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Unformatted text preview: compute the allocation to each agent. Consider
Example 1. We can compute the optimal allocation give the item to agent 1 with
information v1 fv2 ; v3 g, and without knowing the exact value of v1 . Also, it is not even
necessary to compute V and V,i to compute Vickrey payments because common terms
cancel. In Example 1, it is enough to know the value of v2 to compute agent 1's Vickrey
payment because the value of v1 cancels: pvick 1 = v1 , vick 1 = v1 , v1 , v2 = v2 . Useful Properties of Iterative Auctions
Iterative price directed auctions, such as ascendingprice auctions, present an important
class of dynamic mechanisms. In each round of the auction the auctioneer announces prices
78 A B AB
b Agent 1 0 a
Agent 2 10 0
Agent 3 0 0 10
15 Table 3.1: Agent values in Example 3.
on the items, or bundles of items, and a provisional allocation which agent is currently
receiving which items. A reasonable bidding strategy for an agent is myopic bestresponse,
which is simply to bid for the items that maximize its utility at the prices. Although myopic
bestresponse is in general not the optimal sequential strategy for an agent, it can be made
a BayesianNash equilibrium of an iterative auction by computing Vickrey payments at
the end of the auction see Chapter 7.
Useful properties of iterative auctions include:
Iterative auctions can solve realistic problems without complete information from
agents. Consider an ascendingprice auction for a single item. It is su cient that the
two agents with the highest value bid in each round, the other agents do not need
to bid and can sit back and watch the price rise, without providing any information.
Implicit information is provided by not responding to prices.
Agents can follow myopic bestresponse without computing exact values for all bundles. For example, an agent can follow a bestresponse bidding strategy in a pricedirected iterative auction with lower and upper bounds on its values for bundles.
Myopic bestresponse only requires that an agent bids for the bundles with maximum utility value  price in each round. This utilitymaximizing set of bundles can
be computed by re ning the values on individual bundles until the utility of one or
more bundles dominates all other bundles.
The information requested dynamically in each round of an auction implicitly, via
the new prices and the bidding rules of the auction is quite natural for agents and
people to provide. The auction does not ask agents to make mysterious comparisons
across di erent bundles, but rather lets agents consider their bestresponse local
utilitymaximizing strategy given the new prices.
iBundle Par99, PU00a , introduced in Chapter 5, is an ascendingprice combinatorial
auction. Agents can adjust their bids in response to bids placed by other agents, and the 79 auction eventually terminates in competitive equilibrium. iBundle solves the problem in
Figure 3.1 in one round with myopic bestresponse agent strategies, because every agent
will bid for its valuemaximizing bundle in response to zero pric...
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This document was uploaded on 03/19/2014 for the course COMP CS286r at Harvard.
 Fall '13
 DavidParkes

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