Driven by the rapid growth of content traffic and the demand for service quality, Internet content providers (CPs) have started to bypass transit providers and connect with access providers directly via private peering agreements. This peering relationship often raises disputes, e.g., Netflix vs. Comcast, and is not well understood. In this paper, we build a peering contract model and propose the concept of contractual equilibrium, based on which we study the formation and evolution of peering contracts. By using market data, we emulate the strategic peering behavior of providers and shed light on the understanding of private peering~agreements.