不對稱廠商家數之數量競爭與區位選擇

Abstract

假設消費者均勻分布在一圓形市場上，而市場上有三家採取數量競爭之廠商，其中兩家廠商為同一家公司所擁有，或是有勾結之協議。本研究沿用區位－數量賽局理論，探討這三家廠商如何選擇其最佳區位，以追求其廠商利潤之最大化。經由數學分析結果，本研究得到如下結論：1.兩家勾結廠商之最佳區位，是以競爭對手為中心點兩側等距區位。2.如果設定競爭對手之位置為圓形之起點0，則兩家勾結廠商之最佳區位範圍分別為[π/2, √2π/2]與[π/2-√2π/2, 3π/2]。3.當每單位距離之運輸成本趨近於0時，兩家勾結廠商之最佳區位為[方程式略]（往競爭對手方向接近）；而當每單位運輸成本增大到1/π時，兩家勾結廠商之最佳區位為[√2π/2, 2π-√2π/2]，亦即會選擇與競爭對手略微遠離的地點來區位。

This article analyzes a circular market in which two colluded firms compete with a single firm at each point in space. In the location-quantity game, each firm first selects the location for its facility and then selects the quantities to supply to the market, so as to maximize its profit. In equilibrium, there is a unique subgame perfect Nash equilibrium, where the two colluded firms locate equidistant from the rival on the circle. Moreover, when the transportation costs is approaching to zero (or 1 / π), the optimal location of the two colluded firms will situate at [π/2, 3π/2] (or [√2π/2, 2π-√2π/2]); i.e., an increase (decrease) in the transportation costs will make the colluded firms move away from (close to) the rival.