Cooperation through exchange: an emerging paradigm

“Evolution,” in the words of biologist Martin Nowak, “is based on a fierce competition between individuals and should therefore reward only selfish behaviour. Every gene, every cell, and every organism should be designed to promote its own evolutionary success at the expense of its competitors.”

Even so, we observe cooperation on many levels of biological organization. Hence, it is clear that, in many cases, “… selfish replicators forgo some of their reproductive potential to help one another.” How and why? Understanding this is the biological puzzle of cooperation.

In a well-known 2006 paper, Nowak offered an overview of known mechanisms capable of overcoming direct selfishness to support the emergence of cooperation. In a variety of ways, selfish agents by investing a little in cooperative behaviour can ultimately gain more as a result, so that cooperation becomes favoured even from a strictly selfish point of view.

Yet one topic not emphasized in Nowak’s short review is the role of noise or random environmental fluctuations. To be sure, his review didn’t rule out a role for such effects, but passed them by in favour of a higher-level focus on evolutionary competition. But noise may play a more important role in driving the emergence of cooperation than is generally believed. 

In any environment subject to random fluctuations, biological organisms – or economic agents – face important risks from possible bad outcomes out of their control. In such settings, there is clearly potential for a pooling of resources to help buffer individuals from risks, as what befalls one may not affect another. Pooling and sharing resources under such conditions might, in principle, be useful, if it could be organised. But is this qualitative insight mathematically sound?

In a 2018 preprint – recently published – LML researchers Ole Peters and Alex Adamou explored this idea using a simple model in which a number of agents gradually accrue wealth or resources in a fluctuating environment. In this model, an agent’s store of resources grows by a small percentage, x%, in each time period, with x being a random variable reflecting environmental uncertainty. Mathematically, this model is one of geometric Brownian motion, and the time average growth rate of an agent can be readily calculated.

In this setting, Peters and Adamou asked a simple question: suppose two of these agents were to decide to cooperate in a radical way. Just before each random growth event, they pool everything they’ve got and split it evenly. Having done so, the two agents then live through and experience the next period, gaining or losing as may be, and then again pool everything and split it evenly.

Clearly, if both individuals experience the same random outcome, then this exchange will have no effect – once the individuals have pooled and shared for the first time, the wealth of each would evolve in lockstep, and cooperation would have no effect. The agents will be no better or worse off than if they had not exchanged. More realistically, however, agents may well experience different random outcomes. In this case, the analysis found, making the exchange always ends up being beneficial in the long-run for both parties, who accumulate resources or wealth more rapidly than they would in the absence of exchange.

This model suggests that, in the presence of random multiplicative shocks, cooperation through sharing of resources is beneficial. The “return” an individual gets for cooperating doesn’t come from some direct payback from the other party, but from a diversification effect or form of social insurance. Mathematically, exchange reduces the overall variance in their payoffs, which in turn increases the time-average payoffs compared to a situation where each individual acts independently. The wealth or resource stock of agents who engage in exchange grows faster than for those who don’t.

A new pathway to cooperation?

Since this initial work, Peters, Adamou and others have developed this idea further and examined it in a number of settings, including finance, studies of the origin of multicellularity and elsewhere. Early results suggest that exchange-sharing or cooperation may be a mechanism of significantly underappreciated importance for understanding real-world cooperation in biology, economics and human history.

Several researchers presented work extending results in this area at the 2023 Conference on Ergodicity Economics. One important issue to resolve is whether this kind of cooperation is also observed if agents are allowed to be unfair. Physicist Lorenzo Fant of the Instituto Gulbenkian de Ciência in Portugal and colleagues reported theoretical results and  simulation studies suggesting that this is the case:  if one agent shares less of its wealth than its partner, by weakening the partner the beneficial effect of cooperation is diminished and growth is reduced, not increased by the cheating. Hence, agents do not have an incentive to cheat.

Do any human cultures already employ this exchange mechanism to achieve benefits? The answer appears to be yes, as noted by anthropologist Athena Aktipis of the University of Arizona State. With colleagues, she has been studying different modes of resource sharing among the Maasai people of East Africa. The Maasai are pastoralists who depend on their ability to successfully manage large animal herds in a difficult physical environment subject to droughts and disease as well as animal theft. Managing risks associated with such uncertainties is crucial for Maasai survival.

As Aktipis pointed out, the Maasai employ a system for sharing and exchange which comes under the Maasai term “osotua,” for which the rules are straightforward: Ask only if you are in need and only for what is needed, and give if you are able to do so without threatening your own survival. In effect, these rules imply that Maasai individuals at least occasionally enter into exchange relations much like the kind modelled by Peters and Adamou, although in a much more complex setting. In previous modelling, Aktipis and colleagues demonstrated that pairs of herders following the rules of osotua would be expected to have herds that survive longer than others not engaging in such exchange. 

In more recent work, she and colleagues have gone further to compare the benefits of osotua exchange with another debt-based form of sharing also employed by the Maasai but given a different name. Under the system known as “esile,” which roughly translates as “debt,” individuals can offer a resource, such as an animal, but they do then expect eventual repayment. Such debts are kept track of, and if a debtor fails to make repayment, his or her creditor has the option to forgive the debt. If not, the debt can be passed on to offspring. Again using an agent-based model, the researchers compared the effectiveness of these two parallel modes of exchange, finding that under broad conditions the need-based exchange offers better survival prospects than debt-based exchange, although both do better than individuals not engaging in exchange at all.

One may wonder why the Maasai have these two parallel systems, when need-based exchange would be enough. As the researchers noted, some other human cultures also have similar parallel systems of exchange. Aktipis and colleagues speculate that the two systems may find distinct uses depending on the predictability of necessary exchanges, with debt-based exchange used for more routine repeated economic exchanges, and need-based exchange taking care of the more unpredictable shocks from the environment. As they put it,

“…when needs arise asynchronously, it may make good adaptive sense for those with resources to transfer them to those without. The difference between need-based transfers and account-keeping becomes apparent when we consider the predictability of the needs in question. When needs are both asynchronous and highly predictable, account-keeping makes sense. If I know that I will always be in need on Tuesday and you know that you will always be in need on Friday, we can easily set up a system of balanced, tit-for-tat, account-keeping reciprocity that benefits us both. But if needs are not only asynchronous but also unpredictable, need-based transfers may, as our model suggests, make more adaptive sense than account-keeping.”

The authors also note that there is a difference in the simplicity of the need-based and debt-based systems. In essence, need-based sharing requires nothing but an understanding of the prevailing rules, whereas debt-based exchange demands a more burdensome system of accounting and calculation to keep track of the ledger of debts as it builds up over time. Hence, it may not be surprising that these two systems are especially useful in parallel, and attuned specifically to different needs.

Cooperation beyond evolution

It is not yet clear where research on the benefits of exchange based sharing may ultimately lead. But the mechanism seems so rudimentary, and multiplicative growth in the presence of noise a paradigm of such general relevance, that it seems likely that such kinds of cooperation will be found to flower in many settings so far not considered. These might include long-term financial investments, efforts to protect whole economies from damaging negative shocks, or even the ordinary performance of businesses in the face of economic uncertainties. At the Ergodicity Economics Conference, in fact, a UK entrepreneur, James Price, spoke of his initial attempts to grow a network of UK businesses to explore the possible benefits of pooling resources to boost their rate of overall growth.

Where does this kind of cooperation fit into the original framework for “rules for cooperation” as considered by Nowak in his 2006 paper? It would seem clearly to fit best as a form of group selection, where the cooperative group outperforms individuals acting independently. A group able to grow its collective resource base faster than others should generally promote the survival and reproductive success of its members.

But there may also still be scope for this mechanism even in settings where evolutionary dynamics and selection play no role at all. After all, superior performance alone over a period of time is enough to account for the prominence of many business firms or technologies, without any reproduction or selection ever taking place. In fluctuating environments, free exchange and pooling of resources can be enough to give some groups an important edge, and could be enough to account for their persistence. Not all of cooperation has to be explained through natural selection alone.

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