"Random evolutionary games and random polynomials"Duong, HongEvolutionary game theory (EGT), which incorporates game theory into Darwin’s evolution theory, constitutes a powerful mathematical framework for the study of dynamics of frequencies of competing strategies in large populations. Introduced in 1973 by Maynard Smith and Price in 1973, over the last 50 years, the theory has found its applications in diverse disciplines including biology, physics, economics, computer sciences and mathematics. Incorporating stochasticity/randomness into evolutionary games is of vital importance to capture the inevitable uncertainty, which is an inherent property of complex systems due to environmental and demographic noise or may arise from different sources such as lack of data for measuring the payoffs or unavoidable human estimate errors. A key to gain insightful understanding of the feasibility, diversity and stability of random evolutionary processes is to characterize the statistics of the number of equilibrium points of the evolutionary dynamics. To address this problem, our works connect EGT to random polynomial theory (RPT). In this talk, I will discuss these connections and how we employ the methodology and techniques from RPT to study the statistics of the number of internal equilibria in random evolutionary games. |
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