# The Evolutionary Price of Anarchy: Locally Bounded Agents in a Dynamic Virus Game

## TL;DR

This paper introduces a realistic evolutionary game model to analyze the Price of Anarchy in dynamic, locally interacting agents, revealing that equilibrium states are often less prevalent and more costly than traditional static analyses suggest.

## Contribution

It develops the concept of evolutionary Price of Anarchy (ePoA) for dynamic, local-interaction settings, extending traditional static PoA analysis with analytical bounds and stochastic process insights.

## Key findings

- Nash equilibria are not always the most common states in the evolutionary process.
- Different strategy update dynamics can lead to high off-equilibrium behavior.
- The ePoA can be significantly higher than the traditional PoA in dynamic settings.

## Abstract

The Price of Anarchy (PoA) is a well-established game-theoretic concept to shed light on coordination issues arising in open distributed systems. Leaving agents to selfishly optimize comes with the risk of ending up in sub-optimal states (in terms of performance and/or costs), compared to a centralized system design. However, the PoA relies on strong assumptions about agents' rationality (e.g., resources and information) and interactions, whereas in many distributed systems agents interact locally with bounded resources. They do so repeatedly over time (in contrast to "one-shot games"), and their strategies may evolve. Using a more realistic evolutionary game model, this paper introduces a realized evolutionary Price of Anarchy (ePoA). The ePoA allows an exploration of equilibrium selection in dynamic distributed systems with multiple equilibria, based on local interactions of simple memoryless agents. Considering a fundamental game related to virus propagation on networks, we present analytical bounds on the ePoA in basic network topologies and for different strategy update dynamics. In particular, deriving stationary distributions of the stochastic evolutionary process, we find that the Nash equilibria are not always the most abundant states, and that different processes can feature significant off-equilibrium behavior, leading to a significantly higher ePoA compared to the PoA studied traditionally in the literature.