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