Dynamic Pricing Under a General Parametric Choice Model

References

• Agrawal R. The continuum-armed bandit problem. SIAM J. Control Optim. (1995) 33(6):1926–1951Crossref, Google Scholar
• Auer P, Cesa-Bianchi N, Fischer P. Finite-time analysis of the multiarmed bandit problem. Machine Learn. (2002) 47(2):235–256Crossref, Google Scholar
• Auer P, Ortner R, Szepesvári C. Improved rates for the stochastic continuum-armed bandit problem. 20th Conf. Learn. Theory (COLT) (2007) (Springer-Verlag, Berlin) 454–468Crossref, Google Scholar
• Bar-Shalom Y. On the asymptotic properties of the maximum-likelihood estimate obtained from dependent observations. J. Roy. Statist. Soc., Series B (Methodological) (1971) 33(1):72–77Google Scholar
• Basawa IV, Feigin PD, Heyde CC. Asymptotic properties of maximum likelihood estimators for stochastic processes. Sankhya: The Indian J. Statist., Series A (1976) 38(3):259–270Google Scholar
• Ben-Akiva M, Lerman S. Discrete Choice Analysis: Theory and Application to Travel Demand (1985) (MIT Press, Cambridge, MA) Google Scholar
• Bertsimas D, Perakis G. Dynamic pricing: A learning approach. Mathematical and Computational Models for Congestion Charging, Applied Optimization (2003) 101(Springer, New York) 45–79Google Scholar
• Besbes O, Zeevi A. Dynamic pricing without knowing the demand function: Risk bounds and near-optimal algorithms. Oper. Res. (2009) 57(6):1407–1420Link, Google Scholar
• Besbes O, Zeevi A. On the minimax complexity of pricing in a changing environment. Oper. Res. (2011) 59(1):66–79Link, Google Scholar
• Bhat BR. On the method of maximum-likelihood for dependent observations. J. Roy. Statist. Soc., Series B (Methodological) (1974) 36(1):48–53Google Scholar
• Borovkov A. Mathematical Statistics (1998) (Gordon and Breach Science Publishers, Amsterdam) Google Scholar
• Broadie M, Cicek D, Zeevi A. General bounds and finite-time improvement for the Kiefer-Wolfowitz stochastic approximation algorithm. Oper. Res. (2011) 59(5):1211–1224Link, Google Scholar
• Carvalho A, Puterman M. Learning and pricing in an Internet environment with binomial demands. J. Revenue and Pricing Management (2005) 3(4):320–336Crossref, Google Scholar
• Cope E. Bayesian strategies for dynamic pricing in e-commerce. Naval Res. Logist. (2006) 54(3):265–281Crossref, Google Scholar
• Cope E. Regret and convergence bounds for a class of continuum-armed bandit problems. IEEE Trans. Automatic Control (2009) 54(6):1243–1253Crossref, Google Scholar
• Cover T, Thomas J. Elements of Information Theory (1999) (J. Wiley, Hoboken, NJ) Google Scholar
• Crowder MJ. Maximum likelihood estimation for dependent observations. J. Roy. Statist. Soc., Series B (Methodological) (1976) 38(1):45–53Google Scholar
• Den Boer A, Zwart B. Simultaneously learning and optimizing using controlled variance pricing. (2010) . Working paper, Centrum Wiskunde and Informatica and the University of Amsterdam, AmsterdamGoogle Scholar
• Fabian V. Stochastic approximation of minima with improved asymptotic speed. Ann. Math. Statist. (1967) 38(1):191–200Crossref, Google Scholar
• Gallego G, van Ryzin G. Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Sci. (1994) 40(8):999–1020Link, Google Scholar
• Genton MG. Asymptotic variance of m-estimators for dependent Gaussian random variables. Statist. Probab. Lett. (1998) 38(3):255–261Crossref, Google Scholar
• Gill R, Levit B. Applications of the van Trees inequality: A Bayesian Cramér-Rao bound. Bernoulli (1995) 1(1):59–79Crossref, Google Scholar
• Goldenshluger A, Zeevi A. Woodroofe's one-armed bandit problem revisited. Ann. Appl. Probab. (2009) 19(4):1603–1633Crossref, Google Scholar
• Goldenshluger A, Zeevi A. Performance limitations in bandit problems with side observations. IEEE Trans. Inform. Theory (2011) 57(3):1707–1713Crossref, Google Scholar
• Harrison J, Keskin N, Zeevi A. Bayesian dynamic pricing policies: Learning and earning under a binary prior distribution. Management Sci. (2012) 58(3):570–586Link, Google Scholar
• Heijmans RDH, Magnus JR. Consistent maximum-likelihood estimation with dependent observations. J. Econometrics (1986) 32(2):253–285Crossref, Google Scholar
• Kiefer J, Wolfowitz J. Stochastic estimation of the maximum of a regression function. Ann. Math. Statist. (1967) 23(3):462–466Crossref, Google Scholar
• Kleinberg R, Leighton T. The value of knowing a demand curve: Bounds on regret for on-line posted-price auctions. Proc. 44th IEEE Sympos. Foundations Comput. Sci. (2003) (IEEE Computer Society Press, Washington, DC) 594–605Crossref, Google Scholar
• Knuth D. The Art of Computer Programming, Volume 1: Fundamental Algorithms (1997) (Addison-Wesley, Boston) Google Scholar
• Lai T, Robbins H. Asymptotically efficient adaptive allocation rules. Adv. Appl. Math. (1985) 6(1):4–22Crossref, Google Scholar
• Lim A, Shanthikumar J. Relative entropy, exponential utility, and robust dynamic pricing. Oper. Res. (2007) 55(2):198–214Link, Google Scholar
• Lobo M, Boyd S. Pricing and learning with uncertain demand. (2003) . Working paper, Duke University, Durham, NCGoogle Scholar
• Talluri K, van Ryzin G. The Theory and Practice of Revenue Management (2004) (Springer, New York) Crossref, Google Scholar
• Taneja I, Kumar P. Relative information of type s, Csiszár's f-divergence, and information inequalities. Inform. Sci. (2004) 166(1--4):105–125Crossref, Google Scholar
• Tsybakov A. Introduction to Nonparametric Estimation (2009) (Springer, New York) Crossref, Google Scholar