Effect of emotional migration on Cooperation for public goods games on continuous two-dimensional space.

Emotion helps people hide from traitors and follow partners. It greatly affects the actual migration in a public goods game (PGG). How this factor affect the migration and the corresponding cooperation level has still not been investigated yet. An emotional migration in a PGG on continuous two-dimensional space was investigated. An emotional index was proposed to describe the different attitude of a player to his different neighbors. An emotional migration model was proposed by defining a weight function that a cooperator goes with a neighbor who makes him happier and gets away from a neighbor who makes him angry. Results show that the emotional migration mechanism acts as a double-edged sword, with its effects intricately intertwined with migratory velocity and interaction radius. When both migratory velocity and interaction radius are low, stable emotional communication gradually solidifies the foundation of trust. This process motivates individuals to actively engage in public goods provision, fostering a virtuous cycle of win-win cooperation. Conversely, when migratory velocity surges and the interaction scope expands exponentially, excessive emotional migration disrupts the trust equilibrium, undermines resource allocation order, and renders cooperative strategies unsustainable. Ultimately, this leads to the collapse of the entire cooperative system.