Abstract
We propose a projected gradient dynamical system as a model for a bargaining scheme for an asset for which the two interested agents have personal valuations that do not initially coincide. The personal valuations are formed using subjective beliefs concerning the future states of the world, and the reservation prices are calculated using expected utility theory. The agents are not rigid concerning their subjective probabilities and are willing to update them under the pressure to reach finally an agreement concerning the asset. The proposed projected dynamical system, on the space of probability measures, provides a model for the evolution of the agents, beliefs during the bargaining period and is constructed so that an agreement is reached under the minimum possible deviation of both agents from their initial beliefs. The convergence results are shown using techniques from convex dynamics and Lyapunov function theory.

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Our aim was to determine prototypical patterns of eating behaviour among Portuguese higher education students, and to relate these patterns with BMI. Data from 280 higher education students (63.2% females) aged between 18 and 27 years were analysed. Several eating behaviour dimensions (emotional and external eating, flexible and rigid restraint, binge eating, and eating self-efficacy) were assessed, and eating styles were derived through cluster analysis. BMI for current, desired and maximum self-reported weights and the differences between desired and current BMI and between maximum and current BMI were calculated. Women scored higher in emotional eating and restraint, whereas men showed higher eating self-efficacy. Men had higher current, desired and maximum BMI. Cluster analysis showed three eating styles in both male and female subsamples: "Overeating", "High self-efficacy" and "High restraint". High self-efficacy women showed lower BMI values than the others, and restrictive women had higher lost BMI. High self-efficacy men showed lower desired BMI than overeaters, and lower maximum and lost BMI than highly restrictive ones. Restrictive women and men differ on important eating behaviour features, which may be the cause of differences in the associations with BMI. Eating self-efficacy seems to be a central variable influencing the relationships between other eating behaviour dimensions and BMI.