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Price and quantity experimentation: A synthesis
Abstract
This paper compares experimentation about product differentiation in a linear setting under four market structures: quantity-setting and price-setting monopoly, Cournot and Bertrand duopoly. Quantity-setting firms always experiment by raising their quantities and the monopolist experiments relatively more than the duopolists. A price-setting monopolist does not experiment. The value of information to Bertrand duopolists may be positive or negative depending on the degree of product differentiation. When information is valuable, price-setting duopolists experiment by lowering prices. A numerical example indicates that the intensity of experimentation is higher in a Cournot duopoly than in a Bertrand duopoly.
... 2) In this model, the rate of transportation costs t is quadratic. We suppose that the firms I and II declare the prices for the products as i p and the quality as i q ( 1,2) i = . So the utility difference can be denoted by following function ...
... So all customers are divided for two parts respectively their preferences to firms I and II in 'Linear City'. So the demands of the firms I and II ( 1,2) i i D = can be determined by functions ...
... We don't repeat here. If (1 ) (1 ) t b a d p q t b a d − + − ∆ ≤ ∆ ≤ ∆ + − + ∆ , the two firms occupy the market jointly, it is also divided into three cases: ...
Under the assumption of different consumers' preference in the linear market, we propose a the two-stage dynamic and competition location game model of duopoly logistics firms under horizontal and vertical property differences of logistics product of a kind. The sub-game perfect Nash equilibrium of two-stage dynamic game is obtained by backward induction method when each property is dominant analysis the strategies of equilibrium. This model extend the scope of traditional location model and remedy its defect. It makes competition location game model more practical.
... A sample from the extensive economics and econometrics literature that study asymptotic behavior of pricing strategies in competitive environments is Cyert and DeGroot (1970), Kirman (1975), Aghion et al. (1993), Mirman et al. (1993), Fishman and Gandal (1994), Harrington (1995), Bergemann and Valimaki (1996), Gallego (1998), Alepuz and Urbano (1999), Rassenti et al. (2000), Belleflamme and Bloch (2001), Keller and Rady (2003) and Dimitrova and Schlee (2003). These papers typically assume that a particular learning method is used by the competitors, and study whether the price process converges to a Nash equilibrium. ...
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.
... A large stream of economics literature is concerned with the long-term behavior of price adjustment processes in oligopolistic settings, cf. Cyert and DeGroot (1970), Kirman (1975), Aghion et al. (1993), Mirman et al. (1993b), Fishman and Gandal (1994), Harrington (1995), Bergemann and Valimaki (1996), Gallego (1998), Alepuz and Urbano (1999), Rassenti et al. (2000), Belleflamme and Bloch (2001), Schinkel et al. (2002), Keller and Rady (2003), Dimitrova and Schlee (2003), Tuinstra (2004). One usually assumes that firms are using a certain specific learning scheme, and then studies whether the selling prices converge to a Nash equilibrium. ...
The topic of dynamic pricing and learning has received a considerable amount of attention in recent years, from different scientific communities. We survey these literature streams: we provide a brief introduction to the historical origins of quantitative research on pricing and demand estimation, point to different subfields in the area of dynamic pricing, and provide an in-depth overview of the available literature on dynamic pricing and learning. Our focus is on the operations research and management science literature, but we also discuss relevant contributions from marketing, economics, econometrics, and computer science. We discuss relations with methodologically related research areas, and identify directions for future research.
... oneering works of Milgrom and Roberts, 1981, and Matthews and Mirman, 1983). The existing literature has examined experimentation in di¤erent contexts, such as a duopoly market structure (see Mirman, Samuelson and Schlee, 1994, Alepuz and Urbano, 1999 and Belle ‡amme and Bloch, 2001) or learning by a principal in the context of entry-deterrence (Jain, Jeitschko and Mirman (2002, 2003 and 2005)) 1 or information acquisition by an incumbent facing entry when there are no entry costs (Dimitrova and Schlee 2 (DS), 2003 and Patron, 2001)). However, experimentation by an incumbent facing potential entry with entry costs has not been analyzed in a general way, nor has the role of experimentation as an entry-deterrence tool been examined. ...
We examine the effect of a threat of entry on experimentation about demand by an incumbent monopolist when there is a fixed cost of entry. We show that experimentation may itself be used as a tool for entry deterrence and derive conditions under which experimentation reduces the probability of entry. These conditions depend on the entry rule which in turn depends on entry costs. We show that if experimentation does not deter entry, the monopolist incumbent experiments less. We also characterize experimentation and entry in the linear-uniform example, and show that cost of entry and experimentation do not have a monotonic relationship.
Many scholars claimed that the enterprises should proceed gain-sharing plan for technological innovators in the purpose of inspiring enthusiasm of them. In order to maximize net income from innovations, this paper points out the optimum gain-sharing percentage by mathematical models which simulate the relation between innovators and enterprises and game theory, and calculates out the sum of gain-sharing percentages for all technological, innovators in an innovative project is 25%
In this paper, we examine the effect of potential entry on learning by a lender when the demand shock has a general distribution.
We show that under this type of noise, entry does not lead to any changes in the equilibrium expected signals and therefore,
there is no effect on learning by the lender, unlike the case when noise is uniformly distributed. The result holds even when
contracts are not observable.
An incumbent monopolist is uncertain about its linear demand, but can acquire public information at a cost. We determine how an entry threat affects the firm's information acquisition. If returns to scale are constant and the state-contingent demands become more dispersed as output increases, then entry reduces information acquisition. If, however, either the incumbent or entrant has increasing returns; or if the state-contingent demands are nonlinear or fail increasing dispersion, then entry can increase information. Finally, entry can hurt consumers. Although entry always increases output, it can decrease information. Consumers sometimes prefer a better informed monopoly to a duopoly.
This paper explores experimentation and learning in asymmetric duopoly markets with product differentiation and demand uncertainty. We define the concepts of strategic substitutability and strategic complementarity in information and we show how both the mode of information competition and the transmission of information across markets affect duopoly experimentation. We relate information competition with market competition and we find that, when goods are substitutes and the correlation between market shocks is negative, firms will have a higher incentive to experiment in asymmetric markets than in symmetric ones. The opposite result follows when such correlation is positive. Also, when goods are complements the above findings are reversed. Copyright Springer-Verlag Berlin/Heidelberg 2005
This paper explores price-setting behavior in the context of a duopoly in which firms are uncertain about the degree of product differentiation. Firms learn from the difference in their realized demands in light of the price differential. The informativeness of this market experiment is shown to be increasing in the size of the price differential. In markets with highly substitutable products, price dispersion is enhanced as firms adjust their prices so as to generate more information. In markets with highly differentiated products, firms compress their prices as they prefer to reveal less about the extent of product differentiation.
This paper analyzes how learning considerations may influence the pricing behavior of a duopoly facing demand uncertainty. We consider a symmetric duopoly game with product differentiation where firms have imperfect information about some parameters of the market demands. Firm learn about these parameters by observing market sales in the two markets. The central body of this paper consists in showing the conditions under which there exists price dispersion at the equilibrium in pure strategies. In particular, when both -product substitutes- firms experiment in each of the two markets and they have the same ability to make market signals more informative, they will price-disperse as an attempt to increase the informative content of these signals. In this way, a "sampling effect" may arise as the outcome of market learning behavior.
This paper analyzes learning behavior in an industry facing uncertainty. We consider a duopoly game where firms have imperfect information about market demand and they learn through observing market prices. The main body of our study consists of showing how firms make the price a more informative signal through their experimental behavior, and how this behavior compares to its monopoly counterpart. We extend previous analysis to the case where the demand unknown parameter takes values on the real line. We also find that experimentation under Cournot duopoly is smaller than under monopoly whenever the demand's unknown parameter is sufficiently precise.
This paper analyzes how learning behaviors can substantially modify the outcome of competition in an oligopolistic industry facing demand uncertainty. We consider the case of a symmetric duopoly game where firms have imperfect information about market demand and learn through observing the volume of their sales. The main body of the paper consists in showing how market experimentation can explain the existence of price-dispersion in an oligopolistic industry. We study this phenomenon and its dynamic evolution in the context of an Hotelling duopoly model; we then extend the analysis to general demand functions and to N-firm oligopolies. We discuss some implications of the public good aspect of information about market demand. We then conclude with a few comments on what happens when the value of information in the oligopolistic industry is negative.
We examine a monopoly facing an uncertain demand and maximizing profits over a two-period horizon. Conditions are developed under which the firm will find it optimal to "experiment," or adjust initial prices or quantities away from their myopically optimal level in order to increase the informativeness of observed market outcomes and hence increase future profits. We establish conditions under which experimentation will lead a quantity-setting firm to increase or decrease quantity. Finally, we develop conditions under which experimenting firms will choose to be either price-setters or quantity-setters. Copyright 1993 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
This paper studies a duopoly market in which firms can draw inferences concerning (uncertain) market demand from observations of their outputs and market price. Firms may adjust their outputs away from myopically optimal levels to affect the informativeness of the market price. Because firms′ quantities are observed, firms can manipulate the extent to which belief revision occurs rather than the direction in which beliefs are revised (as in signal-jamming models). We develop conditions and present examples under which the value of information is positive and negative and under which firms will increase or decrease quantity to manipulate information. Journal of Economic Literature Classification Numbers: D80, L13.
Market learning and price dispersion. Mimeo. Department of Economics, University of Valencia Duopoly experimentation: Cournot competition
- M D Alepuz
- A P Urbano
- F Belleflamme
Alepuz, M.D., Urbano, A., 1994. Market learning and price dispersion. Mimeo. Department of Economics, University of Valencia. r1582 P. Belleflamme, F. Bloch / Int. J. Ind. Organ. 19 (2001) 1563–1582 Alepuz, M.D., Urbano, A., 1999. Duopoly experimentation: Cournot competition. Mathematical Social Sciences 37, 165–188
Market learning and price dispersion. Mimeo. Department of Economics
- M D Alepuz
- A Urbano
Alepuz, M.D., Urbano, A., 1994. Market learning and price dispersion. Mimeo. Department of Economics, University of Valencia. P. Belleflamme, F. Bloch / Int. J. Ind. Organ. 19 (2001) 1563 –1582
- P Belleflamme
- F Bloch
P. Belleflamme, F. Bloch / Int. J. Ind. Organ. 19 (2001) 1563 –1582