  We study the design of mechanisms in combinatorial auction domains. We focus
on settings where the auction is repeated, motivated by auctions for licenses
or advertising space. We consider models of agent behaviour in which they
either apply common learning techniques to minimize the regret of their bidding
strategies, or apply short-sighted best-response strategies. We ask: when can a
black-box approximation algorithm for the base auction problem be converted
into a mechanism that approximately preserves the original algorithm's
approximation factor on average over many iterations? We present a general
reduction for a broad class of algorithms when agents minimize external regret.
We also present a new mechanism for the combinatorial auction problem that
attains an $O(\sqrt{m})$ approximation on average when agents apply
best-response dynamics.
