Non-ergodicity and the evolution of cooperation

7 July, 2015 at 15:30 | Posted in Economics | 1 Comment

Cooperation, here, is a persistent behavioural pattern of individual entities pooling and sharing resources … Here we point out a very general mechanism – a sufficient null model – whereby cooperation can evolve. The mechanism is based the following insight: natural growth processes tend to be multiplicative. In multiplicative growth, ergodicity is broken in such a way that fluctuations have a net-negative effect on the time-average growth rate, although they have no effect on the growth rate of the ensemble average. Pooling and sharing resources reduces fluctuations, which leaves ensemble averages unchanged but – contrary to common perception – increases the time-average growth rate for each cooperator …

peters2011_cloudEconomics should be the place to look for an explanation of human social structure, but oddly the basic message from mainstream economics seems to be that optimal, rational, sensible behaviour would shun cooperation. In many ways we see cooperation in the world despite, not because of, economic theory.

Many economists are aware of this shortcoming of their discipline and are address- ing it, often from psychological or neurological perspectives, as well as with the help of agent-based evolutionary simulations.

We show that cooperation and social structure arise from simple analytically solv- able mathematical models for economically optimal behaviour. We contend that where economics uses models of such simplicity it ignores essential insights of the last two centuries of mathematics. Specifically, economics uses inappropriate math- ematical representations of randomness. These representations have been essentially unchanged since the 17th century. As a consequence effects of fluctuations and risk (or of dynamics and time) are not properly accounted for …

In our model the advantage of cooperation, and hence the emergence of structure is purely a non-linear effect of fluctuations – cooperation reduces the magnitude of fluctuations, and over time (though not in expectation) this implies faster growth …

The impact of risk reduction on time-average growth suggests that risk man- agement has a rarely recognised significance. Fluctuation reduction (i.e. good risk management) does not merely reduce the likelihood of disaster or the size of up and down swings but also it improves the time-average performance of the structure whose risks are being managed. In a financial context the value of a portfolio whose risks are well managed will not just display smaller fluctuations, but will grow faster in time. Similarly, a well-diversified economy will grow faster in the long run than a poorly diversified economy.

Ole Peters & Alexander Adamou

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  1. Ugh!
    We show that cooperation and social structure arise from simple analytically solv- able mathematical models for economically optimal behaviour.

    Critique: Neoclassical economics is made up of “analytic models” that do not correspond with reality.
    .
    [Truth: a model requires a one to one correspondence between components of the model and components of reality. “Analytic models” are misnamed because their components include causal connections but the causal connections of reality are considered beyond the scope of the endeavor. Mapping is, by definition, not a consideration. Therefore analytic models are, at best, metaphors for reality. As such, they are empty of content. Metaphors contain no new content, they are literary devises to help the reader.]
    .
    Critique: the solution to bad models? We should use a different metaphor that sounds more plausible! We can prove that such a metaphor can be imagined that contains no internal contradictions.
    The crowd: See, there’s a better way than the Chicago Boys!
    .
    [The truth: But, but, it’s just a more plausible version of hand waving! You empower the devil by endorsing the method! (Puts face in hand and shakes head.)]

    are “made” with no attempt to map real causation


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