Social dilemmas in off-lattice populations

TL;DR

This paper investigates how spatial reciprocity influences cooperation in off-lattice populations, revealing both similarities and key differences from lattice models, with implications for microbiological environments.

Contribution

It introduces an off-lattice population approach to study social dilemmas, highlighting differences in cooperation dynamics compared to lattice-based systems.

Findings

Off-lattice populations can enhance spatial reciprocity effectiveness.

Strategies may separate in continuous space, aiding cooperator survival.

Soft borders between patches affect long-term stability of homogeneous domains.

Abstract

Exploring the possible consequences of spatial reciprocity on the evolution of cooperation is an intensively studied research avenue. Related works assumed a certain interaction graph of competing players and studied how particular topologies may influence the dynamical behavior. In this paper we apply a numerically more demanding off-lattice population approach which could be potentially relevant especially in microbiological environments. As expected, results are conceptually similar to those which were obtained for lattice-type interaction graphs, but some spectacular differences can also be revealed. On one hand, in off-lattice populations spatial reciprocity may work more efficiently than for a lattice-based system. On the other hand, competing strategies may separate from each other in the continuous space concept, which gives a chance for cooperators to survive even at relatively high temptation values. Furthermore, the lack of strict neighborhood results in soft borders between competing patches which jeopardizes the long term stability of homogeneous domains. We survey the major social dilemma games based on pair interactions of players and reveal all analogies and differences compared to on-lattice simulations.