Dynamical systems of conflict in terms of structural measures

TL;DR

This paper models conflict dynamics between opponents using measures with self-similar structures, demonstrating the possibility of one opponent dominating the space through controlled redistribution strategies.

Contribution

It introduces a novel framework for analyzing conflict systems with self-similar measures and proves the existence of controlled conflict where one side dominates.

Findings

Existence of controlled conflict with one opponent occupying almost the entire space

Comparison of conflict effects under structural approximations

Strategies for redistributing measures to influence conflict outcomes

Abstract

We investigate the dynamical systems modeling conflict processes between a pair of opponents. We assume that opponents are given on a common space by distributions (probability measures) having the similar or self-similar structure. Our main result states the existence of the controlled conflict in which one of the opponents occupies almost whole conflicting space. Besides, we compare conflicting effects stipulated by the rough structural approximation under controlled redistributions of starting measures.