Inter-role reciprocity in evolutionary trust game on square lattices

TL;DR

This paper introduces a novel lattice-based simulation framework for bipartite games like the trust game, revealing how inter-role spatial reciprocity can foster trust under certain conditions.

Contribution

It proposes a new lattice topology for bipartite game simulation, enabling the study of inter-role reciprocity mechanisms in trust dynamics.

Findings

Moderate return ratios promote trust and cooperation.

Inter-role clusters help sustain trust in the population.

High or low returns negatively impact trustees or trustors.

Abstract

Simulating bipartite games, such as the trust game, is not straightforward due to the lack of a natural way to distinguish roles in a single population. The square lattice topology can provide a simple yet elegant solution by alternating trustors and trustees. For even lattice sizes, it creates two disjoint diagonal sub-lattices for strategy learning, while game interactions can take place on the original lattice. This setup ensures a minimal spatial structure that allows interactions across roles and learning within roles. By simulations on this setup, we detect an inter-role spatial reciprocity mechanism, through which trust can emerge. In particular, a moderate return ratio allows investing trustors and trustworthy trustees to form inter-role clusters and thus save trust. If the return is too high, it harms the survival of trustees; if too low, it harms trustors. The proposed simulation framework is also applicable to any bipartite game to uncover potential inter-role spatial mechanisms across various scenarios.