Date of Award

8-2015

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mathematics

Advisor

Liu, Xin

Committee Member

Sun, Xiaoqian

Committee Member

Park, Chanseok

Abstract

To optimize profit, pricing is of great importance for each company, especially when competitors exist. The optimal pricing strategy we are interested in is to achieve Nash equilibrium (NE) to prevent malignant competition. In this work, we study dynamic pricing for a duopoly with two competing sellers, each of which sells one product, using a simple linear model which incorporates the competition effect. Motivated from the modified pricing policy constructed in Liu and Cooper [12], we propose a policy, referred to as randomized certainty equivalent pricing (RCEP) policy, under which each seller applies certainty equivalent pricing (CEP) policy for most of the times and occasionally choose prices around the previous price according to uniform distribution. We use numerical experiments to investigate the convergence of the prices to NE under RCEP, and our results suggest that RCEP is optimal with probability 1. We also study the so-called controlled variance pricing (CVP) originally proposed by den Boer and Zwart [4] for the monopoly case. The essential idea of CVP is to apply CEP for most of the time, and during a time period, if the sample variance of the seller’s prices is too small, the next price will be chosen to slightly deviate from the current price average to keep the sample variance large enough. The CVP policy is simple to apply, and is shown to be optimal in the monopoly case. However, it is still unknown whether the prices in the duopoly case converge to NE under CVP. Our numerical results show that CVP is actually not optimal with positive probability. We also conduct simulations under CEP and the policy proposed in [12], which support the theoretical results in [12].

Included in

Mathematics Commons

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