By Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent
This choice of chosen contributions supplies an account of contemporary advancements in dynamic video game conception and its purposes, protecting either theoretical advances and new functions of dynamic video games in such parts as pursuit-evasion video games, ecology, and economics. Written by means of specialists of their respective disciplines, the chapters contain stochastic and differential video games; dynamic video games and their purposes in a number of components, equivalent to ecology and economics; pursuit-evasion video games; and evolutionary online game concept and purposes. The paintings will function a state-of-the artwork account of modern advances in dynamic video game concept and its purposes for researchers, practitioners, and complex scholars in utilized arithmetic, mathematical finance, and engineering.
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Extra resources for Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics (Annals of the International Society of Dynamic Games)
Saint-Pierre numerical methods”, pp. 177–247. Annals of the international Society of Dynamic Games, M. S. Raghavan, T. Parthasarathy Eds. Birkhäuser (1999).  Cardaliaguet P. & Plaskacz S. Invariant solutions of differential games and Hamilton-Jacobi equations for time-measurable hamiltonians, SIAM Journal on Control and Optim. 38, no. 5, 1501–1520 (2000). , Quincampoix M. & Saint-Pierre P. , SIAM J. Control and Optimization 39, no. 5, 1615–1632 (2001). , Quincampoix M. & Saint-Pierre P. Differential games with state-constraints.
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Similarly, Y[t,θ] denotes the set of all measurable selections of Y on [t, θ], and V[t,θ] (y(·)) denotes the set of all measurable selections of the mapping V (y(·)) (for a given y(·)) on the same interval. The following suppositions hold true. 1. U , Y and V¯ are compact subsets of finite-dimensional vector spaces, U is convex, the mapping y −→ V (y) ⊂ V¯ is compact valued and Lipschitz continuous. 2. The function f : Rn × U × Y × V¯ → Rn has the form f (x, u, y, v) = f0 (x, y, v) + B(x, y)u, where f0 and B are continuous, locally Lipschitz in x uniformly with respect to the other variables.
Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics (Annals of the International Society of Dynamic Games) by Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent