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• W2770269462 abstract "The current chapter discusses a utilization from the field of evolutionary game dynamics and in particular from its subarea called replicator dynamics . Considering an infinite continuous strategy space, which for example might be considered as the sampling space of a continuously varying trait of a biological population, as well as payoff functions of Gaussian type we build up a non-local degenerate parabolic problem. As it is appropriate for degenerate problems, a regularized approximation is constructed and then some a priori estimates for its solutions are obtained. Using the derived estimates, we prove that solutions converge to the trivial solution if the initial population is small, whereas they undergo a blow-up in finite time if the initial population is large. In particular, in the latter case, it is shown that the blow-up set coincides with the whole strategy space, i.e. the finite-time blow-up is global." @default.
• W2770269462 created "2017-12-04" @default.
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• W2770269462 date "2017-11-29" @default.
• W2770269462 modified "2023-09-23" @default.
• W2770269462 title "A Non-local Model Illustrating Replicator Dynamics" @default.
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• W2770269462 doi "https://doi.org/10.1007/978-3-319-67944-0_6" @default.
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