Evolutionary dynamics of fairness on graphs with migration.

Area of Science:

• Evolutionary Game Theory
• Network Science
• Computational Social Science

Background:

• Individual migration is key to population evolutionary dynamics on networks.
• The networked ultimatum game models fairness and strategic interactions.
• Understanding fairness evolution requires considering population structure and mobility.

Purpose of the Study:

• Investigate the evolutionary dynamics of fairness in the networked ultimatum game.
• Analyze the effects of population dilution and individual migration on fairness strategies.
• Determine the impact of network topology, specifically node degree, on fairness evolution.

Main Methods:

• Generalized the networked ultimatum game to include population dilution and migration.
• Employed numerical simulations to explore evolutionary dynamics on graphs.
• Developed an analytical method to validate simulation findings for pairwise interaction games.

Main Results:

• An optimal node degree was identified, maximizing the population's offer level.
• Population dilution and migration ability decreased offer levels but increased acceptance levels.
• Natural selection favored self-incompatible strategies beyond critical vacancy or migration rates.

Conclusions:

• Network structure, dilution, and migration significantly shape fairness evolution.
• The findings provide insights into the emergence of fairness in dynamic populations.
• The analytical method offers a versatile tool for studying evolutionary dynamics in finite populations.