Risk aversion in economic transactions

Most people are risk-averse (risk-seeking) when they expect to gain (lose). Based on a generalization of ``expected utility theory'' which takes this into account, we introduce an automaton mimicking the dynamics of economic operations. Each operator is characterized by a parameter q which gauges people's attitude under risky choices; this index q is in fact the entropic one which plays a central role in nonextensive statistical mechanics. Different long term patterns of average asset redistribution are observed according to the distribution of parameter q (chosen once for ever for each operator) and the rules (e.g., the probabilities involved in the gamble and the indebtedness restrictions) governing the values that are exchanged in the transactions. Analytical and numerical results are discussed in terms of how the sensitivity to risk affects the dynamics of economic transactions.Comment: 4 PS figures, to appear in Europhys. Let

Exact results for the Barabasi queuing model

Previous works on the queuing model introduced by Barab\'asi to account for the heavy tailed distributions of the temporal patterns found in many human activities mainly concentrate on the extremal dynamics case and on lists of only two items. Here we obtain exact results for the general case with arbitrary values of the list length $L$ and of the degree of randomness that interpolates between the deterministic and purely random limits. The statistically fundamental quantities are extracted from the solution of master equations. From this analysis, new scaling features of the model are uncovered

Single-species fragmentation: the role of density-dependent feedbacks

Internal feedbacks are commonly present in biological populations and can play a crucial role in the emergence of collective behavior. We consider a generalization of Fisher-KPP equation to describe the temporal evolution of the distribution of a single-species population. This equation includes the elementary processes of random motion, reproduction and, importantly, nonlocal interspecific competition, which introduces a spatial scale of interaction. Furthermore, we take into account feedback mechanisms in diffusion and growth processes, mimicked through density-dependencies controlled by exponents $\nu$ and $\mu$, respectively. These feedbacks include, for instance, anomalous diffusion, reaction to overcrowding or to rarefaction of the population, as well as Allee-like effects. We report that, depending on the dynamics in place, the population can self-organize splitting into disconnected sub-populations, in the absence of environment constraints. Through extensive numerical simulations, we investigate the temporal evolution and stationary features of the population distribution in the one-dimensional case. We discuss the crucial role that density-dependency has on pattern formation, particularly on fragmentation, which can bring important consequences to processes such as epidemic spread and speciation