An evolving Stag-Hunt game with elimination and reproduction on regular lattices

• We present an evolving Stag-Hunt game with reproduction and elimination.
• Each player will try to cut off the most adverse links with the given probability.
• Any isolated defector will be eliminated from the system.
• A new player will be inserted into the system simultaneously.
• The interplay between game dynamics and structure promotes the cooperation level.

Based on a regular lattice, we present an evolving Stag-Hunt game model to illustrate the persistence of cooperation in many real-world systems. In our model, starting from a regular lattice, at first agents play the Stag-Hunt game with each other and perform the strategy update same as the traditional game dynamics on graphs; After that, each player tries to cut off the link with the defective neighbor with the highest fitness and build a new link preferentially connected to a high-degree node; If an isolated node is eliminated from the system, a new player will be reproduced and inserted into the system so as to keep the system size constant. Large-scale numerical simulations indicate that the cooperation level can be greatly promoted compared to the standard stag-hunt game behaviors on regular lattices, and the link rewiring and node’s elimination and reproduction represent the co-evolution between the structure and game dynamics, which facilitates the cooperative clusters among nodes. Our model can, to some extent, characterize the realistic cases in which an individual often tries to avoid the future contact with a defective partner. Current findings are beneficial to help us to deeply understand the evolution of cooperation within many natural, social and economic systems.