اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDynamic Pricing and Learning with Competition: Insights from the Dynamic Pricing Challenge at the 2017 INFORMS RM & Pricing Conference
261
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper presents the results of the Dynamic Pricing Challenge, held on the occasion of the 17th INFORMS Revenue Management and Pricing Section Conference on June 29-30, 2017 in Amsterdam, The Netherlands. For this challenge, participants submitted algorithms for pricing and demand learning of which the numerical performance was analyzed in simulated market environments. This allows consideration of market dynamics that are not analytically tractable or can not be empirically analyzed due to practical complications. Our findings implicate that the relative performance of algorithms varies substantially across different market dynamics, which confirms the intrinsic complexity of pricing and learning in the presence of competition.
قيم البحث
اقرأ أيضاً
We consider a firm that sells products over $T$ periods without knowing the demand function. The firm sequentially sets prices to earn revenue and to learn the underlying demand function simultaneously. A natural heuristic for this problem, commonly
used in practice, is greedy iterative least squares (GILS). At each time period, GILS estimates the demand as a linear function of the price by applying least squares to the set of prior prices and realized demands. Then a price that maximizes the revenue, given the estimated demand function, is used for the next time period. The performance is measured by the regret, which is the expected revenue loss from the optimal (oracle) pricing policy when the demand function is known. Recently, den Boer and Zwart (2014) and Keskin and Zeevi (2014) demonstrated that GILS is sub-optimal. They introduced algorithms which integrate forced price dispersion with GILS and achieve asymptotically optimal performance. In this paper, we consider this dynamic pricing problem in a data-rich environment. In particular, we assume that the firm knows the expected demand under a particular price from historical data, and in each period, before setting the price, the firm has access to extra information (demand covariates) which may be predictive of the demand. We prove that in this setting GILS achieves asymptotically optimal regret of order $log(T)$. We also show the following surprising result: in the original dynamic pricing problem of den Boer and Zwart (2014) and Keskin and Zeevi (2014), inclusion of any set of covariates in GILS as potential demand covariates (even though they could carry no information) would make GILS asymptotically optimal. We validate our results via extensive numerical simulations on synthetic and real data sets.
We consider a novel formulation of the dynamic pricing and demand learning problem, where the evolution of demand in response to posted prices is governed by a stochastic variant of the popular Bass model with parameters $alpha, beta$ that are linked
to the so-called innovation and imitation effects. Unlike the more commonly used i.i.d. and contextual demand models, in this model the posted price not only affects the demand and the revenue in the current round but also the future evolution of demand, and hence the fraction of potential market size $m$ that can be ultimately captured. In this paper, we consider the more challenging incomplete information problem where dynamic pricing is applied in conjunction with learning the unknown parameters, with the objective of optimizing the cumulative revenues over a given selling horizon of length $T$. Equivalently, the goal is to minimize the regret which measures the revenue loss of the algorithm relative to the optimal expected revenue achievable under the stochastic Bass model with market size $m$ and time horizon $T$. Our main contribution is the development of an algorithm that satisfies a high probability regret guarantee of order $tilde O(m^{2/3})$; where the market size $m$ is known a priori. Moreover, we show that no algorithm can incur smaller order of loss by deriving a matching lower bound. Unlike most regret analysis results, in the present problem the market size $m$ is the fundamental driver of the complexity; our lower bound in fact, indicates that for any fixed $alpha, beta$, most non-trivial instances of the problem have constant $T$ and large $m$. We believe that this insight sets the problem of dynamic pricing under the Bass model apart from the typical i.i.d. setting and multi-armed bandit based models for dynamic pricing, which typically focus only on the asymptotics with respect to time horizon $T$.
The prevalence of e-commerce has made detailed customers personal information readily accessible to retailers, and this information has been widely used in pricing decisions. When involving personalized information, how to protect the privacy of such
information becomes a critical issue in practice. In this paper, we consider a dynamic pricing problem over $T$ time periods with an emph{unknown} demand function of posted price and personalized information. At each time $t$, the retailer observes an arriving customers personal information and offers a price. The customer then makes the purchase decision, which will be utilized by the retailer to learn the underlying demand function. There is potentially a serious privacy concern during this process: a third party agent might infer the personalized information and purchase decisions from price changes from the pricing system. Using the fundamental framework of differential privacy from computer science, we develop a privacy-preserving dynamic pricing policy, which tries to maximize the retailer revenue while avoiding information leakage of individual customers information and purchasing decisions. To this end, we first introduce a notion of emph{anticipating} $(varepsilon, delta)$-differential privacy that is tailored to dynamic pricing problem. Our policy achieves both the privacy guarantee and the performance guarantee in terms of regret. Roughly speaking, for $d$-dimensional personalized information, our algorithm achieves the expected regret at the order of $tilde{O}(varepsilon^{-1} sqrt{d^3 T})$, when the customers information is adversarially chosen. For stochastic personalized information, the regret bound can be further improved to $tilde{O}(sqrt{d^2T} + varepsilon^{-2} d^2)$
In this paper we apply active learning algorithms for dynamic pricing in a prominent e-commerce website. Dynamic pricing involves changing the price of items on a regular basis, and uses the feedback from the pricing decisions to update prices of the
items. Most popular approaches to dynamic pricing use a passive learning approach, where the algorithm uses historical data to learn various parameters of the pricing problem, and uses the updated parameters to generate a new set of prices. We show that one can use active learning algorithms such as Thompson sampling to more efficiently learn the underlying parameters in a pricing problem. We apply our algorithms to a real e-commerce system and show that the algorithms indeed improve revenue compared to pricing algorithms that use passive learning.
Contextual dynamic pricing aims to set personalized prices based on sequential interactions with customers. At each time period, a customer who is interested in purchasing a product comes to the platform. The customers valuation for the product is a
linear function of contexts, including product and customer features, plus some random market noise. The seller does not observe the customers true valuation, but instead needs to learn the valuation by leveraging contextual information and historical binary purchase feedbacks. Existing models typically assume full or partial knowledge of the random noise distribution. In this paper, we consider contextual dynamic pricing with unknown random noise in the valuation model. Our distribution-free pricing policy learns both the contextual function and the market noise simultaneously. A key ingredient of our method is a novel perturbed linear bandit framework, where a modified linear upper confidence bound algorithm is proposed to balance the exploration of market noise and the exploitation of the current knowledge for better pricing. We establish the regret upper bound and a matching lower bound of our policy in the perturbed linear bandit framework and prove a sub-linear regret bound in the considered pricing problem. Finally, we demonstrate the superior performance of our policy on simulations and a real-life auto-loan dataset.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
