Our hotel price predictor described in
Section 4 assumes that *ATTac-2001*'s bids do not
affect the ultimate closing price (Assumption 3 from
Section 2). This assumption holds in a large economy.
However in TAC, each hotel auction involved agents competing for
hotel rooms. Therefore, the actions of each agent had an
appreciable effect on the clearing price: the more hotel rooms an
agent attempted to purchase, the higher the clearing price would be,
all other things being equal. This effect needed to be taken into
account when solving the basic allocation problem.

The simplified model used by *ATTac-2001* assumed that the th highest
bid in a hotel auction was roughly proportional to (over the
appropriate range of ) for some . Thus, if the predictor
gave a price of , *ATTac-2001* only used this for purchasing two hotel
rooms (the ``fair'' share of a single agent of the rooms), and
adjusted prices for other quantities of rooms by using .

For example, *ATTac-2001* would consider the cost of obtaining rooms to
be . One or two rooms each cost , but each cost ,
each cost , 5 each cost , etc. So in total, rooms
cost , while cost . The reasoning behind this procedure
is that if *ATTac-2001* buys two rooms -- its fair share given that there
are 16 rooms and 8 agents, then the 16th highest bid (*ATTac-2001*'s 2 bids
in addition to 14 others) sets the price. But if *ATTac-2001* bids on an
additional unit, the previous 15th highest bid becomes the
price-setting bid: the price for all rooms sold goes up from to
.

The constant was calculated from the data of several hundred games during the seeding round. In each hotel auction, the ratio of the th and th highest bids (reflecting the most relevant range of ) was taken as an estimate of , and the (geometric) mean of the resulting estimates was taken to obtain .

The LP allocator takes these price estimates into account when
computing by assigning higher costs to larger purchase
volumes, thus tending to spread out *ATTac-2001*'s demand over the different
hotel auctions.

In *ATTac-2001*, a few heuristics were applied to the above procedure to
improve stability and to avoid pathological behavior: prices below $1
were replaced by $1 in estimating ; was used for purchasing
fewer than two hotel rooms; hotel rooms were divided into early
closing and late closing (and cheap and expensive) ones, and the
values from the corresponding subsets of auctions of the seeding
rounds were used in each case.