The evolutionary game of pressure (or interference), resistance and collaboration

TL;DR

This paper extends the evolutionary inspection game framework to analyze conflict interactions involving pressure, resistance, and collaboration among large groups, providing rigorous convergence results for various Markov decision models.

Contribution

It introduces a comprehensive analysis of conflict dynamics with pressure and collaboration, including convergence proofs and rates for models with infinite state spaces.

Findings

Proves convergence of Markov models to deterministic evolution

Provides explicit rates of convergence

Applies results to real-world conflict scenarios

Abstract

In this paper we extend the framework of evolutionary inspection game put forward recently by the author and coworkers to a large class of conflict interactions dealing with the pressure executed by the major player (or principal) on the large group of small players that can resist this pressure or collaborate with the major player. We prove rigorous results on the convergence of various Markov decision models of interacting small agents (including evolutionary growth), namely pairwise, in groups and by coalition formation, to a deterministic evolution on the distributions of the state spaces of small players paying main attention to situations with an infinite state-space of small players. We supply rather precise rates of convergence. The theoretical results of the paper are applied to the analysis of the processes of inspection, corruption, cyber-security, counter-terrorism, banks and firms merging, strategically enhanced preferential attachment and many other.