Computational Mechanism Design Optimal Auction Design

# Finally consider a market with a mixture of agents

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Unformatted text preview: -bid auctions become approximately revenue equivalent for small deliberation costs and high computational e ectiveness c.f. easy local problems, see Fig 3 b i, C = 0:05; 1 , = 0:7. Finally, consider a market with a mixture of agents; some with hard valuation problems  inexperienced agents", and some with easy valuation problems  experienced agents". We assume a fraction f of inexperienced agents; and a fraction 1 , f of experienced agents that know their value vi for the good. Fig 4 plots results for N = 10, and inexperienced agents with = 0:3 and C = 0:5. The ascending-price auction has the best performance, but the sealed-bid auction often outperforms the posted-price auction, even though the e ciency and revenue comes only from experienced agents. For a small to medium fraction of inexperienced agents, f 0:4, the sealed-bid and ascending-price auctions are approximately revenue equivalent, and A  S P . For a medium to large fraction of inexperienced agents, 0:4 f 0:8, we have A S P , and with many inexperienced agents the sealed-bid auction fails and A P S . The posted-price auction performs badly for heterogeneous markets, e.g. f = 0:6, because the seller must choose an ask price to target one type of agent. The other auctions are better able to involve both agent types. Also, we see that when there are only a few experienced agents they are able to use their informational 10 (i) 100 90 100 90 (ii) Efficiency (%) 80 70 60 50 Revenue (%) 0 0.2 0.4 0.6 0.8 Fraction of Inexperienced Agents (iii) 1 80 70 60 50 0 0.2 0.4 0.6 0.8 Fraction of Inexperienced Agents (iv) 1 Average Utility to Inexperienced Agents 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 Fraction of Inexperienced Agents 1 Average Utility to Experienced Agents 1 0.8 0.6 0.4 0.2 0 0 0.2 0.4 0.6 0.8 Fraction of Inexperienced Agents 1 Fig. 4. Performance of the sealed-bid `x', ascending-price `+', and posted-price `o' auctions as the fraction of inexperienced agents in the system increases. N = 10; = 0:3; C = 0:5. The results are computed over 2000 trials. Bid increment = 0:2. advantage, and achieve high average utility from participation in the auction, see Fig 4 iv. 5 Related...
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