Answer: The rishonim give different reasons for why one mustn’t conduct
business transactions on Shabbos. Rambam (Shabbos 23:12) writes that we are
concerned that one may record the transaction. Rashi (Beitza 37a) adds that
there is a prohibition against discussing business matters on Shabbos.
The Gemara (Shabbos
18a) writes that one is allowed to open a flow of water before Shabbos that
will run onto a garden on Shabbos. Thus, the Shulchan Aruch (OC 252:5) writes that one is allowed to have
one’s utensils perform work for them on Shabbos. There is a machlokes as
to whether this applies to business, too, however.
R’ Akiva Eiger (Teshuvos
1:159) writes that one cannot set
up a business transaction before Shabbos that will be performed on Shabbos. R’
Avraham Borenstein
(Avnei Nezer OC:51)
explains why scheduled business transactions are different to other automated melachos.
R’ Meir Simcha of Dvinsk (Ohr Sameach, Shabbos 23:12) maintains,
however, that there is no difference between business and other melachos.
Likewise,
the Maharam Shik (131) writes that one may submit a bid before Shabbos for an
auction that will end on Shabbos. Although the auctioneer announces the final
bid, by submitting the bid in advance, one has set the ball rolling.
Additionally, while winning the actual bid obligates the winner to pay, the
transaction is not complete until they have paid (See Teshuvos Vehanhagos 1:232).
In conclusion, one may bid for an item on eBay that ends on
Shabbos.