Efficient and optimal mechanisms with radio spectrum sharing

Optimal mechanism design with spectrum sharing differs from the traditional setting mainly in that some technological constraints (e.g., non-interference constraints) need to be taken into account explicitly. In this paper we characterize surplus-maximizing (efficient) and revenue-maximizing (optimal) mechanisms in a spectrum sharing context where a principal allocates transmitted power among a group of potentially interested users (transmitter-receiver pairs). Under regularity conditions about value distributions and non-interference constraints, we show that efficiency (optimality) typically involves spectrum sharing by multiple users, and the exact allocation of transmitted power is determined such that the ratio of marginal value (virtual value) over marginal cost (in terms of the cost to the interference generated) is equal among all shared users. We show that efficient and optimal mechanisms in our setting are actually dominant-strategy incentive compatible, and that they can also be implemented by well-designed all-pay or discriminatory-price auctions.