quickly (around 200 cycles, or 5000 years for human generations). The long term average tends to populations that are either parochial altruists or tolerant non-altruists, with very little in-between. From this, Choi & Bowles (2007) conclude the co-evolution of parochial altruism and war.

This paper caused a stir when it came out, and has been heavily cited. From a modeling perspective, I think it suffers from numerous flaws (most introduced in the arbitrary and complicated war mechanism) and could be approached cleaner analytically, but I will save the details of my critique for a future posts. The main achievement of Choi and Bowles (2007) is an attempt to be more realistic that the abstract models typically studied in evolutionary game theory, and to reinforce the important point that hostility and altruism often go hand in hand. Especially in the case of ethnocentrism, it is important to remember the dangers in the cooperation it brings. As I wrote in 2010 in the context of a different model:

The evolution of ethnocentrism … is a double-edged sword: it can cause unexpected cooperative behavior, but also irrational hostility.

Choi JK, & Bowles S (2007). The coevolution of parochial altruism and war. Science (New York, N.Y.), 318 (5850), 636-40 PMID: 17962562

Theorists as connectors: from Poincaré to mathematical medicine

Henri Poincaré (29 April 1854 – 17 July 1912) is often considered to be the last universalist of mathematicians. He excelled in all parts of theoretical physics, applied, and pure mathematics that existed during his time. Since him, top mathematicians have become increasingly more specialized, as have scientists. Poincaré was part pure mathematician, part engineer; he advocated the importance of intuition over formality in mathematics. This put him at odds with the likes of Frege, Hilbert, and Russell — men that are typically considered the grandfathers of theoretical computer science. As an aspiring CSTheorist, I think we are misplaced in tracing our intellectual roots to the surgical and sterile philosophies of logicism and formalism.

A computer scientist, at least one that embraces the algorithmic lens, is part scientist/engineer and part logician/mathematician. Although there is great technical merit to be had in proving that recently defined complexity class X is equal (or not) to a not-so-recently defined complexity class Y, my hope is that this is a means to a deeper understanding of something other than arbitrarily defined complexity classes. The mark of a great theorist is looking at a problem in science (or some other field) and figuring out how to properly frame it in such a way that the formal tools of mathematics at her disposal become applicable to the formulation. I think Scott Aaronson said it clearly (his emphasis):

A huge part of our job description as theoretical computer scientists is finding formal ways to model informally-specified notions! (What is it that Turing did when he defined Turing machines in the first place?) For that reason, I don’t think it’s possible to define “modeling questions” as outside the scope of TCS, without more-or-less eviscerating the subject.

As experimental science becomes more and more specialized, I believe it is increasingly important to have universal theorists or connectors. People with the mission of finding connections between disparate fields, and framing different theories in common languages. That is my goal, and the only unifying theme I can detect between my often random-seeming interests. Of course, CSTheorists are not the only ones well prepared to do take on the job of connectors. Jacob G. Scott (@CancerConnector on twitter; where I borrow ‘connector’ from) suggests that MD trained scientists are also perfect as connectors:

I completely agree with Jacob’s emphasis on creativity, and seeing complex problems as a whole. Usually, I would be reluctant to accept the suggestion of connectors without formal mathematical training, but I am starting to see that it is not essential for a universalist. My only experience with MD trained scientists was stimulating conversations with Gary An, a surgeon at University of Chicago Medical Center and organizer of the Swarmfest2012 conference on complex adaptive systems. He brought a pragmatic view to computational modeling, and (more importantly) the purpose of models, that I would have never found on my own. For me, computational models had been an exercise in formalism and a tool to build intuition on questions I could not tackle analytically. Gary stressed the importance of models as a means of communication, as a bridge between disciplines. He showed me that modelers are connectors.

As most scientists becomes more and more specialized, I think it is essential to have generalists and connectors to keep science unified. We cannot hope for a modern Poincaré, but we can aspire for theorists that specialize in drawing connections between fields, and driving a cross-fertilization of tools. For me, following Turing’s footsteps on the intuitive road of theoretical computer science and algorithmic lens is the most satisfying, but it is not the only way. Jacob shows that translating between distant disciplines like math/physics and biology/medicine and engaging their researchers can drive progress. Gary shows that pragmatism and viewing modeling as a means of communication is equally important. In some way, they (and many like them) act as a 21st century Poincaré by bringing the intuition of mathematics and computer modeling to bare on the engineering of modern medicine.