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

This e-book, an outgrowth of the tenth overseas Symposium on Dynamic video games, offers present advancements of the idea of dynamic video games and its purposes. The textual content makes use of dynamic online game versions to method and remedy difficulties bearing on pursuit-evasion, advertising and marketing, 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 strategies.

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

Example text

2∗ ) Let some convex compact sets A, B, and C be such that the difference ρA − ρB is convex and the function conv {ρB − ρC } has finite value everywhere in R2 . Then the difference conv {ρA − ρC } − conv {ρB − ρC } is also convex. Assume f = ρA − ρC , g = ρB − ρC . The function f − g = (ρA − ρC ) − (ρB − ρC ) = ρA − ρB is convex. Convexity of the function conv f − conv g = conv {ρA − ρC } − conv {ρB − ρC } is shown in the next lemma. 2. Let functions f and g : R2 → R be positively homogeneous, continuous, the difference f − g be convex, and the function conv g have finite value everywhere in R2 .

2. Let functions f and g : R2 → R be positively homogeneous, continuous, the difference f − g be convex, and the function conv g have finite value everywhere in R2 . Then the difference conv f −conv g is a convex function. 2, let us formulate some auxiliary propositions. They are quite simple, so no proofs are given. Let us denote the boundary of a set D by ∂D. Restriction of f to a set D will be written as f D . By conv D f we mean the convex hull of the function f computed in a convex set D. 1◦ Let f : Rn → R be a convex function.

As described in Section 5 in ∗ C is not completely swept by the set the text relating to Figure 5, the set A − ∗ B − C. Therefore, the set Wc2 (t) is not completely swept by the set Wc1 (t). 1 connected to the number of arguments of the payoff function is essential. 8 Conclusion In this chapter, a linear antagonistic differential game with fixed terminal time, geometric constraints on the players’ controls, and continuous quasi-convex terminal payoff function depending on two components of the phase vector is considered.

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Advances in Dynamic Games: Applications to Economics, by Alain Haurie, Shigeo Muto, Leon A. Petrosjan, T. E. S.
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