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.

Monday, May 05, 2008

Imitation and Cooperation - should the model be spatial?

Posted by Simon Halliday | Monday, May 05, 2008 | Category: , , , , , |

This post is a comment on the paper by Rodriguez-Sickert, Rowthorn and Guzmán (2008). It was the basis for the presentation given by Bob Rowthorn at the TECT/SOCCOP meeting.

The main theses of the paper are centred around

  1. Genetic algorithms for specific behaviours

  2. Learning algorithms again for behaviours

As is customary, it is assumed that individuals payoffs are not only a function of their own actions, but of the actions of others. Thus, if one individual is a defector and they interact with (are randomly paired with) a defector/cooperator/cooperator-punisher then their payoff is modified accordingly. The idea of 'learning' models as follows: individuals adopt the learning model of their parents, although this is open to mutation. Individuals therefore have one of three possible learning modules:

  1. Conformism (copying the most common behaviour in their tribe)

  2. Payoff-dependent imitation (copying the most profitable behaviour)

  3. Best responder (homo economicus)

Individuals use these rules in order to choose whether to adopt defection/cooperation/cooperation & punishment behaviours in the relevant interactions that they face. Implicit in these learning algorithms is the belief that access to information is costless. Individuals cannot 'hide' their type. This paper is more about the description of the prevalence of behaviours than the arguments about costliness of behaviour and of arguments about encephalization and brain size. Each of the strategies could be argued to be costly in some manner, the level of the cost is relevant in other models.

The model is based on descriptions of hunter-gatherer society available in Bowles and Choi (2007) which it uses as starting conditions for the society. There are T tribes, each of which have constant and homogeneous size N. There is migration between tribes (through exogamy) and tribes go through cycles of (ritualistic) behaviours: hunting, war, reproduction, migration and learning (individuals interact and gain the strategy of their mentor with some probability, or they 'innovate' and get a strategy that neither agent has, innovation only applies to payoff-dependent agents, not others). Personally, I think that migration should come after war and before reproduction, but I could be wrong.

Selection pressures act at two levels: the within-group level (individual agents maximising their fitness) and the group level (tribes interacting and determining which is better off). I refer you to the model for details, one detail that I mention though is the probability of a cooperator to defect, which I think is necessary. However, if there is a stochastic chance of a cooperator (or punisher) defecting, then I believe strongly that there should be a possibility of a defector mistakenly cooperating. This is for us to remain consistent with what we mean by 'mistakes', otherwise we are saying only that people who cooperate are capable of making mistakes, which I think is problematic. I don't really know how consistent this criticism is with the literature though. I am also not entirely sure of exactly how one would mistakenly cooperate, but can conceive of how one would mistakenly defect. Still not convinced though.

With respect to the inter-group interactions, the simulations that the authors run results in a baseline situation (discarding the first 50 000 years of interactions) of fairly stable percentages of the behaviours. Groups were paired randomly and do battle (the war stage). The group with fewer defectors is more likely to win than the group with more defectors (indicating the tension between within-group and between group selection). The battles are deemed to be 'massacres' with every agent in the losing tribe being 'killed' and replaced as follows: the surviving tribesman 'clone' themselves (rape of women in the previous tribe for example), then clones and remaining tribesmen intermingle to create two new tribes. One problem I have with this model is that it uses a random pairing method for interactions. I think that this is inaccurate and that in order for the model to make more realistic predictions tribes should interact on a spatial matrix and only meet tribes that are within a specific distance of themselves. This could have interesting results for the pervasiveness of specific behaviour patterns.

After the simulations, Best Responders comprise 5% of the population, Payoff-Dependent imitators comprise 20% of the population and Conformists comprise 75% of the total population. When the level of migration is increased to 50% then these percentages change, with Best Responders increasing to 40.5% of the total population, Conformists 38.5% and Payoff-Dependent imitators 19% of the population. Alternatively, holding migration constant and halving the conflict rate, the population consists of 15% Best responders, 60% Conformists and 25% Payoff-dependent imitators. Lower levels of conflict thus result in lower levels of 'cooperation'.

This paper is very interesting in my mind, mainly for the fact that it has a large number of groups (T=20) interacting over the time frame, which is quite good for this kind of work. I do think though that the spatial nature of 'real interactions' is quite crucial and that it could lead to high quality later work on the subject. I refer the reader to Bowles and Choi (2007) for similar work, dealing instead with parochial altruism. I think that a coupling of the two systems would be quite interesting, i.e. learning agents who could be parochial altruists (or altruists in other manners) and see what that might do to the simulations and to the models.

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