# Topology-dependent rationality and quantal response equilibria in structured populations

## TL;DR

This paper investigates how the structure of social networks influences collective rationality, revealing that core-periphery networks outperform scale-free networks in minimizing deviations from rational behavior across various games.

## Contribution

It demonstrates that optimal rationality in networked systems is achieved by core-periphery structures rather than scale-free topologies, supported by analytical and numerical evidence.

## Key findings

- Core-periphery networks reduce rationality deviations more than scale-free networks.
- Optimal network structures vary slightly between different types of games.
- Increasing degree heterogeneity can enhance rationality, but not always in scale-free networks.

## Abstract

Given that the assumption of perfect rationality is rarely met in the real world, we explore a graded notion of rationality in socioecological systems of networked actors. We parametrize an actors' rationality via their place in a social network and quantify system rationality via the average Jensen-Shannon divergence between the games Nash and logit quantal response equilibria. Previous work has argued that scale-free topologies maximize a system's overall rationality in this setup. Here we show that while, for certain games, it is true that increasing degree heterogeneity of complex networks enhances rationality, rationality-optimal configurations are not scale-free. For the Prisoner's Dilemma and Stag Hunt games, we provide analytic arguments complemented by numerical optimization experiments to demonstrate that core-periphery networks composed of a few dominant hub nodes surrounded by a periphery of very low degree nodes give strikingly smaller overall deviations from rationality than scale-free networks. Similarly, for the Battle of the Sexes and the Matching Pennies games, we find that the optimal network structure is also a core-periphery graph but with a smaller difference in the average degrees of the core and the periphery. These results provide insight on the interplay between the topological structure of socioecological systems and their collective cognitive behavior, with potential applications to understanding wealth inequality and the structural features of the network of global corporate control.