Topology-dependent rationality and quantal response equilibria in structured populations

Area of Science:

• Socioeconomics
• Network Science
• Behavioral Economics

Background:

• Real-world actors rarely exhibit perfect rationality.
• Socioecological systems involve networked actors with varying rationality.
• Previous research suggested scale-free networks optimize system rationality.

Purpose of the Study:

• To explore a graded notion of rationality in networked socioecological systems.
• To investigate how network topology influences system-level rationality.
• To identify network configurations that optimize collective cognitive behavior.

Main Methods:

• Parametrizing actor rationality by network position.
• Quantifying system rationality using Jensen-Shannon divergence between Nash and logit quantal response equilibria.
• Employing analytic arguments and numerical optimization experiments on various games (Prisoner's Dilemma, Stag Hunt, Battle of the Sexes, Matching Pennies).

Main Results:

• Increasing degree heterogeneity in complex networks can enhance rationality for certain games.
• Rationality-optimal configurations are not scale-free.
• Core-periphery networks, with dominant hubs and low-degree peripheries, show significantly smaller deviations from rationality compared to scale-free networks for specific games.
• Optimal core-periphery structures vary slightly based on game type (e.g., degree difference between core and periphery).

Conclusions:

• Network topology critically influences collective rationality in socioecological systems.
• Core-periphery network structures are more effective at promoting system rationality than scale-free networks.
• Findings offer insights into wealth inequality and global corporate network structures.