Computational Mechanism Design Chapter 3

# In example 1 it is enough to know the value of v2 to

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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 ascending-price 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 best-response, which is simply to bid for the items that maximize its utility at the prices. Although myopic best-response is in general not the optimal sequential strategy for an agent, it can be made a Bayesian-Nash 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 ascending-price 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 best-response without computing exact values for all bundles. For example, an agent can follow a best-response bidding strategy in a pricedirected iterative auction with lower and upper bounds on its values for bundles. Myopic best-response only requires that an agent bids for the bundles with maximum utility value - price in each round. This utility-maximizing 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 best-response local utility-maximizing strategy given the new prices. iBundle Par99, PU00a , introduced in Chapter 5, is an ascending-price 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 best-response agent strategies, because every agent will bid for its value-maximizing 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.

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