不完美競爭零售商之會員費及均衡價格探討：以倉儲量販俱樂部為例

Abstract

本研究主旨為探討兩家對稱廠商之間需繳交會員費的忠誠計畫（一般通稱為會員制）的引進決策、會員費設定決策以及相關定價行為。假設市場中存在兩種在使用頻率和保留價格上有所區別的消費者：(1)對保留價格有不確定性的重度使用者，以及(2)對使用頻率有不確定性的輕度使用者，每間廠商販售同質產品，且可各自決定是否要引進會員制，若有任何廠商決定引進，則上述兩種消費者必須先面對是否要成為會員的決策。緊接著所有的不確定性消失，兩家廠商同時決定商品售價，最後消費者進行購買決策。本研究的主要結果如下： 一、存在只有一家廠商獨家引進會員制，只能服務成為會員的部分消費者，而另一家廠商不實施會員制，可以服務全部消費者的均衡。 二、廠商可以透過實施會員制阻絕非會員進入消費，進而緩和價格競爭，使自己和競爭對手的均衡利潤均上升。 三、實施會員制的廠商折扣頻率比未實施會員制的廠商高，且折扣頻率和會員數以及高需求的機率（代表保留價格或實際需求量高）成正比。因此平均會員支付價格隨著會員數的增加而降低。本研究提出和Kim and Choi（2007）不同的見解，認為較低的平均會員支付價格會導致實施會員制的折扣頻率較高。 四、在某些狀況中，重度使用者在理性預期實施會員制廠商在下一期會提出較低的價格滿足其需求下，會選擇成為會員；而輕度使用者則不會成為會員，因此平均支付價格比重度使用者高。 五、本研究指出有多重均衡可能出現，且會產生何種均衡和消費者信念有極大的關係。因此要實施會員制的廠商可以透過廣告宣傳已經有多人參加計畫，藉此引導消費者信念到有人願意參加會員制的均衡，如此廠商方可透過會員制獲益。

This paper analyzes the limited loyalty program (i.e., membership program), membership fee decisions, and the associated price dealing behavior of two symmetric firms. Assume consumers differ in their use frequency and in their reservation prices: Heavy users are uncertain about their reservation prices while light users are uncertain about their demand incidence when facing loyalty programs requiring membership fees. Both firms sell homogenous goods and have the option to introduce membership program or not. Then customers need to decide whether to apply as members or not under uncertainties. After that, all uncertainties removed before the shopping day. We derive the following results: (i)There may exist an equilibrium where one firm offers the loyalty program that requires an up-front fee and serves only its members while the other firm chooses not to and access all consumers. (ii)By exclusively offering loyalty program and prevents nonmembers from shopping, a firm mitigates the price competition with its rival and increases its profits and its rival's. (iii)The firm that exclusively offers loyalty program promotes more frequently than its rival. Furthermore, the dealing frequency increases with the size of its members, and the likelihood of high demands (i.e., the reservation price or the demand incidence being high). As a result, the average price paid by members (of one firm) decreases with the size of its members. Unlike Kim and Choi (2007), this paper suggests it is possible that the lower average price paid by members is partly related to the higher dealing frequency of the firm with exclusive membership policy. (iv)Under some conditions, heavy users, rationally expecting the firm that exclusively offers loyalty program will charge a low price to have their needs fulfilled, choose to join its loyalty program while light users choose not to and thus pay a higher price than heavy users. (v)In our model there exists multiple equilibria and the outcome of equilibrium is highly related with customer beliefs; thus the firm which wants to introduce loyalty programs may execute some advertisements to affect customer beliefs and thus lead to a non-Bertrand equilibrium.