Evolution of cooperation in the traveler’s dilemma game on two coupled lattices

• We propose an evolutionary traveler’s dilemma game model on two coupled lattices.
• The coupling effect between two lattices is added into the strategy imitation process.
• The traveler’s dilemma game model parameter R and coupling coefficient commonly dominate the evolution of cooperation.
• The relationship between critical value RcRc leading to extinction of cooperation and strategy range parameter radius is explored.

Although the evolutionary game theory provides a powerful framework to investigate various social dilemmas, the traveler’s dilemma game (TDG) is hardly concerned under this platform within the applied mathematical communities. We put forward an improved traveler’s dilemma game model on two coupled lattices to investigate the effect of coupling effect on the evolution of cooperation based on the traveler’s dilemma game, where the coupling effect between two lattices is added into the strategy imitation process. Large quantities of simulations indicate that the cooperation behavior can be greatly varied when compared to those obtained on the traditionally single lattices. When the model parameter R surpasses a specific threshold, the cooperation will be greatly enhanced, but the cooperation may be inhibited if R   is smaller than this threshold. Meanwhile, we also explore the relationship between the critical value RcRc leading to the extinction of cooperation and the strategy range parameter radius in our model. Our results are surprisingly conducive to understanding the cooperation behavior of traveler’s dilemma game within many real-world systems, especially for coupled and interdependent networked systems.