Optimal Contract Design for an Efficient Secondary Spectrum Market

In this paper we formulate a contract design problem where a primary license holder wishes to profit from its excess spectrum capacity by selling it to potential secondary users/buyers, but needs to determine how to optimally price it to maximize its profit, knowing that this excess capacity is stochastic in nature and cannot provide deterministic service guarantees to a buyer. We address this problem by adopting as a reference a traditional spectrum market where the buyer can purchase exclusive access with fixed/deterministic guarantees. We consider two cases; in one the seller has full information on the buyer, including its service requirement and quality constraint, and in the other the seller only knows possible types and their distribution. In the first case we fully characterize the nature of the optimal contract design. In the second case, we find the optimal contract design when there are two possible types and determine a design procedure and show that it is optimal when the nature of the stochastic channel is common to all possible types.