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By Alain Haurie, Shigeo Muto, Leon A. Petrosjan, T. E. S. Raghavan

ISBN-10: 0817645004

ISBN-13: 9780817645007

ISBN-10: 0817645012

ISBN-13: 9780817645014

This e-book, an outgrowth of the tenth foreign Symposium on Dynamic video games, offers present advancements of the speculation of dynamic video games and its functions. The textual content makes use of dynamic video game types to procedure and clear up difficulties concerning pursuit-evasion, advertising, finance, weather and environmental economics, source exploitation, in addition to auditing and tax evasions. It comprises chapters on cooperative video games, that are more and more drawing dynamic techniques to their classical solutions.

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Read Online or Download Advances in Dynamic Games: Applications to Economics, Management Science, Engineering, and Environmental Management (Annals of the International Society of Dynamic Games) PDF

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Index 407

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Extra resources for Advances in Dynamic Games: Applications to Economics, Management Science, Engineering, and Environmental Management (Annals of the International Society of Dynamic Games)

Example text

The sequence of the continuous functions fi is nonincreasing and is bounded from below by the function conv f . Thus, this sequence has a pointwise limit f˜. The sequence of convex functions hi converges pointwise to ˜ = f˜ − conv g. Hence, the function f˜ = h ˜ + conv g is convex. a convex function h ˜ ˜ Let us prove that f = conv f . One has that f (x) = f (x) (conv f )(x) when x ∈ S. For any x ∈ R2 \S an index i 1 exists such that x ∈ Ci , and, therefore, f˜(x) = fi (x) = conv f Ci i−1 (x) = conv Ci f (x) (conv f )(x).

Kumkov and V. S. Patsko Figure 5: Counterexample for conservation of the complete sweeping after the operation of geometric difference of three-dimensional sets. higher than two. 2 in the case when the positively homogeneous functions have their arguments of dimension three or higher. 2 in the case of functions of the general kind (not positively homogeneous) is demonstrated by the following example. Let the functions f and g be piecewise linear. The graph of the function f can be obtained from a quadrahedral pyramid by cutting it by two planes parallel to the diagonal of the base (Figure 6a).

1 also holds under more general conditions. 1. We use the support functions of the sets under consideration. Recall that every convex compact set A produces a finite positively homogeneous convex function by the formula ρA (l) = max l a : a ∈ A . This function is called the support function of the set A. And vice versa, for any finite positively homogeneous convex function ρ, a convex compact set can be found such that ρ is its support function [16]. Let us establish a correspondence between set operations and operations over support functions.

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Advances in Dynamic Games: Applications to Economics, Management Science, Engineering, and Environmental Management (Annals of the International Society of Dynamic Games) by Alain Haurie, Shigeo Muto, Leon A. Petrosjan, T. E. S. Raghavan

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