Many Agent Games in Socio-economic Systems: Corruption, Inspection, Coalition Building, Network Growth, Security by Vassili N. Kolokoltsov & Oleg A. Malafeyev

Many Agent Games in Socio-economic Systems: Corruption, Inspection, Coalition Building, Network Growth, Security by Vassili N. Kolokoltsov & Oleg A. Malafeyev

Author:Vassili N. Kolokoltsov & Oleg A. Malafeyev
Language: eng
Format: epub
ISBN: 9783030123710
Publisher: Springer International Publishing


For functions on , we shall use the smooth approximation with as in Theorem 2.​5.​1. More precisely,

where is a mollifier, a nonnegative infinitely smooth even function on with compact support and . Thus

The estimates (2.​60) and (2.​62) of Theorem 2.​5.​1 remain the same:

and

(4.26)

for all , and (2.​61) generalizes to

(4.27)

Consequently, arguing as in Theorem 2.​5.​1, we obtain (using similar notation)

And therefore,

To get rid of , we also approximate F by the function , so that



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