Computational Mechanism Design Optimal Auction Design

# The optimal expected value metadeliberation and

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Unformatted text preview: revenue and e ciency is often less than for auctions that set the price dynamically. The optimal expected-value metadeliberation and bidding strategy for an agent that faces a xed price p and has beliefs v; v is to deliberate while its expected value v is close to the ask price, and then accept a price p v, and ^ ^ reject the price otherwise, see Fig 1 b. An agent deliberates while its expected value v is within  =2 of the price, for a threshold   ; C;  that depends on ^ the computational e ectiveness 1 ,  of its deliberation procedure, its cost C for deliberation, and its current uncertainty  in value. The threshold decreases as an agent deliberates, and eventually an agent will not deliberate for any ask price when  = 0. Price Price 3.2 Posted-Price Sequential Price v ∆ α∆ Stop deliberating. Reject price. s3: Leave auction -’ v v -’ v * γ∆ Deliberate. v s2: Wait. Deliberate if auction will close, with probability 1 / (Na- 1) v - v Stop deliberating. Accept price. v s1: Bid a b c 0 0 Fig. 1. a Valuation problem. Upper and lower bounds v and v on value before deliberation, with uncertainty  = v , v; new bounds after deliberation v and v are  apart and consistent with the initial bounds. Optimal Metadeliberation and Bidding Strategies: b Posted-price auction; c Ascending-price auction. 3.3 Ascending-Price The auctioneer in an ascending-price auction announces an initial ask price, p, and increases the price a minimum bid increment whenever a bid is received. The auction closes when no bids are received, with the good sold to the highest bidder for the price that it bid. The optimal metadeliberation and bidding strategy in the ascending-price auction is di erent than in the posted-price auction 6 because: 1 the price of the good can increase over time; 2 an agent that bids for the good at price p cannot be sure that it will win the good. In addition to choosing to deliberate or bid, it can also be useful for agents to wait because the price can increase as the result of bids...
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## This document was uploaded on 03/19/2014 for the course COMP CS286r at Harvard.

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