Synchronization in agents harvesting game with regional nature

In this paper, we consider multiple agents harvesting natural resources. Any agent has two harvesting strategies, moderate or immoderate. The Agent is located at vertex of a graph, its neighborhood in the graph represents its local nature. The local nature can be healthy or damaged according to a fitness function, which depends on its previous value, its recovery ability, the agent´s harvesting strategy and its neighbors´ strategies. The income of agents can be described by a snowdrift game. At each game round, each agent will adopt the harvesting strategy of the most successful one in its neighborhood. Stability analysis of the model is given. Simulations show that both complete synchronization and periodic synchronization can happen.