A Nonatomic‐Game Approach to Dynamic Pricing under Competition

We study a revenue management problem involving competing firms. We assume the presence of a continuum of infinitesimal firms where no individual firm has any discernable influence over the evolution of the overall market condition. Under this nonatomic-game approach, the unanimous adoption of an equilibrium pricing policy by all firms will yield a market-condition process that in turn will elicit the said policy as one of the best individual responses. For both deterministic- and stochastic-demand cases, we show the existence of equilibrium pricing policies that exhibit well-behaving monotone trends. Our computational study reveals many useful insights, including the fact that only a reasonable number of firms are needed for our approach to produce near-rational pricing policies.

[1]  David Housman.  Infinite Player Noncooperative Games and the Continuity of the Nash Equilibrium Correspondence , 1988, Math. Oper. Res..

[2]  Sheryl E. Kimes,et al.  Restaurant revenue management: Could it work? , 2005 .

[3]  C. L. Benkard,et al.  Markov Perfect Industry Dynamics with Many Firms , 2005 .

[4]  Ming Hu,et al.  Dynamic Pricing of Perishable Assets under Competition , 2013, Manag. Sci..

[5]  Yi Xu.  A Structural Empirical Model of R & D , Firm Heterogeneity , and Industry Evolution ∗ , 2007 .

[6]  Garrett J. van Ryzin,et al.  A Multiproduct Dynamic Pricing Problem and Its Applications to Network Yield Management , 1997, Oper. Res..

[7]  Georgia Perakis,et al.  Competitive Multi-period Pricing for Perishable Products: A Robust Optimization Approach , 2006, Math. Program..

[8]  J. Muth.  Rational Expectations and the Theory of Price Movements , 1961 .

[9]  Jeffrey I. McGill,et al.  Revenue Management: Research Overview and Prospects , 1999, Transp. Sci..

[10]  Yuri Levin,et al.  Dynamic Pricing in the Presence of Strategic Consumers and Oligopolistic Competition , 2009, Manag. Sci..

[11]  M. Ali Khan,et al.  On the Existence of Pure Strategy Equilibria in Games with a Continuum of Players , 1997 .

[12]  G. Ryzin,et al.  Optimal dynamic pricing of inventories with stochastic demand over finite horizons , 1994 .

[13]  A. Granas,et al.  Fixed Point Theory , 2003 .

[14]  Benjamin Van Roy,et al.  Markov Perfect Industry Dynamics with Many Firms , 2005 .

[15]  A. Tarski.  A LATTICE-THEORETICAL FIXPOINT THEOREM AND ITS APPLICATIONS , 1955 .

[16]  Benjamin Van Roy,et al.  Computational Methods for Oblivious Equilibrium , 2010, Oper. Res..

[17]  D. M. Topkis.  Supermodularity and Complementarity , 1998 .

[18]  Hong Chen,et al.  Optimal Control and Equilibrium Behavior of Production-Inventory Systems , 2010, Manag. Sci..

[19]  Warren Lieberman,et al.  Expanding the revenue management frontier: Optimal air planning in the cruise industry , 2002 .

[20]  E. Green.  Noncooperative price taking in large dynamic markets , 1980 .

[21]  Baichun Xiao,et al.  Optimal Policies of Yield Management with Multiple Predetermined Prices , 2000, Oper. Res..

[22]  Youyi Feng,et al.  A Continuous-Time Yield Management Model with Multiple Prices and Reversible Price Changes , 2000 .

[23]  X. Qi,et al.  A nonatomic‐game model for timing clearance sales under competition , 2014 .

[24]  H. Sabourian.  Anonymous repeated games with a large number of players and random outcomes , 1990 .

[25]  Pinar Keskinocak,et al.  Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions , 2003, IEEE Engineering Management Review.

[26]  Morris A. Cohen,et al.  Capacity Management in Rental Businesses with Two Customer Bases , 2005, Oper. Res..

[27]  Sunmee Choi,et al.  The Role of Disclosure in Variable Hotel Pricing , 2006 .

[28]  Hong Chen,et al.  Optimal Control and Competitive Equilibrium of Production-Inventory Systems with Application to the Petroleum Refining Industry , 2006 .

[29]  Wenjiao Zhao,et al.  Optimal Dynamic Pricing for Perishable Assets with Nonhomogeneous Demand , 2000 .

[30]  Kyle Y. Lin,et al.  Dynamic price competition with discrete customer choices , 2009, Eur. J. Oper. Res..

[31]  Jian Yang.  Asymptotic interpretations for equilibria of nonatomic games , 2011 .

[32]  Wallace J. Hopp,et al.  A Monopolistic and Oligopolistic Stochastic Flow Revenue Management Model , 2006, Oper. Res..

[33]  Rann Smorodinsky,et al.  Large Nonanonymous Repeated Games , 2001, Games Econ. Behav..

[34]  D. Schmeidler.  Equilibrium points of nonatomic games , 1973 .

[35]  G. Gallego,et al.  Optimal starting times for end-of-season sales and optimal stopping times for promotional fares , 1995 .

[36]  A. Mas-Colell.  On a theorem of Schmeidler , 1984 .

[37]  On the existence of Cournot–Nash equilibria in continuum games , 1999 .

[38]  R. Aumann.  Markets with a continuum of traders , 1964 .

[39]  Nabil I. Al-Najjar.  Large games and the law of large numbers , 2008, Games Econ. Behav..

[40]  Guilherme Carmona.  Nash Equilibria of Games with a Continuum of Players , 2004 .