Abstract
This paper discusses price discrimination in a duopoly in two-dimensional consumer characteristics space. We assume that there is uncertainty about a single unobservable characteristic, willingness-to-pay. We show that the subgame perfect equilibrium supports that both firms choose separate pricing policies, uniform pricing and discriminatory pricing, and the Prisoner’s Dilemma does not occur. This result is maintained when the uncertainty is sufficiently high, and differs from Thisse and Vives’s one-dimensional model in which discriminatory pricing is a dominant strategy. As the uncertainty decreases, the pricing structure converges to Thisse and Vives’s model in which the Prisoner’s Dilemma and all-out competition emerge.
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Notes
Actually, the consumer behavior in Hotelling’s model is not affected by “who bears the transportation costs”. I set the responsibility for delivery different from that Hotelling’s model in order to highlight “consumers choose a firm that offers the lower delivered price.”
Hereafter, we use “mill price” and “price” indiscriminately.
In fact, the result originates from the nature of uniform distribution.
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Acknowledgements
This paper is an extension of Chapter 3 of my doctoral dissertation submitted to Korea University, Seoul. All remaining errors are my own. I would like to thank my advisor, Professor Jae Nahm for his guidance. I also thank Dr. Jaeyong Choi for his wonderful help.
