Advances in Dynamic Game Theory: Numerical Methods, by Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent PDF

By Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent

ISBN-10: 0817643990

ISBN-13: 9780817643997

ISBN-10: 0817645535

ISBN-13: 9780817645533

This selection of chosen contributions supplies an account of contemporary advancements in dynamic video game conception and its functions, protecting either theoretical advances and new functions of dynamic video games in such parts as pursuit-evasion video games, ecology, and economics. Written via specialists of their respective disciplines, the chapters contain stochastic and differential video games; dynamic video games and their purposes in numerous components, reminiscent of ecology and economics; pursuit-evasion video games; and evolutionary video game idea and purposes. The paintings will function a state-of-the artwork account of contemporary advances in dynamic online game concept and its purposes for researchers, practitioners, and complicated scholars in utilized arithmetic, mathematical finance, and engineering.

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Additional info for Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics (Annals of the International Society of Dynamic Games)

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18 P. Cardaliaguet, M. Quincampoix, P. 3. 1. The collection E consists of nonempty compact sets and is closed in the Hausdorff metric. For every compact Z there is some E ∈ E containing Z. 2. There exists a constant LE such that for each ε > 0 and each E ∈ E there exists E ∈ E for which E + εB ⊂ E ⊂ E + εLE B. 3. For every Z ∈ comp(Rn ) there is a unique minimal element of E containing Z. The following dynamic programming principle adapts standard arguments. Proposition 17. 3, for every E ∈ E, t ∈ [0, T ) and s ∈ (t, T ] IE (t, E) = inf sup IE (s, E(s)), α∈A[t,s] y∈Y [t,s] where E(·) := Xα(y),y [t, E](·).

Impulse Differential Inclusions and Hybrid Systems: A Viability Approach, Lecture Notes, University of California at Berkeley (1999). -P. & Da Prato G. Stochastic Nagumo’s Viability Theorem, Stochastic Analysis and Applications, 13, 1–11 (1995). -P. Dynamic Economic Theory: A Viability Approach, SpringerVerlag, Berlin and New York (1997). -P. & Da Prato G. The Viability Theorem for Stochastic Differential Inclusions, Stochastic Analysis and Applications, 16, 1–15 (1998). , Da Prato G. & Frankowska H.

We just show how this principle applies for the minimal time problem. In the minimal time problem, the dynamics of the game is still given by (1). Victor—playing with v—is now the pursuer: he aims at reaching a given target C as fast as possible. Ursula—playing with u—is now the evader: she wants to avoid the target C as long as possible. We assume here that the target C ⊂ RN is closed. If x(·) : [0, +∞) → RN is a continuous trajectory, the first time x(·) reaches C is ϑC (x(·)) = inf {t ≥ 0 | x(t) ∈ C}, with convention inf (∅) = +∞.

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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


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