Computational Mechanism Design Optimal Auction Design

3 the metadeliberation problem the metadeliberation

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Unformatted text preview: r all steps, and independent of the nal outcome of the auction. 3 The Metadeliberation Problem The metadeliberation problem is to determine how much deliberation to perform before placing a bid. The decision is a tradeo between reducing uncertainty about the value of the good so that the bid is accurate, and avoiding the cost of deliberation. An agent's optimal metadeliberation strategy does depend on the bids that other agents will make, even in incentive compatible auctions unlike an agent's optimal bidding strategy. Given our model of an agent's valuation problem and decision procedure we derive optimal metadeliberation strategies for agents within the general framework of Russell and Wefald 22 . The key observation is that the value of deliberation is derived from the e ect of deliberation on an agent's bid. Deliberation 4 can only be worthwhile when: 1 it changes an agent's bid; 2 the new bid has greater expected utility than the old bid. For example, an agent should never deliberate about its value for a good if its current upper bound on value is less than the ask price, because further deliberation can never cause the agent to accept the price. Metadeliberation is hard because of uncertainty, about: the e ect of placing a bid b in an auction this can depend on the bids of other agents; the outcome of further deliberation otherwise deliberation is unnecessary!, and the value of goods. We describe normative metadeliberation strategies for agents in each auction below, but see 19 for derivations. We assume risk-neutral agents, who receive utility vi , p for purchasing a good at price p.2 3.1 Second-Price Sealed-Bid In a second-price sealed-bid Vickrey auction agents need distributional information about the bids from other agents to make good metadeliberation decisions. For example, if an agent does not have any information about the bids from other agents it cannot know the probability of winning the auction with a bid b, or its expected surplus if it wins this depends on the second-highest bid received. Uninformed agents are left to either follow a worst-case metadeliberation strategy don't deliberate, a best-case strategy that recommends too much deliberation, or an ad-...
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