Optimal Auction Design for Agents with Hard Valuation Problems

. As traditional commerce moves on-line more business trans-actions will be mediated by software agents, and the ability of agent-mediated electronic marketplaces to e(cid:14)ciently allocate resources will be highly dependent on the complexity of the decision problems that agents face; determined in part by the structure of the marketplace, resource characteristics, and the nature of agents’ local problems. We compare auction performance for agents that have hard local problems, and uncertain values for goods. Perhaps an agent must solve a hard optimization problem to value a good, or interact with a busy and expensive human expert. Although auction design cannot simplify the valuation problem itself, we show that good auction design can simplify meta -deliberation { providing incentives for the \right" agents to deliberate for the \right" amount of time. Empirical results for a particular cost-bene(cid:12)t model of deliberation show that an ascending-price auction will often support higher revenue and e(cid:14)ciency than other auction designs. The price provides agents with useful information about the value that other agents hold for the good.


Introduction
As traditional commerce moves on-line more business transactions will be mediated by software agents, and dynamically negotiated between multiple and fluidly changing partners.The ability of agent-mediated electronic marketplaces to efficiently allocate resources will be highly dependent on the complexity of the decision problems that agents face; determined in part by the structure of the marketplace, resource characteristics, and the nature of agents' local problems.
While many of the costs that are associated with traditional auctions, such as the cost of participation (making bids and watching the progress of an auction), are unimportant in agent-mediated electronic auctions, the cost of valuation remains important [17].The value of a good is often uncertain, and an accurate Optimal Auction Design for Agents with Hard Valuation Problems 207 valuation can require that an agent solves a hard optimization problem, or interacts with a busy and expensive human expert.In fact, electronic markets may make the valuation problem more difficult, because of mitigating factors such as decreased aggregation, increased product differentiation, and increased dynamics [1,4,5].In this paper we compare auction performance for agents that have hard local problems, and uncertain values for goods.
Just as careful market design can reduce the complexity of the bidding problem, for example by providing incentives for agents to reveal their true value for a good [28], careful market design can also reduce the loss in efficiency that is associated with agents that have hard valuation problems.Unlike the bidding problem, market design can not simplify the valuation problem itself.However market design can improve the quality of an agent's decisions about when to reason about the value of a good.A well structured marketplace can provide information to enable the "right" agents to deliberate for the "right" amount of time.Roughly, agents with high values should deliberate more than agents with low values.
For example, consider a bidding agent that participates in an on-line auction for a flight to Stockholm, initialized by a user with a lower bound v on value.The user does not know her exact value for the flight, but finds it relatively easy to bound her value.Although the agent can absorb the costs of monitoring the auction and placing bids, the agent cannot easily refine the user's value for the flight.The value of non-standard and short-supply goods is often subjective, and can depend on many factors that an agent cannot know.However, in an ascending-price auction the agent can bid up to v, and then prompt the user for a more accurate value.Compare this to a sealed-bid auction where the user needs a priori information about the distribution of bids from other agents to make a good decision about how much time to spend deliberating about her value for the flight.The ascending-price auction provides dynamic information on the value of other participants, and can enable the user to avoid deliberation altogether -for example if the price increases above an upper bound on value.
We compare the performance of three market designs with agents that have hard valuation problems: a posted-price sequential auction; a second-price sealedbid auction; and a first-price ascending-price auction [12].In the posted-price auction the seller offers the good at a fixed price to each agent in turn, and does not sell the good if no agent accepts the price.The price is set dynamically in the ascending-and sealed-bid auctions, and we allow the seller to optimize the ask price for distributional information about the values of agents in the posted-price auction.
In Section 2 we introduce a simple model for agents with hard valuation problems that allows the derivation of optimal expected-case metadeliberation and bidding strategies for risk-neutral agents in each auction; we describe the optimal strategies in Section 3. Section 4 presents empirical results from simulation, comparing the efficiency and revenue in each auction for different numbers of agents and different levels of local problem complexity.Finally we discuss related