The Ausubel Auction Problem








 


Description:

 Nowadays auctions have become an important method of buying and selling a great variety of assets in different markets around the world. The increasing use of this mechanism has led to a growing interest in the subject. Thus the number of paper published on both the field of auction theory and its experimental examination is increasing considerably.





 



Click here to get this description in tex format and here to get the figure in eps format.

The specific problem to be solved is finding optimal bidding strategies for a dynamic multi-unit auction, which is usually referred to as Ausubel auction with dropout information [Aus04]. This auction scheme has had an important role on recent auctions of 3G licenses and spectrum. The solution would represent the bidding strategy (defined as the action to be taken under different auction conditions) that maximizes the bidder's payoff.

Instances and best known solutions for those instances:


Even though we are aware of previous strategy generation efforts [AM95] [AJ02] , as far as we know, no specific attempt has been made to identify strategies for this specific auction type.

The experimental settings to be considered consist of an independent-private-value framework in which bidders have weakly diminishing marginal values, are risk neutral and have no budget constrains. With these assumptions, in Ausubel auctions with dropout information, sincere bidding (SB), that is bidding what you think the item is worth, by every bidder constitutes an efficient equilibrium.

The approach that we suggest [MQI05] is based on artificial adaptive agents. We have developed a genetic algorithm (GA) that can be employed to evolve bidding strategies in the Ausubel auction with pure private values. The algorithm generates different bidding strategies or actions to be taken according to the auctions conditions which are defined by three indicators: tendency towards elasticity in price demand, the number of bidders active in the auction with respect to the total number of bidders at the beginning of the auction and the number of objects that have not been clinched with respect to the number of objects demanded by the GA bidder.

The actions are defined in terms of deviation from SB. For each possible state of the auction we consider the following four: bid half of the SB quantity; bid the SB quantity; bid 50% more of the SB quantity or bid twice as much as the SB quantity.

The algorithm is tested under several experimental environments that differ in the elasticity of their demand curves, number of bidders and quantity of lots auctioned. The number of lots auctioned and the number of bidders are considered as external variables with the following values: m = 10, 15, 20 and 25; n= 4, 6 and 8.


 

Lots

B

i

d

d

e

r

s

 

10

15

20

25

4

16%

16%

60%

24%

76%

36%

88%

36%

6

4%

16%

16%

36%

36%

44%

44%

52%

8

16%

0%

16%

24%

36%

28%

32%

44%


The table reports the likelihood of the GA strategy beating SB using the suggested approach over 25 experiments. The results achieved using inelastic utility curves on top and elastic below.



 





Related Papers:

[Aus04] L.M. Ausubel, "An Efficient Ascending-Bid Auction for Multiple Objects", American Economic Review, Vol. 94, 5, pp. 1452-1475 (2004)

[AM95] J. Andreoni J., J.H. Miller, "Auctions with artificial adaptive agents", Games and Economic Behavior, Vol. 10, pp. 39 - 64 (1995)

[AJ02] P. Anthony, N.R. Jennings, "Evolving bidding strategies for multiple auctions", Proceedings of the 15th European Conference on Artificial Intelligence. 178 - 182 (2002)

[MQI05] A. Mochón, D. Quintana, P. Isasi, Y. Sáez, ·Genetic Algorithms versus Human Bidding Strategies for Auctions", Proceedings of the 4th IEEE International Workshop on Soft Computing as Transdisciplinary Science and Technology. 619-628 (2005)


Click here to get the bibliography in bibtex format.



 

 

 



Last Updated: 10 /7/05                                                                                 For any question or suggestion, click here to contact with us.