The aim of this paper is modeling of brain as a multi-agent system and then theoretical study of game-theoretic solution concepts in competitive and cooperative multi-agent interactions in this system. Brain as a cognitive function implementer is composed of large-scale neural networks of cognition (neurocognitive networks) which are considered as expert agents that do what they think in their on best expertness. Neurocognitive networks implement the cognitive functions in brain and thorough understanding of cognition is not possible without knowledge of how they operate individually and socially. In this study dynamic interaction among those expert agents are formulated as competitive and cooperative behaviors. We obtain the equilibrium behavior in the long run, and characterize the collective behavior of these expert agents as responsible of intricacies of cognition. By this work, it was shown how complex collective behavior of brain can emerge from the locally optimal behavior of each agent. In the end we will see how these neural networks organize themselves in a way that the collective behavior will be intelligent. It will be shown that the best structure in brain for having intelligent behavior is multilevel hierarchical organization with nesting structures.