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研究生:傅冠鈞
研究生(外文):Kuan-Chun Fu
論文名稱:廣義膨脹第二價格拍賣
論文名稱(外文):General Second Price auction with price inflation
指導教授:陳和麟
口試委員:張時中呂學一魏宏宇
口試日期:2016-07-29
學位類別:碩士
校院名稱:國立臺灣大學
系所名稱:電機工程學研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2016
畢業學年度:104
語文別:英文
論文頁數:46
中文關鍵詞:關鍵字拍賣廣義第二價格拍賣Vickrey拍賣底價機制膨脹機制
外文關鍵詞:keyword auctiongeneral second price auctionVickrey auctioninflated price mechanismreserve price mechanism
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拍賣(auction)是一個傳統的機制去競標一個物品,Vickrey提出一個Vickrey拍賣(Vickrey auciton)也稱作第二價格拍賣(second price auction)。廣義第二價格拍賣(general second price)是從Vickrey拍賣沿伸的。兩者不同之處是廣義第二價格拍賣是多樣物品,Vickrey拍賣是一個物品。廣義第二價格拍賣常常被使用在關鍵字拍賣(keyword auction)上面。在收益方面,關鍵字拍賣對於這些公司(Google, Facebook, Microsoft等等)扮演著相當重要的角色。

Vickrey拍賣跟廣義第二價格拍賣最大的缺點是比起其他的拍賣機制,獲益可能會很低。為了增加收益替公司賺取更多的獲益,最佳拍賣(optimal auction)是一個可以讓期望收益最大化的拍賣。
在單一物品時,Myerson提出了底價(reserve price)的機制去達到最佳拍賣。另外,在單一物品時,Fu et al.提出了膨脹(inflate price)的機制去賺取更多的獲益,Bulow and Klemperer提出了額外增加一個競標者(bidder)的機制去賺取更多的獲益。然而在多樣物品時,最佳拍賣還是一個開放的問題。Edelman and Schwarz實驗了廣義第二價格拍賣融合低價機制。

因此,我們專注在廣義第二價格拍賣。第一,我們結合了廣義第二價格與膨脹機制。第二,在廣義第二價格拍賣中,我們同時融合膨脹機制跟底價機制。在我們的實驗跟參數設定下,第一,我們比較了廣義第二價格拍賣跟廣義第二價格拍賣與膨脹機制,我們發現廣義第二價格拍賣與膨脹機制可以比廣義第二價格拍賣多賺取百分之五的獲利。
第二,我們比較了廣義第二價格拍賣與底價膨脹機制跟廣義第二價格拍賣與底價機制,我們發現廣義第二價格拍賣與底價膨脹機制可以比廣義第二價格拍賣與底價機制多賺取百分之三的獲利。

總結,此論文提供了多種變形的廣義第二價格拍賣可以幫助拍賣者(auctioneer)賺取更多的獲益。我們證明了在多種變形的廣義第二價格拍賣下,存在兩種均衡(equilibrium)。另外,做了多組實驗,比較在不同的變因下的獲益。

Auction is a traditional process to sell items.Vickrey proposed the Vickrey auction in 1961.The general second price auction which sells multiple items is generalized from Vickrey auction.The general second price auction is a widely used mechanism for keyword auctions.Keyword auction which can earn lots of revenue plays an important role for the companies. (Google, Facebook, Microsoft and so on)

The largest drawback for Vickrey and general second price is that the revenue could be much lower compared to other auction mechanisms.To increase the revenue and help the companies to make more money, an optimal mechanism is proposed by Myerson. An optimal mechanism is a mechanism that maximizes the expected revenues of the auctioneer.
In single item auction, an optimal mechanism was obtained by Myerson with reserve price mechanism. Moreover, in single item auction, Fu et al. proposed the inflated mechanism helping to earn more revenue and Bulow and Klemperer proposed that adding one more bidder helping to earn more revenue.However, in the keyword auction which is a multiple advertising slots auction, optimal mechanism is an open problem.Edelman and Schwarz experimented the general second price auction with reserve price.

Hence, we focous on general second price auction.
First, we combine general second price auction with inflated price.Second, we combine the inflated price mechanism and reserve price mechanism into general second price auction.In our simulations and parameter setting, first, we compare the revenue between general second price auction and general second price auction with inflated price. We find that the revenue of general second price auction with inflated price 5% more than the revenue of general second price auction.Second, we compare the revenue between general second price auction with reserve price and general second price auction with inflated price and reserve price. We find that the revenue of general second price auction with inflated price and reserve price is 3% more than the revenue of general second price auction with reserve price.

In summary, the thesis provided variant general second price auctions which can earn more revenue for auctioneer.
In the variant general second price auctions, we proved there exist two equilibria. Moreover, we executed experiments and compare revenue under different factors.

List of Figures ix
List of Tables xi
Chapter 1 Introduction 1
1.1 Auction and Keyword Auction...................... 2
1.2 Related work and revenue ........................ 3
1.3 Our results ................................ 4
1.4 Organization ............................... 4
Chapter 2 Related Work 6
2.1 Auction .................................. 7
2.2 KeywordAuctions ............................ 11
Chapter 3 Model 13
3.1 General second price auction with inflated price . . . . . . . . . . . . 14
3.2 General second price auction with reserve price . . . . . . . . . . . . 19
3.3 General second price auction with reserve and inflated price . . . . . 21
Chapter 4 Experiment 24
4.1 Simulating general second price auction with inflated price . . . . . . 25
4.2 Versus all of mechanism ......................... 37
Bibliography 44

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[3] Edelman, Benjamin, and Michael Schwarz. “Optimal Auction Design in a Multi- unit The Case of Sponsored Search Auctions”, Unpublished manuscript, Harvard Business School, 2006.
[4] Vickrey, William. “Counterspeculation, Auctions, and Competitive Sealed Tenders”, The Journal of Finance 16.1: 8-37, 1961.
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[13] Feng, Juan, Hemant K. Bhargava, and David M. Pennock. “Implementing sponsored search in web search engines: Computational evaluation of alternative mechanisms”, INFORMS Journal on Computing 19.1: 137-148, 2007.
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[18] Moldovanu, Benny, and Manfred Tietzel. “Goethe’s SecondPrice Auction.”, Journal of Political Economy 106.4: 854-859, 1998.

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