# Topological enslavement in evolutionary games on correlated multiplex networks

## TL;DR

This paper explores how in multiplex networks with strong degree correlations, the network topology can dominate the evolutionary game dynamics, making outcomes independent of payoffs and initial conditions.

## Contribution

It reveals the phenomenon of topological enslavement in multiplex networks, showing how network structure can override incentives in evolutionary games.

## Key findings

- Strong degree correlations lead to outcome independence from payoffs.
- Topology can enslave the dynamics, fixing cooperation or defection.
- Initial conditions determine the final state under certain network configurations.

## Abstract

Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoner's dilemma or the harmony game, with imitation dynamics. Adjusting the incentives by changing the payoff parameters can favor cooperation, as found in the harmony game, over defection, which prevails in the prisoner's dilemma. Here, we show that this is not always the case if individuals engage in strategic interactions in multiple domains. In particular, we investigate evolutionary games on multiplex networks where individuals obtain an aggregate payoff. We explicitly control the strength of degree correlations between nodes in the different layers of the multiplex. We find that if the multiplex is composed of many layers and degree correlations are strong, the topology of the system enslaves the dynamics and the final outcome, cooperation or defection, becomes independent of the payoff parameters. The fate of the system is then determined by the initial conditions.