optimal dynamic pricing of inventories with stochastic demand over finite horizons in many industries managers face the problem of selling a given stock of items by a deadline we investigate the problem of dynamically pricing such inventories when demand is price sensitive and stochastic and the firm s objective is to maximize expected revenues examples that fit this framework include retailers selling fashion and seasonal goods and the travel and leisure industry which markets space such as seats on airline flights cabins on vacation cruises and rooms in hotels that become worthless if not sold by a specific time we formulate this problem using intensity control and obtain structural monotonicity results for the optimal intensity resp price as a function of the stock level and the length of the horizon for a particular exponential family of demand functions we find the optimal pricing policy in closed form for general demand functions we find an upper bound on the expected revenue based on analyzing the deterministic version of the problem and use this bound to prove that simple fixed price policies are asymptotically optimal as the volume of expected sales tends to infinity finally we extend our results to the case where demand is compound poisson only a finite number of prices is allowed the demand rate is time varying holding costs are incurred and cash flows are discounted the initial stock is a decision variable and reordering overbooking and random cancellations are allowed

pricing and lot sizing decisions for perishable goods when demand depends on selling price reference price product freshness and displayed stocks abstract price is an important factor affecting demand rate based on economic and marketing theory in addition today s health conscious consumers prefer a product further from its expiration date because it is fresher and can be stored longer furthermore a large display of goods in a supermarket induces customers to buy more due to its visibility variety and seasonality as a result we develop a joint pricing and lot sizing model for retailers selling perishable products in which the demand depends on not only the selling price and reference price but also the product freshness linked to expiration date and displayed stock level we then formulate the problem as a deterministic model in which the retailer determines the optimal selling prices and ending inventory levels to maximize the discounted total profit furthermore we discuss the retailer s optimal decisions under two scenarios of demand behavior loss neutrality and loss aversion our theoretical analysis shows that the optimal pricing and ending inventory level strategies are both monotonic in time and the equilibrium of the system is unique for these two scenarios of demand behavior finally a set of structural properties and sensitivity analysis is also developed to characterize the impacts of model parameters on the optimal decisions

optimal dynamic pricing for deteriorating items with reference price effects when inventories stimulate demand abstract in this paper we incorporate reference price effects into a deteriorating inventory problem when the demand rate depends on displayed stock level and selling price simultaneously reference price effects are formed empirically by customers to adjust current price perception on the basis of past purchases the market demand is assumed to be responsive to the difference between the current selling price and the reference price which is perceived as a loss or a gain we consider three scenarios of market demand loss neutrality loss aversion and loss seeking an optimal dynamic pricing model is established to determine a pricing strategy maximizing the discounted total profit over an infinite time horizon theoretical results are derived to demonstrate the existence of the optimal solutions and to explore the relationships between optimal pricing decisions and an initial reference price based on mild assumptions numerical example and sensitivity analysis are presented to illustrate the theoretical results and managerial insights finally concluding remarks are offered

optimal retailer investments in green operations and preservation technology for deteriorating items abstract this paper examines the impact of dynamic retailer investments in green operations while considering the reference price effect a replenishment problem based on joint pricing dynamic investment in green operations preservation technology and optimal replenishment times for deteriorating items is considered as a way to maximize retailer profit in this problem the demand rate depends on the sales and reference prices as well as green concern level optimal control theory is employed to obtain a dynamic investment rate and a simulated annealing algorithm is used to find the solution of the nonlinear constraint optimization problem which determines the price preservation technology investment and replenishment cycle time in addition computational simulations and sensitivity analyses are carried out to offer managerial insights the findings suggest that continuous investment in green operations and preservation technology can significantly improve the retailer s financial performance the consumer reference price is an important influence on the retailer s decision to invest in green operations furthermore results show that the higher price sensitivity of the market always discourages the retailer from investing in green operations the retailer needs to invest more in green operations for products with relatively high unit value

technical note intertemporal price discrimination via reference price effects we consider the dynamic pricing problem a monopolistic seller faces when customers arrive in heterogeneous time periods and their purchase decisions are affected by reference prices formed from their past observations of prices we illustrate that a new form of price discrimination opportunity exists in such situations where the seller s optimal pricing strategy is a cyclic one even when the customers are loss neutral and their demand functions are identical this result differs from those of prior studies where the optimal price paths are shown to be asymptotically constant and thus is unique due to the interaction between the heterogeneous arrivals and the reference price effects we also provide the cycle length of the optimal pricing policy when the demand function is linear and when customers are loss neutral in this era when customer information is easier accessible our results suggest the sellers consider this new dimension of price discrimination in conjunction with the old ones to take advan

environmental quality competition and eco labeling abstract a three stage game of investment environmental quality provision and price competition is developed to study the impact of green technology investment eco labeling in a duopoly model of vertical product differentiation the firms incentives to invest in green technologies depend on their relative cost structure when firms are identical with respect to fixed costs both firms will always invest but if one firm is more efficient in investing then the other firm may or may not invest depending on the level of unit cost of investment quality competition will be tighter when the low quality firm is more efficient and looser when the high quality firm is more efficient in investing socially optimal investment for both firms is always positive but lower than in the duopoly solution in the absence of environmental externalities the quality dispersion chosen by profit maximizing firms may be too high or too low while environmental externalities increase the possibility low quality dispersion that is too low within the market solution finally and importantly ecolabeling can be used as a means of reducing excessive investment and increasing environmental quality that is too low

eco labelling competition and environment endogenization of labelling criteria this paper suggests a modelling of the labelling procedure consistent with empirical observations that allows the endogenous calculation of labelling criteria the authority in charge of the labelling program chooses the level of labelling criteria so as to maximise the social surplus anticipating competition between firms in environmental qualities and prices while accounting simply for the informational role of labels this model allows to understand observed behavior such as firms ignorance of a label resistance support or indifference of firms to the labelling program and the decision of the authority not to set up a label

behavioral anomalies in consumer wait or buy decisions and their implications for markdown management the decision to buy an item at a regular price or wait for a possible markdown involves a multidimensional trade off between the value of the item the delay in getting it the likelihood of getting it and the magnitude of the price discount such trade offs are prone to behavioral anomalies by which human decision makers deviate from the discounted expected utility model we build an axiomatic preference model that accounts for three well known anomalies and produces a parsimonious generalization of discounted expected utility we then plug this behavioral model into a stackelberg nash game between a firm that decides the price discount and a continuum of consumers who decide to wait or buy anticipating other consumers decisions and the resultant likelihood of product availability we solve the markdown management problem and contrast the results of our model with those under discounted expected utility we analytically show that accounting for the behavioral anomalies can result in larger markdowns a

dynamic pricing strategies with reference effects we consider the dynamic pricing problem of a monopolist firm in a market with repeated interactions where demand is sensitive to the firm s pricing history consumers have memory and are prone to human decision making biases and cognitive limitations as the firm manipulates prices consumers form a reference price that adjusts as an anchoring standard based on price perceptions purchase decisions are made by assessing prices as discounts or surcharges relative to the reference price in the spirit of prospect theory we prove that optimal pricing policies induce a perception of monotonic prices whereby consumers always perceive a discount respectively surcharge relative to their expectations the effect is that of a skimming or penetration strategy the firm s optimal pricing path is monotonic on the long run but not necessarily at the introductory stage if consumers are loss averse we show that optimal prices converge to a constant steady state price characterized by a simple implicit equation otherwise the optimal policy cycles the range of steady states is wider the more loss averse consumers are steady state prices decrease with the strength of the reference effect and with customers memory all else equal offering lower prices to frequent customers may be suboptimal however if these are less sensitive to price changes than occasional buyers if managers ignore such long term implications of their pricing strategy the model indicates that they will systematically price too low and lose revenue our results hold under very general reference dependent demand models

dynamic quality policies with reference quality effects abstractdynamic pricing policies with reference price demand have been intensely analysed less studied are dynamic quality policies with reference quality demand this article studies the dynamic quality policy of a firm whose consumers use a reference point in their decision making in line with the principles of behavioural economics more specifically i consider reference quality formation in an optimal control setting by solving on the basis of pontryagin s maximum principle i obtain analytical solutions to the optimal quality policy the managerial implications of quality reference for dynamic quality policy are discussed

are markets with loss averse consumers more sensitive to losses behavioral pricing and revenue management aim to incorporate realistic consumer behavior into firms pricing and inventory models the key input to these models is market demand which is often assumed to inherit the characteristics of consumer behavior as when for example one assumes that a market consisting of loss averse consumers is more responsive to losses than to gains yet market demand and consumer behavior need not be related and so we argue that approach to modeling market demand is misguided this paper proposes an approach that accounts for the heterogeneity in consumer valuation we aggregate the demand of individual loss averse consumers to obtain market demand and show that market demand may be more responsive to gains or losses or it may be equally responsive our results have profound implications not only for how best to characterize the market demand of behaviorally biased consumers but also for determining the firm s optimal pricing policy this paper was accepted by serguei net

the impact of heterogeneity in purchase timing and price responsiveness on estimates of sticker shock effects the notion that individuals have an internal reference price against which they compare observed prices is well supported by several psychological theories empirically several papers in the marketing literature employing scanner panel data have modeled the impact of reference prices on brand choice via the sticker shock formulation in which consumers evaluate choice alternatives using differences between shelf prices and reference prices most of the studies reported thus far have not accounted for heterogeneity in price response among consumers and have typically imputed reference prices from the shelf prices of brands that a consumer is supposed to have observed on previous purchases in the category since category marketing activity can differentially affect the purchase timing of households we argue that this measure of reference price may follow certain systematic patterns across consumers and when combined with unaccounted for price response heterogeneity may result in a spurious sticker shock effect specifically we show that estimates of sticker shock are biased upward if households that are price sensitive in the brand choice decision are also more responsive to category promotion activity in their purchase timing decision we discuss some general conditions under which the bias occurs and conduct a simulation experiment to confirm our specific hypotheses our simulation results show that changes in purchase timing are a critical determinant of the bias in the sticker shock effect we also show that unaccounted for price response heterogeneity can in itself result in a biased sticker shock parameter however this requires very large differences in price sensitivities across consumers far greater than what is normally observed we develop a hierarchical bayes version of the nested logit model which models heterogeneity via individual level parameters in a continuous random effects framework we estimate the model on scanner panel data from the yogurt and ketchup categories we find in both categories that the 95 probability interval of the posterior distribution of the mean sticker shock coefficient contains the value zero therefore at least for the data used in this study there is no evidence for the sticker shock effect at the aggregate level in contrast the corresponding coefficient from a standard model which ignores this heterogeneity is highly significant and supports the existence of a possibly spurious sticker shock effect consistent with our explanation of the underlying cause of the bias households that are more price sensitive in the choice decision are also found to be more responsive to category promotion activity in their decision to purchase in the category the results highlight the measurement problems associated with imputing reference prices from past prices since the frequency duration and price level of a retailer s promotional program depend on its size and prevalence accurate estimates of the sticker shock effect are essential for formulating optimal promotion strategies an adequate accounting of consumer heterogeneity is critical to this effort

optimal design of social comparison effects setting reference groups and reference points in this paper we study how social planners should exploit social comparisons to pursue their objectives we consider two modes of social comparison referred to as behind averse and ahead seeking behaviors depending on whether individuals experience a utility loss from underperforming or a utility gain from overperforming relative to their peers modeling social comparison as a game between players we find that ahead seeking behavior leads to output polarization whereas behind averse behavior leads to output clustering a social planner can mitigate these effects in two ways i by providing the full reference distribution of outputs instead of an aggregate reference point based on the average output and ii by assigning players into uniform rather than diverse reference groups social planners may thus need to tailor the reference structure to the predominant mode of social comparison and their objective a performance focused social planner may set the reference structure so as to maximize the output of either the top or the bottom player depending on whether she puts greater marginal weight to larger or smaller outputs when the social planner also cares about utility she faces a dilemma because performance optimization may not be aligned with utility maximization inevitably the social planner will have to confront equity issues because better performance may not reflect greater effort or greater ability this paper was accepted by serguei netessine operations management

dynamic stochastic inventory management with reference price effects we analyze the joint inventory and pricing decisions of a firm when demand depends on not only the current selling price but also a memory based reference price and customers are loss averse the presence of reference price effect leads to a nonconcave one period expected revenue in price and reference price we introduce a transformation technique that allows us to prove under some mild assumptions the optimality of a reference price dependent base stock list price policy which is characterized by a base stock level and a target reference price in addition we show that the target reference price is increasing in the reference price but except in the loss neutral case the base stock level is not monotone in the reference price we also show that in the steady state of the model with the reference price effect the optimal price is lower while the optimal base stock level is higher than their counterparts in the model without the reference price effect

multiattribute loss aversion and reference dependence evidence from the performing arts industry we study the prevalence of multiattribute loss aversion and reference effects in a revenue management setting based on data of individual level purchases over a series of concert performances the reference dependence that drives consumer choice is not only based on the price but also on observed sales as a fraction of the seating capacity during their past visits we find that consumers suffer from loss aversion on both prices and seats sold consumers incur significant utility loss when prices are above their references or when the actual seat sales are lower than their references we suggest pricing policies that can address consumer decisions driven by such reference dependence and loss aversion this paper was accepted by vishal gaur operations management

price coordination in distribution channels a dynamic perspective abstract in this study we investigate two important questions related to dynamic pricing in distribution channels i are coordinated pricing decisions efficient in a context where prices have carry over effects on demand ii should firms practice a skimming or a penetration strategy if they choose to coordinate or to decentralize their activities to answer these questions we consider a differential game that takes place in a bilateral monopoly where the past retail prices paid by consumers contribute to the building of a reference price the latter is used by consumers as a benchmark to evaluate the value of the product and by firms to decide whether to adopt a skimming or a penetration strategy we then compute and compare strategies total channel profits and individual profits under vertical integration and decentralization at steady state and along the optimal time paths one of our main findings states that for some values of the initial reference price there is a time interval where channel decentralization performs better than coordination during this transition period at least one of the channel members could be tempted to end his cooperation especially if he is not farsighted and if there are no binding agreements with the other channel partners

empirical generalizations from reference price research considerable theoretical justification for consumers use of psychological reference points exists from the research literature from a managerial perspective one of the most important applications of this concept is reference price an internal standard against which observed prices are compared in this paper we propose three empirical generalizations that are well supported in the marketing literature first there is ample evidence that consumers use reference prices in making brand choices second the empirical results on reference pricing also support the generalization that consumers rely on past prices as part of the reference price formation process third consistent with other research on loss aversion consumers have been found to be more sensitive to losses i e observed prices higher than reference prices than gains we also propose topics for further research on reference prices

pricing and revenue management the value of coordination the integration of systems for pricing and revenue management must trade off potential revenue gains against significant practical and technical challenges this dilemma motivates us to investigate the value of coordinating decisions on prices and capacity allocation in a stylized setting we propose two pairs of sequential policies for making static decisions on pricing and revenue management that differ in their degree of integration hierarchical versus coordinated and their pricing inputs deterministic versus stochastic for a large class of stochastic price dependent demand models we prove that these four heuristics admit tractable solutions satisfying intuitive sensitivity properties we further evaluate numerically the performance of these policies relative to a fully coordinated model which is generally intractable we find it interesting that near optimal performance is usually achieved by a simple hierarchical policy that sets prices first based on a nonnested stochastic model and then uses these prices to optimize nested capacity allocation this tractable policy largely outperforms its counterpart based on a deterministic pricing model jointly optimizing price and allocation decisions for the high end segment improves performance but the largest revenue benefits stem from adjusting prices to account for demand risk this paper was accepted by yossi aviv operations management

revenue management with costly price adjustments we consider a novel variant of the perishable inventory profit management problem faced by a firm that sells a fixed inventory over a finite horizon in the presence of price adjustment costs in economics literature such price adjustment costs are widely studied and are typically assumed to include a fixed component e g advertising costs an inventory dependent component e g inventory relabeling costs as well as a component that depends on the magnitude of the price adjustment e g cognitive and coordination managerial costs we formulate the firm s profit management problem as a finite horizon dynamic program in which the state of the system is described by the inventory level as well as the current price level we derive first order properties of the optimal value function and give a complete characterization of optimal policies for the case of ample inventory through a set of examples we demonstrate the complex and counterintuitive nature of optimal price adjustment policies consequently we focus on developing easily computable and implementable heuristics with demonstrably good performance to this end we develop and solve a fluid model based on the original stochastic dynamics and propose three fluid based heuristic policies we derive expressions for the expected profit generated by each one of these heuristics when applied to the stochastic problem and derive sufficient conditions for the asymptotic optimality of the policies when the initial inventory levels and planning horizons are proportionally scaled up we test the performance of the heuristics in a numerical study and demonstrate a robust near optimal performance of one of the heuristics which we call the fluid time heuristic for a wide range of problem parameters finally we demonstrate the importance of proper accounting of price adjustment costs in several alternative business settings

high price or low price an experimental study on a markdown pricing policy abstract this study examines whether strategic customers behavioral patterns remain consistent in different pricing scenarios under a markdown pricing policy these customers decision patterns have been widely discussed because they significantly influence the expected monetary output contrary to rational assumptions the behavioral research literature indicates that customers behavioral biases manifest in their reference dependency risk and loss attitudes and fill rate misperceptions however the relationship between behavioral biases and various pricing scenarios has not been carefully examined accordingly we conducted laboratory experiments to observe customers behavioral performance in a series of pricing scenarios to provide pricing suggestions for sellers our experimental results demonstrate that behavioral factors reflecting risk and loss attitudes as well as reference dependency can clearly describe customers behavioral biases meanwhile our estimation shows that the degrees of risk and loss attitude are not constant but depend on price settings the lower the full price in the initial period the higher the degrees of aversion to both risk and loss given such behavioral patterns we suggest that sellers should set their full prices lower than the normative value when the fill rate in period two is low and set them higher than the normative value when the fill rate in period two is high

designing pricing contracts for boundedly rational customers does the framing of the fixed fee matter the format of pricing contracts varies substantially across business contexts a major variable being whether a contract imposes a fixed fee payment this paper examines how the use of the fixed fee in pricing contracts affects market outcomes of a manufacturer retailer channel standard economic theories predict that channel efficiency increases with the introduction of the fixed fee and is invariant to its framing we conduct a laboratory experiment to test these predictions surprisingly the introduction of the fixed fee fails to increase channel efficiency moreover the framing of the fixed fee does make a difference an opaque frame as quantity discounts achieves higher channel efficiency than a salient frame as a two part tariff although these two contractual formats are theoretically equivalent to account for these anomalies we generalize the standard economic model by allowing the retailer s utilities to be reference dependent so that the up front fixed fee payment is perceived as a loss and the subsequent retail profits as a gain we embed this reference dependent utility function in a quantal response equilibrium framework where the retailer is allowed to make decision mistakes due to computational complexity the key prediction of this behavioral model is that channel efficiency decreases with loss aversion for sufficiently nash rational retailers consistent with this prediction the estimated loss aversion coefficient is 1 37 in the two part tariff condition significantly higher than 1 27 in the quantity discount condition at the same time loss aversion dominates contract complexity in explaining the data lastly we conduct a follow up experiment to confirm the central role of loss aversion as a behavioral driver in one condition the retailer becomes less loss averse when we temporally compress the fixed fee payment and the realization of retail profits which supports the loss aversion theory in the other condition the retailer s contract acceptance rate does not decline when we reward the manufacturer a higher cash payment for each experimental point earned which rules out the competing hypothesis that the retailer rejects contract offers due to fairness concerns

dynamic capacity management with uncertain demand and dynamic price inspired from practices of chinese real estate firms we study dynamic capacity management problems for a firm that sells homogeneous goods over a finite or infinite selling horizon provided that demand is uncertain retail price is exogenous but changes according to an auto regressive process and there is holding cost for remaining inventory in each period the capacity problems facing the firm include to determine an initial stock at the beginning of the selling season and to allocate the remaining quantity for the current and future sale in each period to maximize the firm s total expected discounted profit by using markov decision processes we show the optimality of a so called save up to level policy i e it is optimal to allocate as much as the save up to level to future periods if possible in each period and the existence of the optimal initial stock moreover we characterize monotone properties of the optimal save up to level and the optimal initial stock numerical analysis shows that compared to the policy with zero save up to level i e always allocating all the remaining inventory to the current period the advantage of the policy proposed in the present paper is significant when price rising trend is large holding cost is low initial price is high or demand variation is either high or low

asymmetric consumer learning and inventory competition we develop a model of consumer learning and choice behavior in response to uncertain service in the marketplace learning could be asymmetric that is consumers may associate different weights with positive and negative experiences under this consumer model we characterize the steady state distribution of demand for retailers given that each retailer holds a constant in stock service level we then consider a noncooperative game in steady state between two retailers competing on the basis of their service levels the demand distributions of retailers in this game are modeled using a multiplicative aggregate market share model in which the mean demands are obtained from the steady state results for individual purchases but the model is simplified in other respects for tractability our model yields a unique pure strategy nash equilibrium we show that asymmetry in consumer learning has a significant impact on the optimal service levels market shares and profits of the retailers when retailers have different costs it also determines the extent of competitive advantage enjoyed by the lower cost retailer

explicit solutions of optimization models and differential games with nonsmooth asymmetric reference price effects models in marketing with asymmetric reference effects lead to nonsmooth optimization problems and differential games which cannot be solved using standard methods in this study we introduce a new method for calculating explicitly optimal strategies open loop equilibria and closed loop equilibria of such nonsmooth problems application of this method to the case of asymmetric reference price effects with loss aversive consumers leads to the following conclusions 1 when the planning horizon is infinite after an introductory stage the optimal price stabilizes at a steady state price which is slightly below the optimal price in the absence of reference price effects 2 the optimal strategy is the same as in the symmetric case but with the loss parameter determined by the initial reference price 3 competition does not change the qualitative behavior of the optimal strategy 4 adopting an appropriate constant price strategy results in a minute decline in profits

efficient algorithms for the dynamic pricing problem with reference price effect we analyze a finite horizon dynamic pricing model in which demand at each period depends on not only the current price but also past prices through reference prices a unique feature but also a significant challenge in this model is the asymmetry in reference price effect which implies that the underlying optimization problem is nonsmooth and no standard optimization methods can be applied we identify a few key structural properties of the problem which enable us to develop strongly polynomial time algorithms to compute the optimal prices for several plausible scenarios we complement our exact algorithms by proposing an approximation heuristic and provide an upper bound on the optimal objective value finally we conduct numerical experiments to study the optimal price path and demonstrate the value of dynamic pricing when demands are seasonal we further compare numerically one of the exact algorithms with the heuristic and offer managerial suggestions this paper was accepted by yinyu ye optimization

the kaldor compensation test and rational choice abstract it is well known that the kaldor compensation test can be inconsistent in the sense that it leads to contradictory or cyclical recommendations in some situations this paper shows that there is a close relationship between the consistency of this test and the rationalizability of choices from given utility possibilities sets this observation suggests that if the kaldor test is consistent social decisions can be made using a social welfare ordering in the first place therefore the information assumptions embodied in some social welfare ordering have to be accepted if the kaldor test is to be applied consistently

technical note dynamic pricing with gain seeking reference price effects we study a dynamic pricing problem of a firm facing reference price effects at an aggregate demand level where demand is more sensitive to gains than losses we find that even the myopic pricing strategy belongs to one type of discontinuous maps which can exhibit complex dynamics over time our numerical examples show that in general the optimal pricing strategies may not admit any simple characterizations and the resulting reference price price dynamics can be very complicated we then show for a special case that a cyclic skimming pricing strategy is optimal and we provide conditions to guarantee the optimality of high low pricing strategies

the impact of reference price effects on the profitability of price promotions this paper investigates the impact of reference price effects on retailer price promotions and describes why these effects can make promoting profitable first we analyze the profit impact of reference price effects generated by a single period of promotion the promotion can increase profit if the gain that these effects create in the promotion period outweighs the loss they create in future periods we then describe how retailers can estimate the optimal strategy of recurring promotions that maximizes profits from reference price effects over a time horizon examples of such strategies are presented for a retailer selling a national brand of peanut butter we obtain insights into how promotion prices timing and profits are affected by changes in costs interest rates consumers reactions to reference price effects and error in estimates used in the model the retailer s optimal reaction to a trade deal is also examined this strategy involves a phase of increased promotion activity sandwiched between phases of decreased activity we explain these results using the effects described in the single period model

an investigation of reference price segments abstract empirical research on reference price has typically assumed that consumers use either an internal reference price irp or an external reference price erp but not both in brand choice decisions in this article the authors assume that consumers use both irp and erp but may consider one of them more salient than the other the authors develop a model that segments consumers on the basis of the differences in the importance they assign to each type of reference price as well as in their brand preferences and responses to marketing mix variables the authors calibrate the model on data for four categories liquid detergents ketchup tissue and yogurt in all four categories the proposed model performs significantly better than the one that assumes that consumers use either irp or erp exclusively the authors discuss the managerial implications of this finding

axiomatic bargaining theory on economic environments abstract axiomatic bargaining theory is reexamined by focusing upon the economic exhange environment instead of the traditional utility possibility set it is argued that the axioms of the traditional theory impose stronger restrictions than can be supported by their motivating economic intuitions weaker alternative axioms making explicit use of economic information are used to characterize the standard bargaining solutions a key idea is to impose consistency of the solution with respect to changes in the dimension of the commodity space even these weaker economic axioms however may be unrealistic restrictions to impose on the bargaining solution in the context of many economic bargaining problems

pricing and manufacturing decisions when demand is a function of prices in multiple periods in most deterministic manufacturing decision models demand is either known or induced by pricing decisions in the period that the demand is experienced however in more realistic market scenarios consumers make purchase decisions with respect to price not only in the current period but also in past and future periods we model a joint manufacturing pricing decision problem accounting for that portion of demand realized in each period that is induced by the interaction of pricing decisions in the current period and in previous periods we formulate a mathematical programming model and develop solution techniques we identify structural properties of our models and develop closed form solutions and effective heuristics for various special cases of our models finally we conduct extensive computational experiments to quantify the effectiveness of our heuristics and to develop managerial insights

markdown or everyday low price the role of behavioral motives we study a seller s optimal pricing and inventory strategies when behavioral nonpecuniary motives affect consumers purchase decisions in particular the seller chooses between two pricing strategies markdown or everyday low price and determines the optimal prices and inventory level two salient behavioral motives that impact consumers purchase decisions and the seller s optimal strategies are anticipated regret and misperception of product availability regret arises when a consumer initially chooses to wait but encounters stockout later or when the consumer buys the product at the high price but realizes that the product is still available at the markdown price in addition consumers often perceive the product s future availability to be different than its actual availability we determine and quantify that both regret and availability misperception have significant operational and profit implications for the seller for example ignoring these behavioral factors can result in up to 10 profit

natural oligopolies a vertical differentiation model this article contains a more complete characterization of conditions under which vertically differentiated markets are or are not natural oligopolies than has been found previously in the literature specifically previous results on markets in which firms have cost functions with constant returns are incomplete these results are expanded moreover results are provided for markets with firms having increasing or decreasing marginal cost functions

supermarket competition the case of every day low pricing every day low pricing edlp strategy has proved to be a successful innovation resulting in higher profits to supermarkets adopting it in competition with promotional pricing promo conventional wisdom attributes this success either to lower costs or to edlp better serving time constrained consumers while discouraging cherry pickers who seek promotions however it is unclear that such cost savings are being fully realized since edlp stores also engage in price promotions also continued existence of promo stores means that costs are not the only factor and they compete effectively without relying just on the cherry pickers furthermore experimental evidence suggests that a supermarket cannot obtain higher profits by merely setting constant low prices leading to the question exactly what makes edlp successful this question is of particular relevance to both academics and practitioners who have been intrigued by the success of this retailing strategy more generally the retailing issues addressed in this paper the economic analysis of competition and the empirical findings should be of interest to the broader community of researchers and managers we investigate the factors contributing to edlp s success by analyzing the competition between supermarkets through a game theoretic analysis of a market consisting of both time constrained consumers and cherry pickers key features of our model are consumers shop and purchase a basket of goods based on price announcements by stores and rational expectations of unannounced prices stores carry more than one good and compete through prices service convenience and appropriate communication strategies and no exogenous cost asymmetries we derive the conditions under which retailers choosing different strategies edlp and promo is a perfect nash equilibrium our analysis shows that the edlp store s offering of constant every day low prices is an equilibrium outcome endogenously determined successful implementation of the edlp strategy involves communication of relative basket prices implying that merely setting constant low prices is not viable we further demonstrate that while time constrained consumers find every day low prices at edlp attractive and cherry pickers the promotions at promo clientele effects are in fact more complicated specifically in equilibrium the promo store offers a higher service level as desired by time constrained consumers and the edlp store a lower service level in keeping with the needs of cherry pickers this choice of service by the two stores results in a cleaner segmentation of the market the higher relative basket price and service at the promo store results in a larger base of time constrained consumers to shop at the promo store and a larger base of cherry pickers to shop at the edlp store even though some cherry pickers continue to visit the promo store to avail of the price specials in this way our results contradict the conventional wisdom on edlp strategy as being mainly geared towards time constrained consumers finally industry profits are higher in an edlp promo equilibrium than when stores adopt identical strategies our analysis and results also offer a more complete characterization of the edlp and promo strategies indeed we show that edlp and promo strategies are positioning strategies rather than merely pricing strategies with different elements price promotions service and communications while the edlp store uses basket prices to attract both segments the promo store uses service and price specials to compete in the time constrained and cherry picking segment respectively given these different approaches of the two stores the communication strategies of the edlp and the promo stores emphasize these differences as well in this way we show as suggested by corstjens and corstjens 1994 that positioning in a retail context involves developing multidimensional strategies appealing to all segments while each element of the strategy may focus on a different consumer segment this is in contrast to the traditional view of segmentation in which different products in a product line for example are designed to appeal to different segments we complete the analysis by examining the data from the trade press and a survey conducted in a major metropolitan area these data while limited in scope support our theoretical results

asymmetric reference price effects and dynamic pricing policies we consider a group of frequently purchased consumer brands which are partial substitutes and examine two situations the first where the group of brands is managed by a retailer and second where the brands compete in an oligopoly we assume that demand is a function of actual prices and reference prices and develop optimal dynamic pricing policies for each situation in addition to researchers studying pricing strategy our results may interest retailers choosing between hi lo pricing and an everyday low price and manufacturers assessing whether to follow procter gamble s lead and replace a policy of funding consumer price reductions through trade deals with a constant wholesale price a reference price is an anchoring level formed by customers based on the pricing environment the literature suggests that demand for a brand depends not only on the brand price but also whether the brand price is greater than the reference price a perceived loss or is less than it a perceived gain the responses to gains and losses are asymmetric broadly speaking we find that when enough consumers weigh gains more than losses the optimal pricing policy is cyclical likewise when they weigh losses more than gains a constant price is optimal thus we provide a rationale for dynamic pricing which is quite distinct from the three explanations previously offered 1 decreasing unit variable costs due to learning effects 2 the transfer of inventory to consumers who face lower inventory holding costs than do retailers and 3 competitive effects our explanations apply even when the other explanations do not i e in mature product categories where learning effects are minimal when retailer inventories are minimized through the use of just in time policies and when competitive effects do not exist as in a monopoly greenleaf 1995 has shown numerically that in the presence of reference price effects the optimal pricing policy for a monopolist can be cyclical we first analytically extend greenleaf s result to a monopolist with a constant cost of goods facing a homogeneous market where all customers either weigh gains more than losses or vice versa using this building block we examine a monopolist retailer managing multiple brands we assume that demand is a linear function of prices of multiple brands and together with an expression which reflects the reference price effect further we assume that the retailer maximizes average profit per period next we analyze a duopoly and extend the results to an oligopoly we assume that the manufacturers are able to set the retail prices as in an integrated channel here we retain the same demand function as for the retailer and derive markov perfect nash equilibria we use two alternative processes of reference price formation the exponential smoothed es past price process which is frequently used in the literature and for the multi brand situations the recently proposed reference brand rb process hardie johnson and fader 1993 in the latter the reference price is the current price of the last brand bought the reference brand we adapt the individual level rb formulation in hardie et al to an aggregate demand specification for the es process we obtain most results analytically for the rb process we use simulation finally we extend our results to a population with two customer segments segment 1 which weighs gains more than losses and segment 2 which does the opposite i e is loss averse when the market consists exclusively of segment 1 customers and es is the reference price process we find that prices are cyclical in all cases analyzed i e for a monopoly a monopolist retailer managing multiple brands a duopoly and an oligopoly if the rb formulation is the underlying process a monopolist retailer managing two brands uses cyclical prices but in a duopoly the equilibrium solution is for the brands to maintain constant prices when all customers belong to segment 2 i e they are loss averse constant prices are optimal in all cases for both reference price formulations when the population consists of both segment 1 and segment 2 and the es process applies we develop a sufficient condition for cyclical pricing policies to be optimal the condition is expressed in terms of the proportion of the two segment sizes the absolute difference between the gain and loss parameters of each segment and their respective exponential smoothing constants interestingly for reasonable values of the latter two factors cyclical policies are optimal even when the proportion of segment 1 is quite small similar magnitudes are obtained numerically for the rb case

reference price and price perceptions a comparison of alternative models reference price effects on consumer price perceptions are often explained by helson s adaptation level theory in which the cognitive representation of reference price is the prototype of the relevant category however recent conceptualizations and empirical evidence suggest the possibility of an exemplar model which may be specified using volkmann s range theory or parducci s range frequency theory in two experiments these three contextual models of reference price effects are pitted against one another based on the manova and model fitting range frequency theory accounted for reference price effects that the other theories could not suggesting that consumers compare the target price against specific members of the category rather than the category prototype a third experiment demonstrated that range and frequency effects are moderated by the stimulus presentation condition suggesting that consumers place greater weight on extreme prices anchoring the range for internal reference prices than for external reference prices

a model of mental accounting and reference price adaptation consumers possess a mental account that stores the worth of items purchased and yet to be consumed reference prices act as the book values of these items movements in the account the comparison between the reference price and the price paid at entry and the comparison between the benefit of consumption and the reference price at exit yield hedonic benefits the reference price is determined by a psychological process of adaptation to the price evoked by the trade the model is integrative in that it explains a wide array of observed anomalies such as sunk cost effects payment depreciation reluctance to trade preference for prepayment and the flat rate bias the model also generates new testable implications this paper was accepted by james smith decision analysis

dynamic pricing with loss averse consumers and peak end anchoring we study the dynamic pricing implications of a new behaviorally motivated reference price mechanism based on the peak end memory mode this model suggests that consumers anchor on a reference price that is a weighted average of the lowest and most recent prices loss averse consumers are more sensitive to perceived losses than gains relative to this reference price we find that a range of constant pricing policies is optimal for the corresponding dynamic pricing problem this range is wider the more consumers anchor on lowest prices and it persists when buyers are loss neutral in contrast with previous literature in a transient regime the optimal pricing policy is monotone and converges to a steady state price which is lower the more extreme and salient the low price anchor is our results suggest that behavioral regularities such as peak end anchoring and loss aversion limit the benefits of varying prices and caution that the adverse effects of deep discounts on the firm s optimal prices and profits might be more enduring than previous models predict

loss aversion under prospect theory a parameter free measurement agrowing body of qualitative evidence shows that loss aversion a phenomenon formalized in prospect theory can explain a variety of field and experimental data quantifications of loss aversion are however hindered by the absence of a general preference based method to elicit the utility for gains and losses simultaneously this paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions thus it is the first to obtain a parameter free elicitation of prospect theory s utility function on the whole domain our method also provides an efficient way to elicit utility midpoints which are important in axiomatizations of utility several definitions of loss aversion have been put forward in the literature according to most definitions we find strong evidence of loss aversion at both the aggregate and the individual level the degree of loss aversion varies with the definition used which underlines the need for a commonly accepted definition of loss aversion