By Steffen Jorgensen, Marc Quincampoix, Thomas L. Vincent
This number of chosen contributions offers an account of modern advancements in dynamic video game concept and its purposes, overlaying either theoretical advances and new purposes of dynamic video games in such components as pursuit-evasion video games, ecology, and economics. Written by means 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 lined include:
* stochastic and differential games
* dynamic video games and their functions in numerous 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 video game idea and its purposes for researchers, practitioners, and complex 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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Extra info for Advances in Dynamic Game Theory: Numerical Methods, Algorithms, and Applications to Ecology and Economics
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](·). 2. Definition 18. Let E be a closed collection of nonempty compact sets in Rn and J : E −→ R will be a lower semicontinuous function. Let E ∈ E be fixed and let F : E → comp(Rn ) be a set-valued field on E. We define the lower Dini derivative of J at E in the direction of the field F as DE− J (E; F ) := liminf inf h,δ→0+ J (E ) − J (E) , E ∈ E, (I + F)(E) ⊂ E + hδB .
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.
Viability Theory. Birkhäuser, Boston (1991). -P. 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).