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HKEJ Column

Home Research Thought Leadership HKEJ Column
All theory might not be grey, but the golden tree of actual life springs ever green

All theory might not be grey, but the golden tree of actual life springs ever green

13 Sep 2023
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理論未必灰色 生命之樹長青

前不久香港發生一宗命案,其駭人聽聞程度不下於任何經典驚慄片。才華滿溢、資金豐厚的電影製作人,不論如何絞盡腦汁,其創作不見得一定比真實世界奇異精采,很多時反而是從現實世界中找尋獨特的元素,經整理鋪陳後呈現於觀眾眼前。觀眾覺得可觀,往往因為不曾經歷的新鮮感而已,其實現實世界才是電影精采情節的泉源。

經濟學家提出各種經濟理論,其貢獻在相當程度上也源於自身的實際經驗,或事後對實際經驗的總結。本文將分享一些現實生活的例子,以及經濟學家所作的檢視。

銷售價格保證

不守承諾這種情況,除了關乎個人,也會在公司、組織中出現。舉例說,一間百貨公司的新產品售出一部分之後,就有動機透過降價以招徠新顧客。但若舊客戶早知道該公司隨後有降價行動,當時就可能不會購買,而會等待日後降價的好時機。

鑑於公司不守信譽,反而會影響當前銷路,有些公司於是會提供銷售價格保證,擔保顧客所購產品在一段期間(例如90天)之內不會降價,否則消費者憑單據可獲相當於價格差額的賠償。消費者既然不會因早買而損失,也就不必延遲消費。

基於銷售價格保證的約束,公司一旦違約,就要向買家賠償,減價動機自然大減。如此一來,既有售價保證,也能發揮加強公司信譽的作用。價格保證並非只是向消費者提供的優待,同時也有助於監察公司,避免作出短視行為。此舉也許應驗了這個說法:世上沒有無緣無故的愛!

又以「一致競爭條款」(meeting-competition clauses)為例。假設市場上有兩家銷售類似產品的寡頭百貨公司,為方便討論,價格只有高低之分。【表1】顯示兩家公司在不同價格組合之下的利潤。若雙方定價相同,即可平分市場;若一家高價,另一家低價,消費者就會流向低價的公司。

從總體利益來看,甲、乙公司都收高價當然最好(總利潤為20;各得10),但是基於自利目的,不管對方怎樣做,每間公司都有動機選擇低價,因此在一次博弈中,雙方都會選擇「低價,低價」這個組合。然而這結果顯然不如理想,因為總利潤和每間公司的利潤(分別為10,5)均低於「高價,高價」的價格組合。甲乙面對的處境,就是經典的「囚徒困境」(the prisoner’s dilemma)。

我們可以把「高價,高價」稱為合作雙贏的結果,而「低價,低價」則為不合作雙輸的結果。在不能簽署合作協議(在很多地方這是違法行為)的情況下,這兩家公司該如何才能實現合作雙贏?

類似上述銷售價格保證的做法,甲、乙公司可以利用一致競爭條款,巧妙地通過消費者的參與,達到合作雙贏的目的!

若一家公司在銷售中採取這種條款,即表示承諾一旦顧客發現另一家公司的產品價格較低,就會把價格相應調低至同一水平。這種貌似保障消費者的條文,其實降低了這兩家公司降價競爭的動機,原因何在?

若甲公司已經採用一致競爭條款(並採納了高價),乙公司就沒有動機選擇低價了。因為選擇高價就是合作雙贏,若選低價,對方自動會給顧客降價,相當於對方從高價自動變成低價,形成「低價,低價」的雙輸局面。【表2】顯示兩家公司在採用一致競爭條款所得的利潤。

以上兩個例子都屬博弈論經典例子;無獨有偶,銷售價格保證和一致競爭條款也都遠在博弈論普及之前就已使用!

次價招標

拍賣和投標理論是博弈論中的一大用途。拍賣的方法很多,最常見的是首價招標(first-price sealed-bid auction)。投標者先把出價寫下來遞交,成交價是勝出買家所寫的價錢。

這種投標過程相當簡單,但有一個難處,就是該如何出價,叫人頗費思量。舉例說,對於某件拍賣品,若你的最高願付價錢(maximum willingness to pay)是100萬元,並如實填寫,中標後你雖然取得拍品,但要付出100萬元,一加一減,等於白忙了一趟,和沒有參與過一樣!正因如此,出價應低於100萬元,但低至哪個水平,則取決於投標人數和其他相關因素。

1961年,經濟學家維克里(William Vickery)發表了一篇著名的文章,提出一種新穎的招標方法。與上述首價招標一樣,價高者得,唯一不同的是,勝出買家所付的是次高入標價,而非他自己的出價;此稱為次價招標(second-price sealed-bid auction)。

維克里還證明了這方法有非常明顯的優點:投標者只須如實按自己心目中的價格「如實呈報」(truth telling)就可以,而毋須像在首價招標中,利用降低自己出價的策略而得益;背後的道理大致如下。若你如實出價(以M代表),中標後所付價錢是次高入標價(以X代表),你的盈利就是M – X >0。若你降低出價,則可能投不到拍品;要是降價後投得拍品,你仍然是付出X,盈利依然為M -X。換言之,降低出價並不能增加中標後的盈利,反之可能降低勝出的機會。由此可見,降低出價並不是有利可圖的做法,「如實呈報」才是最佳策略。

次價招標雖然看來有點奇怪,其實優點極大。維克里亦因這篇文章而名聞天下,後來還拿了諾貝爾經濟學獎!

初次聽聞次價招標的讀者,一定會佩服發明人的超凡想像力。然而真實世界往往比思想家更富想像力!事實上,這種招標方式在商界已經沿用多年,例如在1893年,就已應用於集郵界。

據說在1797年,德國思想家歌德通過次價招標成功賣出一份手稿。傑出的思想家為我們帶來了具創意的發明,然而現實世界可謂更多姿多采。許多時候思想家的發明,不過是對現實世界經驗的總結而已。歌德有句名言:「理論是灰色的,生命之樹常青」。筆者不妨在這裏稍加修改:「理論未必一定灰色,生命之樹則確實常青」!

 

趙耀華博士
港大經管學院經濟學榮譽副教授

(本文同時於二零二三年九月十三日載於《信報》「龍虎山下」專欄)

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