By Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent

This choice of chosen contributions supplies an account of modern advancements in dynamic video game thought and its purposes, overlaying either theoretical advances and new functions of dynamic video games in such parts 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 overseas Symposium on Dynamic video games and Applications.

Key themes coated include:

* stochastic and differential games

* dynamic video games and their purposes in a variety of components, reminiscent of ecology and economics

* numerical tools and algorithms in dynamic games

* 0- and nonzero-sum games

* pursuit-evasion games

* evolutionary video game thought and applications

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

**Read or Download Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics PDF**

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

**Sample text**

Define the extended closed collection of compact setsˆE in R × Rn as ˆE := {(t, E), t ≥ 0, E ∈ E}. Theorem 19. c. solution of the differential inequality sup min DˆE− J (t, E; (1, f (·, u, y, V (y)))) ≤ 0 y∈Y u∈U with the condition J (t, E) ≥ G(t, E), ∀ (t, E) ∈ ˆE, ˆ ∀ (t, E) ∈ E. c. solution of (18), (19)}. (18) (19) Differential Games Through Viability Theory 19 The proof of this theorem is based on a generalization of Theorem 5 but in the context of tubes with values in collections of sets [53] and with results on the regularity of such tubes [54].

A VR-strategy for Victor at initial condition x0 = (y0 , z0 ) is defined symmetrically as a map B : SG,P (y0 ) −→ SH,Q (z0 ) such that for any θ > 0, and for any trajectories y(·) and y(·) ˜ of SG,P (y0 ) which coincide on [0, θ ], the trajectories z(·) = B(y(·)) and z˜ (·) = B(y(·)) ˜ coincide on [0, θ ]. We denote by B(x0 ) the set of VR-strategies for Victor at x0 . We define, for all x = (y, z) ∈ Rn and all D ⊂ Rn closed, the functions H(x, D) := sup π ∈NPD (x) sup inf f (x, u, v), π u∈U v∈V , LV (x, D) := inf χD (y, q(z, ν)), (26) ν∈N LU V (x, D) := sup inf χD (p(y, µ), z), inf χD (p(y, µ), q(z, ν)) , ν∈N µ∈M (25) (27) where f (x, u, v) = f ((y, z), u, v) = (g(y, u), h(z, v)), and χD (·) denotes the characteristic function of the set D: χD (x) = 0 if x ∈ D +∞ otherwise.

Opti. 36, 125–146 (1997). , Quincampoix M. & Saint-Pierre P. Numerical methods for differential games, in “Stochastic and differential games: Theory and 32 P. Cardaliaguet, M. Quincampoix, P. Saint-Pierre numerical methods”, pp. 177–247. Annals of the international Society of Dynamic Games, M. S. Raghavan, T. Parthasarathy Eds. Birkhäuser (1999). [26] Cardaliaguet P. & Plaskacz S. Invariant solutions of differential games and Hamilton-Jacobi equations for time-measurable hamiltonians, SIAM Journal on Control and Optim.