Nash-equilibrium Seeking Algorithm for Power-Allocation Games on Networks of International Relations

TL;DR

This paper develops a Nash-equilibrium seeking algorithm tailored for power-allocation games in international relations networks, enhancing the modeling of strategic interactions with real-world data.

Contribution

It introduces a novel algorithm that guarantees the existence of pure-strategy Nash equilibria in revised international security games on signed graphs.

Findings

Algorithm successfully predicts country survivability using 1940 data.

Enhanced framework captures complex strategic behaviors in international relations.

Provides a more realistic modeling approach for networked security scenarios.

Abstract

In the field of international security, understanding the strategic interactions between countries within a networked context is crucial. Our previous research has introduced a ``games-on-signed graphs'' framework~\cite{LiMorse2022} to analyze these interactions. While the framework is intended to be basic and general, there is much left to be explored, particularly in capturing the complexity of strategic scenarios in international relations. Our paper aims to fill this gap in two key ways. First, we modify the existing preference axioms to allow for a more nuanced understanding of how countries pursue self-survival, defense of allies, and offense toward adversaries. Second, we introduce a novel algorithm that proves the existence of a pure-strategy Nash equilibrium for these revised games. To validate our model, we employ historical data from the year 1940 as the game input and predict countries' survivability. Our contributions thus extend the real-world applicability of the original framework, offering a more comprehensive view of strategic interactions in a networked security environment.