How and why cooperation is able to prevail in social dilemma situations is an intensely investigated subject with much relevance for the well-being of human societies. Many mechanisms that promote cooperation have been identified within the theoretical framework of evolutionary game theory. Here, we advance the subject by relaxing the simplified assumption that each player in the population has the same number of interaction neighbors. This assumption indeed contradicts actual conditions, and it is, thus, important to understand what consequences this has for the evolution of cooperation. We therefore take into consideration that replacement and interaction neighbors can differ, and moreover, that each player can randomly select the number of interaction neighbors. The results of Monte Carlo simulations reveal that the introduction of neighborhood diversity elevates the level of cooperation in various types of social dilemmas, including the prisoner's dilemma and the snowdrift game. We also show that the same mechanism of cooperation promotion remains valid in evolutionary multigames. Taken together, our results strongly support the assertion that diversity, in general, is a strong facilitator of cooperation even under the most testing conditions and they provide a rationale for engineering better social systems.
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