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This paper analyses a mathematical model with time delay for the labor force on a market. Three variables are taken into account: the number of unemployed and employed persons in the market and the number of new vacancies created by the government and the private sector, which is based on a past value of the unemployment number in the creation of new vacancies. The positivity of the solutions is examined and the existence of a unique equilibrium point of the mathematical model is proved. A local stability analysis is undertaken, showing that the unique equilibrium is locally asymptotically stable, for any value of the time delay. Numerical simulations are carried out which substantiate the theoretical statements and suggest that the positive equilibrium point is globally asymptotically stable. [ABSTRACT FROM AUTHOR]

In this paper, we consider evolutionary games and construct a model of replicator dynamics with bounded continuously distributed time delay. In many circumstances, players interact simultaneously while impacts of their choices take place after some time, which implies a time delay exists. We consider the time delay as bounded continuously distributed other than some given constant. Then, we investigate the stability of the evolutionarily stable strategy in the replicator dynamics with bounded continuously distributed time delay in two-player game contexts. Some stability conditions of the unique interior Nash equilibrium are obtained. Finally, the simple but important Hawk–Dove game is used to verify our results. [ABSTRACT FROM AUTHOR]