Prominent structural patterns such as small-world and core-periphery structures amount to some of the most important emergent characteristics of a social network. Yet little work is done to interpret these emergent phenomena in a unified way. Towards a unified interpretation framework, we connect the establishment of social patterns with social capital. Social capital captures the benefits that an individual gains from its social surrounding. We argue that individuals’ desire to gaining higher social capital may give rise to important network properties. To validate this claim, we propose social capital game that mathematically conceptualizes bonding and bridging social capital. This framework allows us to regard individuals in a social network as learning agents who gain social capital through iteratively building interpersonal ties. The link-building decisions of these agents are guided by a multi- agent reinforcement learning (MARL) algorithm which improves agents’ capability through repeated game plays. We conduct a series of experiments which demonstrate (1) the collective behaviors of the agents give rise to salient social patterns, and (2) by varying agents’ preferences to different forms of social capital, different types of social patterns emerge. In particular, bonding social capital plays a pivotal role in the formation of a community structure in the network while bridging social capital is instrumental to the emergence of core-periphery structure. Our work sheds light on the formation of complex network phenomena.