Given a large population of players, each player has three possible choices between option 1 or 2 or no option. The two options are equally favorable and the population has to reach consensus on one of the two options quickly and in a distributed way. The more popular an option is, the more likely it is to be chosen by uncommitted players. Uncommitted players can be attracted by those committed to any of the other two options through a cross-inhibitory signal. This model originates in the context of honeybees swarms, and we generalize it to duopolistic competition and opinion dynamics. The contributions of this work include (1) the formulation of an evolutionary game model to explain the behavioral traits of the honeybees, (2) the study of the individuals and collective behavior including equilibrium points and stability, (3) the extension of the results to the case of structured environment via complex network theory, (4) the analysis of the impact of the connectivity on consensus, and (5) the study of absolute stability for the collective system under time-varying and uncertain cross-inhibitory parameter.

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Background and aims:The COVID-19 pandemic represents a source of stress and potential burnout for many physicians. This single-site survey aimed at assessing perceived stress and risk to develop burnout syndrome among physicians operating in COVID wards.Methods: This longitudinal survey evaluated stress and burnout in 51 physicians operating in the COVID team of Gemelli Hospital, Italy.Participants were asked to complete the Maslach Burnout Inventory (MBI) and the Perceived Stress Questionnaire on a short run (PSQs) (referring to the past 7 days) at baseline (T0) and then for four weeks (T1-T4). Perceived Stress Questionnaire on a long run (PSQl) (referring to the past 2 years) was completed only at T0. Results:Compared with physicians board-certified in internal medicine, those boardcertified in other disciplines showed higher scores for the Emotional Exhaustion (EE) score of the MBI scale (P < .001). Depersonalisation (DP) score showed a reduction over time (P = .002). Attending physicians scored lower than the resident physicians on the DP scale (P = .048) and higher than resident physicians on the Personal Accomplishment (PA) scale (P = .04). PSQl predicted higher scores on the EE scale (P = .003), DP scale (P = .003) and lower scores on the PA scale (P < .001). PSQs showed a reduction over time (P = .03). Attending physicians had a lower PSQs score compared with the resident physicians (P = .04).

Abstract-This paper provides a mean field game theoretic interpretation of opinion dynamics and stubbornness. The model describes a crowd-seeking homogeneous population of agents, under the influence of one stubborn agent. The game takes on the form of two partial differential equations, the Hamilton-Jacobi-Bellman equation and the KolmogorovFokker-Planck equation for the individual optimal response and the population evolution, respectively. For the game of interest, we establish a mean field equilibrium where all agents reach ε-consensus in a neighborhood of the stubborn agent's opinion.