How widely can the objective of mechanism design be generalized?

Question

The mechanism design lectures I've been watching have focused on the objective of maintaining performance guarantees in terms of either total surplus or total revenue/virtual surplus (while also paying attention to inventive compatibility guarantees and polynomial runtime guarantees).

How far away from this objective can a mechanism designer wander, and still use the discipline of mechanism design to formulate games? For example, can the mechanism designer care about some specific combination of surplus and revenue, or about minimizing the number of rounds an ascending auction is expected to finish in relative to revenue (maybe the auction venue charges by the hour), etc.? Can surplus optimization and revenue optimization (subject to incentive compatibility and polynomial runtime) be extended to cover the vast majority of real world design objectives for auctions and other mechanisms, and if not, does mechanism design have the tools to address other real world objectives, or is the field too limited by how new it is?

Answer 1

The short answer is that all the questions you asked fit with the area of mechanism design. The long answer is a bit more complicated.

Usually, a mechanism is defined to be a function from message profiles to outcomes. In many cases, it is without loss of generality to take messages to be types by a suitable revelation principle. Then one can look for the restriction the solution concept used imposes on the relationship between outcomes and type profiles. This is completely independent of any specific objective. The integral conditions used to prove the revenue equivalence theorem are of this type, as are impossibility results like the Gibbard-Satterthwaite theorem and the Myerson-Satterthwaite theorem.

The other questions you have are either about specific algorithmic implementation of mechanisms (polynomial runtime) or a specific class of dynamic mechanisms (number of rounds in ascending auction). The first area is part of algorithmic mechanism design, the flavor practiced mostly by computer scientists, and involves specific methods that are often closely tied to a specific problem. Here, it might be a bit harder to adapt the methods to different problems. Dynamic mechanism design, the area of your second question, is a relatively new subfield. The magic of mechanism design is that you can often find optimal mechanisms in the class of all mechanisms, including ones you would never have thought of. This requires an abstract mathematical specification of a mechanism. I gave the usual one above. To discuss your problem, you would need to have a formal definition of an ascending auction that should be rich enough to not reduce to a specific mechanism but not so rich as not to deserve the name ascending auction. This might require a lot of work.