In an independent private value auction environment, we are interested in strategy-proof mechanisms that maximize the agents' residual surplus, that is, the utility derived from the physical allocation minus transfers accruing to an external entity. We find that, under the assumption of an increasing hazard rate of type distributions, an optimal deterministic mechanism never extracts any net payments from the agents, \ie it will be budget-balanced. Specifically, optimal mechanisms have a simple ``posted price'' or ``option'' form. In the bilateral trade environment, we obtain optimality of posted price mechanisms without any assumption on type distributions, thereby providing a rationale for confining attention to budget-balanced mechanisms.
Mechanism design private information bilateral trade budget balance Myerson-Satterthwaite Theorem