Multiple Steady States, Limit Cycles and Chaotic Attractors in Evolutionary Games with Logit Dynamics

This paper investigates, by means of simple, three and four strategy games, the occurrence of periodic and chaotic behaviour in a smooth version of the Best Response Dynamics, the Logit Dynamics. The main finding is that, unlike Replicator Dynamics, generic Hopf bifurcation and thus, stable limit cycles, do occur under the Logit Dynamics, even for three strategy games. Moreover, we show that the Logit Dynamics displays another bifurcation which cannot to occur under the Replicator Dynamics: the fold catastrophe. Finally, we find, in a four strategy game, a period-doubling route to chaotic dynamics under a 'weighted' version of the Logit Dynamics.

The emergence of reciprocally beneficial cooperation

We offer a new and robust model of the emergence and persistence of cooperation when interactions are anonymous, the population is well-mixed, and evolution selects strategies according to material payoffs. The model has a Prisoner’s Dilemma structure, but with an outside option of non-participation. The payoff to mutual cooperation is stochastic; with positive probability, it exceeds that from cheating against a cooperator. Under mild conditions, mutually beneficial cooperation occurs in equilibrium. This is possible because the non-participation option holds down the equilibrium frequency of cheating. Dynamic properties of the model are investigated theoretically and through simulations based on replicator dynamics

Protection against Diarrhea Associated with Giardia intestinalis Is Lost with Multi-Nutrient Supplementation: A Study in Tanzanian Children

Giardia intestinalis is a well-known cause of diarrhea in industrialized countries. In children in developing countries, asymptomatic infections are common and their role as cause of diarrhea has been questioned. In a cohort of rural Tanzanian pre-school children, we assessed the association between the presence of Giardia at baseline and subsequent diarrhea risk. The study was conducted in the context of a randomised trial assessing the effect of supplementation with zinc and other micro-nutrients on malaria, and half of the children daily received a multi-nutrient supplement. Surprisingly, we found that the presence of Giardia at baseline was associated with a substantial reduction in diarrhea risk. Multivariate statistical analysis showed that this protection could not be explained by differences in age or walking distance to the dispensary between children with and without Giardia. Because we cannot exclude that children differed in other (unmeasured) characteristics, we cannot draw firm conclusions about the causality of the observed association, but our findings support the view that the parasite is not an important cause of diarrhea in highly endemic settings. Striking was that the Giardia-associated protection was lost when children received multi-nutrients. Our data do not provide information about the mechanisms involved, but suggest that multi-nutrients may influence the compositionor pathogenicity of intestinal biota