Economics, Literature and Scepticism

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I am a PhD student in Economics. I am originally from South Africa and plan to return there after my PhD. I completed my M. Comm in Economics and my MA In Creative Writing (Poetry) at the University of Cape Town, where I worked as a lecturer before starting my PhD.

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Wednesday, July 23, 2008

Diversity and Cooperation

Posted by Simon Halliday | Wednesday, July 23, 2008 | Category: , , | Diversity facilitates cooperation according to research published in the latest Nature. The paper fits well into the literature in evolutionary game theory on the prisoner's dilemma and public goods games. I'll give a very brief look at some of the points I found pertinent in the paper.

Santos, Santos and Pacheco's main assertion is that diversity promotes cooperation, specifically:
[C]ooperation is promoted by the diversity associated with the number and size of the public goods game in which each individual participates and with the individual contribution to each such game. (213)
Crucially for their results, they posit the following:
Whenever interactions are not repeated, and reward and punishment can be ruled out, several mechanisms were explored that promote cooperation. Individuals were either constrained to interact only with their neighbours on spatial lattices, or given the freedom to opt out of participating, leading to a coexistence of cooperators and defectors, even on spatial lattices.(213)
The non-repetition is important, especially in the light of recent research (as yet unpublished, still being written in fact) by Simon Gaechter using economic experiments to repeat public goods games for fifty rounds. Preliminary results from his research indicates that long-run repetition such as this results in almost complete cooperation. Summarizing therefore, (213) "Here we investigate what happens in the absence of reputation and punishment and when participation is compulsory."

Moving on from these concerns they get to grips with the models and their use of heterogeneous graphs to represent the social networks of individuals. They observe watershed levels for cooperation, (214) "In infinite, well-mixed populations, a sharp transition from defection to cooperation takes place." See Figure 2. For which we should understand the role of eta:

Eta is the renormalized enhancement factor, where r is the multiplication factor for the contribution and z is the average connectivity of the population graph. We see in the graphs that as eta decreases, the fraction of cooperators increases. Both of the graphs assume that z = 4, i.e. connectivity remains constant. Customarily, when the rewards to cooperation increase (which they do if the multiplication factor increases), then the likelihood of cooperation should increase. We have a replication of that result here: as r increases, so too does the incidence of cooperation. However, we see a difference in the scale free vs. the regular graphs. For fixed cost per game the tipping point towards cooperation is a similar level of eta. For fixed cost per individual (spread through their network of k+1 individuals) the tipping point for cooperation is much sooner in the scale free graph than in the normal graph. It is worth reiterating that 'real life' is traditionally held to be somewhere between scale free and regular.

Changing tack somewhat, consider the following statements:
"Depending on the problem at stake, any contribution may be necessary and even welcome, however small. Below we show that, whenever all contributions are interpreted as acts of cooperation, cooperation blooms." (214)
Also that (215), "In this study any contribution has been identified with cooperation."
And finally (215),
In communities under the influence of social norms, individual contributions will be easily classified as acts of cooperation (or not). In this context, our results suggest the possibility that successful communities are those in which the act of giving is more important than the amount given. This may be of particular relevance whenever the survival of the community is at stake, in which case any help is necessary. Most probably in such cases selection is strong, as is considered here.
The problem I have with the assumption 'all contributions indicate cooperation' is that, 'in real life', the social norm could tend to be a contribution to the good relative to the size of one's income. If a really poor person contributed relatively large amounts, whereas a rich person contributed relatively small amounts people could interpret this as defection by the rich person for not contributing their 'fair share'. What they assert could be perceived to be inconsistent with the research by Ernst Fehr and others on inequality aversion. Such a consideration is even more important when we take note of the statement that they make on the social nature of the decision-making process, as contributions and the prevalence of cooperation "depends on the social context of the individual" (214). Surely the social context includes social norms on what is a 'fair share', rather than simply 'contribution is cooperation'.

They replicate a customary result when increases in defector dominance results in lower fitness and even possible extinction of defectors (214): "Ds are victims of their own success—successful Ds breed Ds in their neighbourhood, inducing a negative feedback mechanism that reduces their fitness."

There are some final comments on egalitarian vs. power law distributions of wealth in all-cooperator worlds. This in and of itself requires further examination and I will try to comment on this later.
In a more economical perspective, our results also portray different evolutionary outcomes even in communities in which all individuals cooperate. Now we consider populations of 100% cooperators and look at their ‘wealth’ (fitness) distribution according to different underlying models. We consider homogeneous (regular) and heterogeneous (scale-free) graphs. In Fig. 4 we plot the fraction of the population that holds a given fraction of the total wealth. The differences are striking. On regular graphs an egalitarian wealth distribution is obtained, irrespective of the contribution model. On scale-free graphs wealth distributions follow a power law. However, for a fixed cost per individual, the population has significantly fewer poor and more rich. (215)
Some things that could have been incorporated or discussed: ideas of prosocial behaviour relating to behavioural rules, such as the use of learning rules that Rowthorn, et al (2007) (based on previous work by Henrich, Boyd and Bowles) consider and as proposed in an upcoming paper by Frederike Mengel (2008) in JEBO. [Noting which, I plan to review the Mengel piece at a later date, and will refer you back to this post when I do.] Mengel also has another unpublished paper with Constanza Fosco, 'Cooperation through Imitation and Exclusion in Networks', which looks at a similar topic - they too observe defection on the borders of the social network.

Additional Refs:
Fosco, Costanza and Friederike Mengel, (2008), Cooperation through Imitation and Exclusion in Networks, unpublished, University of Alicante.
Mengel, Frederike, (2008-forthcoming), Matching structure and the cultural transmission of social norms, Journal of Economic Behaviour and Organisation.
Rodriguez-Sickert, Carlos, Robert Rowthorn and Ricardo Andres Guzman (2008), The Social Benefit of Slow Learner, unpublished, University of Cambridge.

Santos, F.C., Santos, M.D., Pacheco, J.M. (2008). Social diversity promotes the emergence of cooperation in public goods games. Nature, 454(7201), 213-216. DOI: 10.1038/nature06940

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