By Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent

This selection of chosen contributions offers an account of modern advancements in dynamic video game thought and its functions, protecting either theoretical advances and new functions of dynamic video games in such components as pursuit-evasion video games, ecology, and economics. Written by way of specialists of their respective disciplines, the chapters are an outgrowth of shows from the eleventh foreign Symposium on Dynamic video games and Applications.

Key subject matters lined include:

* stochastic and differential games

* dynamic video games and their purposes in quite a few parts, similar to ecology and economics

* numerical equipment and algorithms in dynamic games

* 0- and nonzero-sum games

* pursuit-evasion games

* evolutionary online game idea and applications

The paintings will function a state-of-the paintings account of contemporary advances in dynamic online game thought and its functions for researchers, practitioners, and complex scholars in utilized arithmetic, mathematical finance, and engineering.

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Additional resources for Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics

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63] Saint-Pierre P. Viable capture basin for studying differential and hybrid games: application to finance. Int. Game Theory Rev. 6, no. 1, 109–136 (2004). [64] Saint-Pierre P. Approximation of capture basins for hybrid systems, in Proceedings of the 2001 European Control Conference, Porto, Portugal, September 4–7 (2001). , Moitie R. & Leitmann G. Viability analysis of an aircraft flight domain for take-off in a windshear. Lyapunov’s methods in stability and control. Math. Comput. Modelling 36, no.

The goal of the pursuer is to drive a trajectory of the system (1) to the terminal set M ∗ in a finite time. The goal of the evader is the opposite one: to deviate the system’s trajectory from the terminal set as long as possible. We will treat the game, standing on the pursuer’s side. 1. Any compact segment [a, b] contains a finite number of instants τi . Differential Games with Impulse Control 39 Assume that the pursuer can affect the system (1) only at discrete instants τi and that his impact at these moments is of impulse nature, and described using the Dirac delta function [13]: ∞ u(t) = ui δ(t − τi ).

Let us suppose that x1 ∈ α1 [M − ξ(n, x, ω)] ∩ [Wi (n, v(·)) − wi (n)], x2 ∈ α2 [M − ξ(n, x, ω)] ∩ [Wi (n, v(·)) − wi (n)], α1 , α2 ∈ A. Due to the convexity of the sets M − ξ(n, x, ω) and Wi (n, v(·)) − wi (n), the inclusion λx1 + (1 − λ)x2 ∈ (λα1 + (1 − λ)α2 )[M − ξ(n, x, ω)] ∩ [Wi (n, v(·)) − wi (n)] holds for any λ ∈ [0, 1]. From this it follows that λα1 + (1 − λ)α2 ∈ A and the set A is convex. Convexity of the set A implies that α[M − ξ(n, x, ω)] ∩ [Wi (n, v(·)) − wi (n)] = ∅ for all α such that 0 ≤ α ≤ α˜ k (n, x, v(·), ω).

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