# Self-Stabilization Through the Lens of Game Theory

## TL;DR

This paper applies game theory to formalize and analyze Dijkstra's self-stabilization solutions, providing insights into their convergence properties and step complexity in fault-tolerant computing.

## Contribution

It introduces a game-theoretic framework for understanding self-stabilization and quantifies the steps needed for convergence in Dijkstra's first solution.

## Key findings

- Formalization of self-stabilization via game theory
- Determination of exact steps for convergence in Dijkstra's solution
- Enhanced understanding of fault-tolerance mechanisms

## Abstract

In 1974 E.W. Dijkstra introduced the seminal concept of self-stabilization that turned out to be one of the main approaches to fault-tolerant computing. We show here how his three solutions can be formalized and reasoned about using the concepts of game theory. We also determine the precise number of steps needed to reach self-stabilization in his first solution.