Aspiration dynamics and the sustainability of resources in the public goods dilemma

• We establish a game model to capture the sustainable time of public goods.
• We propose a theoretical method to study how fast an evolutionary process ends.
• Strong selection shortens the evolutionary time of public resource dilemma.
• Compared with imitation process, aspiration dynamics prolong the sustainable time.
• The sustainable time is the shortest for the intermediate aspiration level.

How to exploit public non-renewable resources is a public goods dilemma. Individuals can choose to limit the depletion in order to use the resource for a longer time or consume more goods to benefit themselves. When the resource is used up, there is no benefit for the future generations any more, thus the evolutionary process ends. Here we investigate what mechanisms can extend the use of resources in the framework of evolutionary game theory under two updating rules based on imitation and aspiration, respectively. Compared with imitation process, aspiration dynamics may prolong the sustainable time of a public resource.