Dynamics on Games: Simulation-Based Techniques and Applications to Routing

TL;DR

This paper develops a general framework for analyzing the termination of strategy-update dynamics in multi-player graph games and applies it to interdomain routing problems.

Contribution

It introduces a novel preorder-based framework to reason about the termination of game dynamics, inspired by simulation and graph minor theories.

Findings

Framework preserves termination properties across different game classes

Applicable to interdomain routing, demonstrating practical relevance

Provides theoretical tools for analyzing strategy dynamics in complex networks

Abstract

We consider multi-player games played on graphs, in which the players aim at fulfilling their own (not necessarily antagonistic) objectives. In the spirit of evolutionary game theory, we suppose that the players have the right to repeatedly update their respective strategies (for instance, to improve the outcome w.r.t. the current strategy profile). This generates a dynamics in the game which may eventually stabilise to an equilibrium. The objective of the present paper is twofold. First, we aim at drawing a general framework to reason about the termination of such dynamics. In particular, we identify preorders on games (inspired from the classical notion of simulation between transitions systems, and from the notion of graph minor) which preserve termination of dynamics. Second, we show the applicability of the previously developed framework to interdomain routing problems.