Collaboration in networks with randomly chosen agents

•We develop a model of global but rare interaction and local observation.•Local observation is characterized by an arbitrary, fixed network.•Minimum effort game is repeatedly played by a small proportion of randomly chosen agents.•Selected agents observe their own and neighbors’ experiences in the most recent interaction and imitate the most successful choices, though occasionally make mistakes.•Agents will exert the highest effort level when each agent's information neighborhood is large.

The present paper considers a finite population of agents located in an arbitrary, fixed network. In each period, a small proportion of agents are randomly chosen to play a minimum effort game. They learn from both their own and their neighbors’ experiences and imitate the most successful choices, though they may occasionally make mistakes. We show that in the long run all agents will choose the highest effort level provided that each agent's neighborhood is large.