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Computational Mechanism Design Optimal Auction Design

# 3 02 01 0 01 average utility 02 015 01 005 0 1 2 02

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Unformatted text preview: ber of Agents (iv) 0.4 0.3 1 10 2 0 0.5 1 1.5 Bid Increment (iv) 2 0.4 0.4 0.3 Average Computational Cost 0.25 Average Computational Cost 0.3 0.2 0.1 0 −0.1 Average Utility 0.2 0.15 0.1 0.05 0 1 2 0.2 0.1 0 −0.1 Average Utility 0 0.5 1 1.5 Bid Increment 2 0.2 0.1 0 −0.1 10 Number of Agents 10 a 10 Number of Agents 1 10 2 0 0.5 b 1 1.5 Bid Increment 2 Fig. 2. a Auction performance: `x' sealed-bid; `o' posted-price sequential; `+' ascending-price. Agents with = 0:7; C = 0:1. Bid increment in the ascending-price auction is adjusted to provide agents with positive expected utility from participation. Averaged over 1000 trials. b Performance of ascending-price auction. N = 10 agents, = 0:7; C = 0:1. where it falls, the average utility for participation can only remain positive if the total computational cost also remains approximately constant or increases to no more than the surplus. The only auction that can sustain a xed but positive amount of deliberation as the number of agents increases is the postedprice mechanism, because it isolates agents from the e ect of more agents by o ering the good sequentially to each agent. E ciency and revenue tend to decrease as the number of agents increases, again contrary to the performance markets with agents that have easy valuation problems. Performance decreases because the surplus from participation is less able to support the amount of deliberation that is necessary for high e ciency and revenue with large numbers of agents. Fig 2 b plots the performance of the ascending-price auction for = 0:7, C = 0:1 and N = 10, as the bid-increment is increased. Small bid increments support more e cient allocations and higher revenue, but also lead to more deliberation and can result in agents receiving negative utility from participation in the auction. In this example the agents have positive utility for participation with a bid increment 0:25, see Fig 2 b iv, and the seller is able to achieve a revenue that is almost as good as that possible with very small bid increments. 4.2 Adjusting the Complexity of the Valuation P...
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