Evolutionary stable strategies in networked games: the influence of topology

TL;DR

This paper investigates how network topology influences the evolutionary stability of strategies in networked games, revealing that certain strategies like Zero-determinant can survive or dominate in non-homogeneous networks, contrary to well-mixed populations.

Contribution

It introduces the concept of topological stability, showing how network structure, evolutionary process, and initial conditions affect strategy stability in networked populations.

Findings

Zero-determinant strategies can survive in non-homogeneous networks.

Network topology significantly impacts strategy dominance.

Topological stability varies with initial strategy distribution.

Abstract

Evolutionary game theory is used to model the evolution of competing strategies in a population of players. Evolutionary stability of a strategy is a dynamic equilibrium, in which any competing mutated strategy would be wiped out from a population. If a strategy is weak evolutionarily stable, the competing strategy may manage to survive within the network. Understanding the network-related factors that affect the evolutionary stability of a strategy would be critical in making accurate predictions about the behaviour of a strategy in a real-world strategic decision making environment. In this work, we evaluate the effect of network topology on the evolutionary stability of a strategy. We focus on two well-known strategies known as the Zero-determinant strategy and the Pavlov strategy. Zero-determinant strategies have been shown to be evolutionarily unstable in a well-mixed population of players. We identify that the Zero-determinant strategy may survive, and may even dominate in a population of players connected through a non-homogeneous network. We introduce the concept of `topological stability' to denote this phenomenon. We argue that not only the network topology, but also the evolutionary process applied and the initial distribution of strategies are critical in determining the evolutionary stability of strategies. Further, we observe that topological stability could affect other well-known strategies as well, such as the general cooperator strategy and the cooperator strategy. Our observations suggest that the variation of evolutionary stability due to topological stability of strategies may be more prevalent in the social context of strategic evolution, in comparison to the biological context.