# Relationships between dilemma strength and fixation properties in coevolutionary games

## TL;DR

This paper explores how the arrangement of cooperators and defectors on networks influences the strength of social dilemmas, revealing that certain network structures lead to higher cooperation-favoring coefficients.

## Contribution

It establishes a relationship between structure coefficients and dilemma strength scaling, highlighting the impact of network topology on cooperation dynamics.

## Key findings

- Certain graphs allow large structure coefficients for specific arrangements.
- Large structure coefficients correspond to extensive regions of dilemma strength parameters.
- Network structure significantly influences cooperation outcomes in evolutionary games.

## Abstract

Whether or not cooperation is favored over defection in evolutionary games can be assigned by structure coefficients for any arrangement of cooperators and defectors on any network modeled as a regular graph. We study how these structure coefficients relate to a scaling of dilemma strength in social dilemma games. It is shown that some graphs permit certain arrangements of cooperators and defectors to possess particularly large structure coefficients. Moreover, these large coefficients imply particularly large sections of a bounded parameter plane spanned by scaling gamble-intending and risk-averting dilemma strength.