When you come across a line like this in a paper, you can't help but laugh, "We now discuss and explain the cumulative number of sheep played in all rounds of the game." Yes, subjects played sheep. You may wonder how. I shall attempt to explain.

In three papers based on work in South Africa and Namibia, Bjørn Vollan and, in one paper, his co-author Bernd Hayo investigate several different experiments with the Nama people. They ran trust games, trust games with third party punishment, and common pool resource games with groups of villagers in the Northern Cape Province of South Africa and the southern region of Namibia. Their work was supported by BIOTA, a biodiversity and conservation project.

So what kinds of things did they find out? And how on earth were sheep involved? Well, the Nama people spend substantial amounts of time on subsistence herding of goats and sheep. Consequently, when they played the common pool resource game, the game was framed as though the subjects were exploiting common grazing ground by choosing a number of 'sheep' to 'graze' the resource. The game works like a multi-player prisoner's dilemma where the self-interested thing for a subject to do is to 'defect' by having as many sheep as possible in the hope that no one else will choose lots of sheep, but everyone chooses lots of sheep. The social optimum occurs when people exercise self-restraint and jointly have several sheep, but not too many such that the common resource vanishes. Strangely enough, people often don't play completely self-interestedly, instead they choose something in between the individual optimum and the social optimum (see Cardenas and Carpenter, 2008 and Velez et al, 2006). In Bjørn Vollan's work, we see that the Nama also cooperate to some extent with the option to exploit the resource, and, after several rounds, they also are able to vote on adopting a self-regulating policy of punishment, reward or communication, any of which seem to result in a higher degree of cooperation. The experiments were run with groups of five. In the control, when the subjects were given the choice of between 10 and 90 sheep(in tens), 51.6% of people chose the less cooperative options of 60-90 sheep. When, in the latter rounds, a treatment for reward, punishment, or communication, could be voted on the amount of outright defection decreased to 30.7% of the sample, with 46.5% of the sample choosing the highly cooperative 10, 20 or 30 sheep (everyone choosing 20 would be the social optimum).

So we know that introducing some kind of voted rule works, but does any one rule work better? Does 'buy-in' matter? One problems is that the rankings were different in South Africa and Namibia. In the South African community, punishment resulted in lower numbers of sheep chosen with the choice stabilising at around 4 sheep on average; it worked best of all when more people in the group participating in the experiment voted for it. So a community with 'buy-in' to norms could operate more effectively (interesting enough, in the Hayo and Vollan paper there's a strong correlation between voting for punishment and being a Lutheran, one of the few religious affiliation effects they found in the subjects' behavior). Conversely, in Namibia rewards work much better, though the positive effect of decreasing the number of sheep chosen peter off. Vollan argues that this can be explained by rewards 'crowding out' intrinsic motivations to cooperate (read his paper for the full argument).

So, we know what's happened in the CPR game, but what about the trust game and the trust game with third party punishment? Recall that the trust game is a bargain between two subjects: a Trustor and a Trustee. The Trustor chooses some fraction of an endowment to give to the Trustee, the total amount of which is multipled by 3 (this act is called 'trust' below). The Trustee may then send an amount back to the Trustor. In the third party punishment (TPP) variation, a Third Party is introduced with the power to 'punish' the other players: the Third Party can pay to reduce the payoffs of players whose behavior she did not like, either the Trustor, the Trustee or both. In Vollan's results, and moving from sheep to money, we see that South African Nama trust 20% of their endowment to their partner, whereas Namibian Nama trust 40% of their endowment to their partner. The South African group is at the bottom end of all results of trust games internationally (see Cardenas and Carpenter, 2008, Camerer, 2003). Then, in the second set of experiments examing trust, punishment and relatedness, Vollan finds the results presented in the table below.

The paper presents the aggregated results and I could not dis-aggregate them for South Africa and Namibia as in Vollan's other paper. Nevertheless, the results are instructive. We can see, first, that there are substantially different results between villagers, friends and family. Moreover, introducing punishment substantially increases the likelihood that subjects act 'trustingly' (send money to the Trustee) and 'trustworthily' (send money back to the Trustor). But the effect of punishment differs greatly: villagers behave 48.4% more trustingly, friends behave 44.2% more trustingly, and family only 21.9% more trustingly. The relationship is different for trustworthiness: friends come out on top, behaving 65% more trustworthily, villagers 50% more trustworthily, and family 37% more trustworthily. Obviously these rankings occur because family members behave the most trustingly and trustworthily from the outset, but it goes to show that third party punishment may be its most effective between non-relatives in promoting trusting and trustworthy behavior.

The papers are all fascinating, particularly for a South African interested in doing similar work. I hope that the few results I have shown might have piqued your interest enough for you to go and read the papers. I presented what I perceived as the most interesting results without critiquing Vollan's methods too much. That said, Vollan could have done one or two things to improve his methods. For example, and somewhat pettily, with translation into Afrikaans (the language in which the experiments were conducted), Vollan should have translated and back-translated for consistency. Also, we could be given some additional ethnographic information about the Nama's particular institutional structures of third party punishment, though Vollan does provide information about reciprocity, gift-giving, and trusting/trustworthy behavior. He also finds (2008, 16) that the subject display inequity aversion, so I'd think that given the prevalence literature on this topic it would be worth investigating this idea more and offering some insights in the conclusion after the later results. Overall, they're a good contribution to the experimental economics, resource economics and behavioral economics literature and I thoroughly enjoyed reading them.

References

• Hayo, Bernd & Bjørn Vollan. 2009. "Individual Heterogeneity, Group Interaction, and Co-operative Behaviour: Evidence from a Common-Pool Resource Experiment in South Africa and Namibia." Philipps-Universitt Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
• Vollan, Bjørn. 2008a. "Kinship and friendship in a trust game with third party punishment." Philipps-Universitt Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
• Vollan, B. 2008b. Socio-ecological explanations for crowding-out effects from economic field experiments in southern Africa, Ecological Economics, 67 (4), 560-573 DOI: 10.1016/j.ecolecon.2008.01.015