Computational Mechanism Design Optimal Auction Design

All agents have deliberation procedures with 07 c 01

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Unformatted text preview: justing the Number of Agents Fig 2 a compares the performance of each auction mechanism as the number of agents is varied between 5 and 100 log scale. All agents have deliberation procedures with = 0:7; C = 0:1. We plot e ciency i, revenue ii, average computational-cost iii, and average utility iv. The bid-increment in the ascending-price auction is set to enable agents to achieve positive expected utility from participation in the auction, while maximizing performance. For N 10 we have A S P , with agents achieving positive expected utility for participation in all auctions. For 10 N 35 it at rst appears that S A, however the agents in the sealed-bid auction now have negative utility for participation iv.6 So, discounting the performance of the sealed-bid auction, for 10 N 70 agents we have A P S . Finally, for large numbers of agents, N 70 we have P A S . Therefore, the ascending-price auction performs best for small to medium numbers of agents N 70, and the postedprice auction performs better than the sealed-bid auction for medium to large numbers of agents N 10, and better than the ascending-price auction for large numbers of agents N 70. Although the surplus to the winning agent remains approximately constant in all auctions as the number of agents increases unlike in regular auctions, Agents that deliberate in the ascending-price auction assume that they will win the good for current ask price p if they bid. The auction actually remains open and other agents can bid. 6 This is because there are no homogeneous beliefs that agents can hold about the distribution of bids from agents that are consistent with the actual distribution of bids that occurs when agents hold the beliefs. The inaccuracy in agents' models leads to a loss in utility. 5 8 (i) 100 90 70 80 (ii) (i) 100 90 100 90 (ii) Efficiency (%) Efficiency (%) Revenue (%) 80 70 60 50 40 1 2 80 70 60 50 Revenue (%) 0 0.5 1 1.5 Bid Increment (iii) 2 80 70 60 50 60 50 40 10 Number of Agents (iii) 0.3 10 10 Num...
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