Start of ethnocentric cooperation

Szabo & Fath attribute the first study of evolution of tag-based cooperation to Hales (2000); an unfortunate attribution for two reasons. First, Hales (2000) used tags in a way that is significantly different from the modern treatment. Instead of interacting with people regardless of tag, and then making a decision to cooperate or defect based on tag, the agents decided to interact or not based on tag. In Hales (2000), agents interact only with others of the same tag, thus it is simpler to think of the tags as loci on which agents live. This approach is more consistent with patch-structured or island models of the sort used by Taylor (1992). Cooperation in patch-structured models with limited dispersal was already well understood in biology by the time of Hales (2000). It was a lack of identification that these tags were patches and Hales publishing in computer science not biology that lead to the duplication of efforts. Second, if we admit this theme of tag-dependent interaction, then the first papers should be attributed to Holland (1993) & Riolo (1997). Holland (1993) outlined the mechanism in general and showed how to study it computationally, but did not run simulations. Riolo (1997) studied the mechanism through computer simulation (and some crude analytic approximations) for both iterated and single-shot prisoner’s dilemma. However, I prefer to think of these models as patches with limited dispersal and so do not consider them as the start of the current treatment of tag-based cooperation.

For me, the founding paper on ethnocentric cooperation is Riolo, Cohen & Axelrod (2001). Each agent is represented by two traits, a real number tag in [0,1] and a tolerance. The agents interact at random and a focal agent cooperates with every partner that has a tag within tolerance of the focal agent’s tag. Even with zero tolerance, an agent still cooperates with others of identical tag: an unconditional defector (or selfish agent in our terminology) is impossible. Therefore, the emergence of cooperation is not a surprising result but it is not the only result.

Population dynamics for the first 500 generations of a typical run. (a) is the proportion of cooperative interactions, and (b) is the average tolerance of the population. This is figure 1 from Riolo, Cohen, and Axelrod (2001), reproduced with permission from Nature Publishing Group.

The above figure shows the results of a typical run. In the top panel we have the proportion of cooperative interactions, and in the bottom — average tolerance. Note the cyclic behavior emphasized by the dotted lines. The population is initially populated by few agents of similar tag and low tolerance. This population is a phenotype-space (or tag) cluster and grows rapidly through cooperative interactions inside the cluster. As the cluster dominates the population, the selective pressure on low tolerance is relaxed and the cluster starts to do a random walk through tolerance space. Since there is a lower-bound on the tolerance (can’t be less than 0), the average starts to slowly increase. As the tolerance increases, a low tolerance mutant of slightly different tag appears. This focal mutant is within the large tolerance of the cluster, but most of the cluster’s agents are outside the focal agent’s tolerance. Thus, the focal agent defects from the cluster that continues to cooperate with him, feeding fitness to the focal’s progeny. As the focal agent’s low-tolerance progeny starts to grow, the rate of cooperation and tolerance drops in the population. When the focal mutant’s progeny grows to dominate the population, the cycle repeats. This cycle between emergence of cooperative tag-clusters and invasion by less tolerant defectors has been named chromodynamics by Jansen & van Baalen (2006).

Traulsen & Schuster (2003) were the first to carefully study this oscillatory behavior through an analytic treatment of a minimal variant of the RCA model. This paper was important not only for the aditional clarity it brought to chromodynamics, but also in its move towards discrete tags. Traulsen & Schuster eliminated the two real parameters of tag and tolerance, by having only two tags (Red & Blue) and two tolerances (0 and 1). In other words, they looked at a model with just ethnocentrics and humanitarians and paved the way for future work like our familiar Hammond & Axelrod model.

Beyond the oscillations, the RCA model displays a strange temporal structure effect. In the simulation, there are two events per generation that allow us to define a time-scale: interaction, and reproduction. Each generation is defined by a reproductive step, but before each reproductive step an agent is paired with some number of interaction partners at random to determine his fitness based on the interaction outcomes. As the number of pairing per generation is varied, we start to determine if evolution is fast or slow compared to interaction: fast if the number of pairing per generation is low, and slow otherwise. Usually, increasing the speed of evolution in this way only changes the noise and thus spread through phenotype-space of the population (Roca, Cuesta & Sanchez, 2009). In this case, however, a very high spread results in the impossibility of cooperation.

Mean proportion of cooperation versus number of pairing per generation. Generated with data from Table 1 of Riolo, Cohen, & Axelrod (2001).

The figure above shows the drastic transition in cooperation that happens between 2 and 3 pairings. Unfortunately, the authors do not carefully explain what causes this. Intuitively I expect that the fast evolution causes a very noisy fitness value at each generation, which promotes a diversity of tags and prevents a large cluster from forming. However, this needs to be tested in the model, and at first sight the small wiggle room (from 2 to 3) makes it seem difficult. However, we could consider fractional pairings like 2.1 by saying that with 90% probability an agent has twi pairings, and three with 10% probability. We might look at this more closely in a replication of the authors’ model in a future post.

References

Hales, D. (2000). Cooperation without space or memory: Tags, groups and the prisoner’s dilemma. In S. Moss & P. Davidsson (Eds.), Multi-Agent-Based Simulation, Lecture Notes in Artificial Intelligence (Vol. 1979, pp. 157-166). Berlin: Springer.

Holland, J. (1993). The effects of labels (tags) on social interactions. Santa Fe Institute Working Paper 93-10-064. Santa Fe, NM.
Jansen, V.A.A., & van Baalen, M. (2006). Altruism through beard chromodynamics. Nature, 440, 663-666.

Riolo, R. (1997). The effects of tag-mediated selection of partners in evolving populations playing the iterated prisoner’s dilemma. Santa Fe Institute Working Paper 97-02-016. Santa Fe, NM.

Riolo, R., Cohen, M., & Axelrod, R. (2001). Evolution of cooperation without reciprocity. Nature, 414 (6862), 441-443 DOI: 10.1038/35106555

Roca, C.P., Cuesta, J.A., & Sanchez, A. (2009). Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics. Physics of Life Reviews 6, 208-249.

Taylor, P.D. (1992) Altruism in viscous populations – an inclusive fitness model. Evolutionary Ecology, 6(4), 352-356.

Traulsen, A., & Schuster, H.G. (2003). Minimal model for tag-based cooperation. Physical Review E, 046129.

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About Artem Kaznatcheev
From the ivory tower of the School of Computer Science and Department of Psychology at McGill University, I marvel at the world through algorithmic lenses. My specific interests are in quantum computing, evolutionary game theory, modern evolutionary synthesis, and theoretical cognitive science. Previously I was at the Institute for Quantum Computing and Department of Combinatorics & Optimization at the University of Waterloo and a visitor to the Centre for Quantum Technologies at the National University of Singapore.

9 Responses to Start of ethnocentric cooperation

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  4. metalliska says:

    Ok, a question regarding the pairings at the bottom half of this post:

    Given noisy interactions, by what (determinable) causal effect can one predict future fitness, and how can one discern that a ‘self-pairing’, or mini-loop of length 1, isn’t preserving fitness? Are the agents coded such that it’s impossible to reinforce one-to-one similarities in pairings?

    Or, in my layman-speak, are the defectors likely to contribute more to barely-tolerable defectors in the next round because they’re not weeded out?

    • I don’t really understand your question. What is a self-pairing or mini-loop of length 1? Pairing are usually done this way: take a focal individual then select another individual in the population uniformly at random. These two individuals interact, the focal individual’s fitness is adjusted and another focal individual is selected. Once everybody has been a focal individual (i.e. has a defined fitness) the agents reproduce in proportion to their fitness. The cycle is then restarted, with the updated population and everything is done randomly again. What do you mean by:

      Are the agents coded such that it’s impossible to reinforce one-to-one similarities in pairings?

      I’ve described everything that is coded in the agent: their tag (a real number between 0 and 1) and their tolerance (another real number between 0 and 1). The agent’s mind contains nothing else.

      I agree with you though, that the pairing result is the most curious part. I can understand that 1-pairing would be fundamentally different, since only being paired once often changes the nature of the game (you want to win, not maximize profit; i.e. if you are maximizing profit then you would prefer to get 2 over 1 point even if your opponent gets 3 over 0 points, but if you are trying to win then it is the opposite.

      If you are really curious about this effect and do some programming then I would be happy to replicate this model with you, so we can test that phase transition more carefully. Send me an email if you are interested.

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