  In many settings agents participate in multiple different auctions that are
not necessarily implemented simultaneously. Future opportunities affect
strategic considerations of the players in each auction, introducing
externalities. Motivated by this consideration, we study a setting of a market
of buyers and sellers, where each seller holds one item, bidders have
combinatorial valuations and sellers hold item auctions sequentially.
  Our results are qualitatively different from those of simultaneous auctions,
proving that simultaneity is a crucial aspect of previous work. We prove that
if sellers hold sequential first price auctions then for unit-demand bidders
(matching market) every subgame perfect equilibrium achieves at least half of
the optimal social welfare, while for submodular bidders or when second price
auctions are used, the social welfare can be arbitrarily worse than the
optimal. We also show that a first price sequential auction for buying or
selling a base of a matroid is always efficient, and implements the VCG
outcome.
  An important tool in our analysis is studying first and second price auctions
with externalities (bidders have valuations for each possible winner outcome),
which can be of independent interest. We show that a Pure Nash Equilibrium
always exists in a first price auction with externalities.
