By Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent
This number of chosen contributions provides an account of modern advancements in dynamic online game thought and its functions, overlaying either theoretical advances and new purposes of dynamic video games in such components as pursuit-evasion video games, ecology, and economics. Written through specialists of their respective disciplines, the chapters contain stochastic and differential video games; dynamic video games and their purposes in a variety of components, similar to ecology and economics; pursuit-evasion video games; and evolutionary online game idea and purposes. The paintings will function a state-of-the paintings account of modern advances in dynamic online game conception and its purposes for researchers, practitioners, and complex scholars in utilized arithmetic, mathematical finance, and engineering.
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Extra info for Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics (Annals of the International Society of Dynamic Games)
The Hybrid Guaranteed Capture Basin Algorithm in Economics, Preprint (2004). , Quincampoix M. & Rainer C. Existence of stochastic control under state constraints. C. R. Acad. Sci. Paris Sér. I Math. 327, no. 1, 17–22 (1998). , Quincampoix M. & Saint-Pierre P. Some Algorithms for Differential Games with two Players and one Target, RAIRO Mathematical Modeling and Numerical Analysis 28, no. 4, 441–461 (1994).  Cardaliaguet P. A differential game with two players and one target, SIAM J. Control and Optimization 34, no.
Here this occurs as soon as it reaches the equilibrium set. 2 Towards Dynamical Meta-Games In fact, we do not really know what dynamical equations govern the evolution of the resource. We could fix Malthusian feedbacks u in a given class U of continuous feedbacks as parameters and study the viability kernel Viabu ([a, b]) of the interval [a, b] under the system (i) x (t) = (u(x(t)) − v(t))x(t) C , (32) ,v (ii) v(t) ∈ V (x(t)) := γ x(t) − c where the control parameter is v, but, instead of fixing feedbacks, we can study “meta-games” by setting bounds c and d on the velocities of the growth rate u(t) and the exploitation effort v(t), regarded as meta-controls, whereas the meta-states of the meta-game are the triples (x, u, v): (i) x (t) = (u(t) − v(t))x(t) (ii) u (t) ∈ B(0, c) (33) (iii) v (t) ∈ B(0, d) subjected to the viability constraints u(t) ∈ R and C γ x(t)−c ≤ v(t) ≤ v.
IEEE Trans. Automat. Control 47, no. 1, 2–20 (2002). , Capuzzo-Dolcetta I. Optimal control and viscosity solutions of Hamilton-Jacobi-Bellman equations. Systems and Control: Foundations and Applications. Birkhäuser, Boston (1997). , Jensen R. A geometric characterization of viable sets for controlled degenerate diffusions. Calculus of variations, nonsmooth analysis and related topics. Set-Valued Anal. 10, no. 2–3, 129–141 (2002).  Barles G. Solutions de viscosité des équations de Hamilton-Jacobi.
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