....¹

Recall that $200 is the maximum possible value of E to any client under the TAC parameters.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... so.²

As computed by Shou-de Lin of the TAC organizing team.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... goods.³

The general allocation problem is NP-complete, as it is equivalent to the set-packing problem [Garey JohnsonGarey Johnson1979]. Exhaustive search is computationally intractable even with only 8 clients.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... skyrocketed⁴

With just 2 high-bidders, the only way to have the price escalate would be if they bid for a combined total of 16 rooms of the same hotel type. That could only happen if all of their clients were to stay in the same hotel on the same night, a very unlikely scenario given the TAC parameters.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... average.⁵

In general, ATTac-2000's average score decreased with increasing numbers of high-bidders, as games became more volatile.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.

... earlier⁶

This change has been adopted in the specification of TAC-01.

.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.