General Approach

In a wide variety of decision-theoretic settings, it is useful to be
able to evaluate hypothetical situations. In computer chess, for
example, a static board evaluator is used to heuristically measure
which player is ahead and by how much in a given board situation. The
scenario is similar in auction domains, and our bidding agent
*ATTac-2001* uses a situation evaluator, analogous to the static board
evaluator, which estimates the agent's expected profit in a
hypothetical future situation. This ``profit predictor'' has a wide
variety of uses in the agent. For example, to determine the value of
an item, the agent compares the predicted profit assuming the item is
already owned to the predicted profit assuming that the item is not
available.

Given prices for goods, one can often compute a set of purchases and
an allocation that maximizes profit.^{2}
Similarly, if closing
prices are known, they can be treated as fixed,
and optimal bids can be computed (bid high for anything you want to
buy). So, one natural profit predictor is simply to calculate the
profit of optimal purchases under fixed predicted prices. (The
predicted prices can, of course, be different in different situations,
e.g., previous closing prices can be relevant to predicting future
closing prices.)

A more sophisticated approach to profit prediction is to construct a
model of the probability distribution over possible future prices and
to place bids that maximize *expected* profit. An approximate solution
to this difficult optimization problem can be created by
stochastically sampling possible prices and computing a profit
prediction as above for each sampled price. A sampling-based scheme
for profit prediction is important for modeling uncertainty and
the value of gaining information, *i.e.*, reducing the price
uncertainty.

Section 2.1 formalizes this latter approach within a
simplified sequential auction model. This abstraction illustrates
some of the decision-making issues in our full sampling-based approach
presented in Section 2.2. The full setting that
our approach addresses is considerably more complex than the abstract
model, but our simplifying assumptions allow us to focus on a core
challenge of the full scenario. Our guiding principle is to make
decision-theoretically optimal decisions given profit predictions for
hypothetical future situations.^{3}