Ising models to study effects of risk aversion in socially interacting individuals

Ising models have been applied not only to describe physical systems but also systems of inter-acting animals and humans. In contrast to physical entities, animal and humans exhibit more complex behaviour such as risk aversion, so that certain payoffs are, for given expected payoff, preferred to uncertain payoffs. Here I extend the classical Ising model to consider risk aversion, and show that this affects the model's stability domains: if individuals are risk averse and their choices differ by the associated risk levels, then higher coupling constants are required to sustain system states in which the riskier choice is abundant; otherwise the risky choice is accompanied (bistability) or even replaced in the system by the less risky choice. The model and results are applied to an economic incentive scheme for the conservation of biodiversity, the agglomeration bonus, that induces not only conservation measures but rewards their spatial agglomeration. Here conservation is the risky choice whose abundance in the land-use system is shown to decline if the landowners are risk-averse.