DYNAMIC PRICE AS BARGAINING RESULT FOR REVENUE MAXIMIZATION IN RETAIL

The application of dynamic price and its modeling was an authentic revolution for the traditional concept of price setting in business environment. The article reviews the essence and the main principles of dynamic price as a bargaining basis. Dynamic price fluctuation range in this paper is collated with the zone of agreement and introduced as an overlap between the maximum purchase price that the buyer is willing to pay and the minimum sell price that the seller is willing to accept. Therefore, the aim of this paper is to analyse the dynamic price as the bargaining basis, research problems, and to assess the dynamic price efficiency based on the dynamic price setting model experiment results. The experimental results suggest that dynamic price is a successful tacit bargaining practice.


Introduction
In the research literature and organizations' practice, more and more attention is paid to the price setting based on current product demand and supply conditions -a dynamic price and its modelling.Appropriate price setting still remains a very challenging task requiring the organization's knowledge not only of their operating costs, but also of the possibility to understand the dynamic price based on the product demand and supply parameters.
Research on dynamic price modelling has been undertaken by economists and operational researchers from a range of perspectives, and the benefits of dynamic price methods have long been known in airlines, electricity, and other industries.Nowadays, there has been an increasing adoption of dynamic price in the retail sector when selling a fixed inventory over a finite selling horizon.
Due to the development of information technologies and e-commerce, many-sided information about the customer has become easier available and thus has determined an increased interest to the dynamic price setting research and its application in various sectors of services and industries.Dynamic price setting has been caused both in scientific field and in practice by the following factors: availability of statistical data on the demand of a good; the possibility quickly to change goods' prices, caused by the IT development, reliability, and availability of mathematical decision-making methods to analyze demand and supply data.The experience of foreign companies (IBM, Inditex, Compaq, Hewlett-Packard, Dell, etc.) has revealed that companies which apply the dynamic approach in their price setting may achieve the best results in business.Therefore, the increasing competition, uncertain demand, shortening lifecycles of goods, surplus stocks of goods, the growing economic risk of companies have induced trade companies to examine their current price-setting methods and to start looking for dynamic pricesetting methods which would allow for revenue maximization.
The bargaining mechanism itself is the vast literature subject, but the relation between dynamic price and bargaining is rarely purified in practice.While the majority of dynamic price researchers assume that buyers and sellers are uncertain about each other's valuations of the good, we state that dynamic price is the concept where two parties bargain over a surplus split -the difference between the total surplus and the sum of their reservation utilities.
The purpose of this paper is to analyse the dynamic price as the bargaining basis, its research problems, and to assess dynamic price efficiency based on the dynamic price-setting model experiment results.In the article, we solve the research problem how and what type of bargaining influences dynamic price, and how dynamic price setting affects the company's results.The main research methods include both qualitative and quantitative methods.The dynamic price forming factors were evaluated using the Analytic Hierarchy Process (AHP) method.This decision-making method, originally developed by T.L. Saaty, allows some small inconsistency in judgment where the main idea is to derive ratio scales from paired comparisons.For dynamic price modelling, due to the existing categorical variables, it was decided to use the general linear model (GLM).In fact, it is the ordinary linear regression and analysis of variance models' compound that allows using the quantitative and qualitative variables and their various interactions instead of the explanatory variables.
The paper begins with an overview of the dynamic price conception and its research problems from the theoretical standpoint.It is followed by a discussion on the link between dynamic price and bargaining.Then, based on the purpose of this paper, we apply the AHP method to identify the dynamic price forming factors and GLM modelling to assess the dynamic price efficiency.
We should note that to define DP reliably is still a complex task for several reasons, most important being the following: different interpretations of this conception by representatives of various scientific spheres, and the orientation of DP researchers towards different academic branches.Therefore, the DP concept analysis suggests that up to now in the literature there is no unanimous and widely used DP definition.

FIG.1. Dynamic price research objects in different research fields
Source: compiled by authors.
In the context of economic research, DP is often associated with the price discrimination: DP is understood as an attempt of a seller to force a customer to pay the highest price he is ready to pay.An important contribution of this scientific direction is presenting DP as the best reflecting product demand / supply balance, (Bitran, 2002;Schwind, 2007;and more).A conclusion was formulated by P. Krugman (2000), H. Varian (1980Varian ( , 2007) ) that DP is a new practice of the old price discrimination.According to researchers, modern technologies made DP useful not only for different areas of industries/services, but also for economics.
L. Philips (1983) summarizes a typical economist attitude towards price discrimination and states that DP is necessary in order to allocate resources in the optimum way in real-life situations.This statement may sound strange, because usually the economic analysis states that in the competitive market the price is equal to marginal costs and thus maximizes welfare.However, based on the modern true-life situations, many sectors of industry such as pharmacy, telecommunications and information technologies, experience high fixed costs and lower marginal costs.When prices are set according to Economics: DP is a tool for revenue maximization.
Marketing: DP is a tool to reflect the state of the current demand for optimal price.
Operations: DP is a tool for optimal resource allocation.
Management: DP is a tool for revenue management & process optimization Dynamic price marginal costs, it would be impossible to retrieve the initial investment, so in this case DP is assessed positively.
We state that DP definition has a tendency to show which academic field governs the knowledge of this research problem.I. Yeoman et al. (1999) claimed that the widely accepted DP definition is the allocation of resources and inventory for the right buyer, for the right price in order to maximize revenue and profitability (Ng, 2005).Despite the influence of other disciplines, operational research still clearly dominates in the literature concerning revenue management.
In the nowadays operation management, researchers state that product demand is the integral part of DP research (Boyd, Bilegan, 2003); the definitions are still concentrated on supply as evidenced by S.E.Kimes and G.M. Thompson's (2004) definition: DP is the form of resource management where supply is controlled by manipulating useful life and price.This is not consistent with the definition of M. Fleischmann et al. ( 2004): DP is related to price-fixing for perishable resources taking into account the demand so that to maximize the revenue or profit (according to Ng, 2005).
This paper defines DP as a bargaining form and as a dynamic price regulation for consumers, evaluating the current product demand / supply to maximize the revenue.Using DP, the seller dynamically, over time and in response to parameters such as product demand and supply, adjusts the product prices.This understanding is the opposite of DP definitions in the operations management research provided by K.T. Talluri and G.J. van Ryzin (2004), L. Weatherford and S. Bodily (1997) where the demand profile is separated from both the resource allocation and a company's price policy.
We state that not only the lack of a uniform DP definition is the only problem in the DP research (Fig. 2).Most of the DP models are rarely purified in the practice.The majority of them remains only on the theoretical level; as also the mathematical algorithm modelling complicates their application.As a result, in this paper, we argue that DP models should be based on the practice, versatility, and simplicity principles.Another DP research problem is the variety of DP determinants and indicators.An abundance of research in various areas of science has led not only to the lack of a unified concept of DP, but also to the abundance of its forming factors.

FIG. 2. The main problems in dynamic price research
Source: compiled by authors.

The lack of uniform DP definition The variety of DP determinants and indicators
The lack of DP models applicability in practice Simulation of the only one determinants group (supply or demand side) In most studies, DP is modelled in a specific area, and the model is constructed on the basis of factors that are only important for a particular researcher or a specific business area, resulting in the lack of DP models' versatility.In this context, it is worth to analyze W. Elmaghraby and P. Keskinkocak (2003) research papers which indicate that before modelling DP it is important to define and evaluate the following characteristics: • replenishment or no replenishment of inventory.The inventory policy plays an important role in revenue management models.If inventory replenishment is allowed by the time horizon, the retailer should make a joint inventory and price decision during the time horizon; if the replenishment is not allowed, the retailer should make the price decision based on the given inventory; • dependent or independent demand over time.If a retailer has a durable product to sell, the demand for the product might be a dependent function across multiple periods of time.For this type of product, the benefit duration of the product is longer than the selling horizon.On the other hand, if the costumers' knowledge about the product plays an important role in their decision to buy the product, the demand would also be dependent on time; • myopic or strategic customers.The retailers should take into account the purchasing behavior of the customers in order to have an efficient price policy.If a customer makes his decision based only on the price he sees when he arrives, we call this customer a myopic customer.In the opposite case, we call it a strategic customer.The literature analysis has confirmed that, although organizations give a higher importance to DP, its systematic application in practice is limited (Bitran, 2002;Caro, Gallien, 2012;Schwind, 2007;Cross, 1997;Smith, Achabal, 1998;Walker, 1999).Practical DP models results are also rarely presented (Andersen, 1997;Chan, Seetharaman, 2004;Cleophas, 2012;Desiraju, Shugan, 1999;Elmaghraby, Keskinkocak, 2003;Florian et al., 2006).The successful applicability in business (Table 1), especially in retail, aviation, hospitality services, confirms that DP has been quite an innovative method whose advantage is the fact that, compared with other price methods such as static price, business income has increased, while costs have remained unchanged (Feng, 2010).

Dynamic price as the bargaining result
Very few economic research papers to date have considered and analyzed DP as a bargaining form.We should note that DP in economics is analyzed as a revenue management form with a limited research on the buyer and seller interactions.M. Schwind (2007), M. Bichler et al., (2003) argue that it is a two-way process in which the buyerseller, according to different purposes, seek a mutually satisfactory price level (beneficial agreement).Here, the buyer's and the seller's power is equivalent.For this reason, the price bargaining is difficult to manage, and misunderstandings abound.Basically, in economics there are two classical bargaining models: the Nash bargaining solution and the Rubinstein model (Fig. 3).Under the Nash bargaining solution, two parties bargain over a surplus split the difference between the total surplus and the sum of their reservation utilities (also known as disagreement payoffs).The Rubinstein model, on the other hand, regards bargaining as a series of alternating offers between the two parties bargaining over a surplus.In its most basic form, the Rubinstein model assumes that the two parties have full information regarding each other's utilities, and they make alternating offers with a fixed time interval between two successive offers to maximize the discounted utility (Kuo, 2008).Researchers (Cope, 2007;Cross, 1997;Elmaghraby, Keskinkocak, 2003;Bitran, 2002, and more) also wish to model the situations in which some of the parties are not certain of the characteristics of some of the other parties (a Bayesian game).
In Fig. 3, auctions are resource allocation mechanisms based on a competitive bidding process over a single issue (e.g., price) of a single well-defined object, and involve Bichler et al. (2003).Reverse pricing enables both buyer and seller to influence the final price of a product or service, if a buyer's bid does not surpass the seller's threshold price, the option to place additional bids depends on the characteristics of the mechanism design as defined by the seller or a third party.DP discrimination in its basic form is defined when different customers are quoted for the same product at different prices.And finally, the revenue management is designed to find the optimal revenue management for perishable assets (Schwind, 2007).
DP of supply and demand response based on bargaining is highly dependent on the frequency of the bargaining process.The high cost of the bargaining process leads to the small share of the market.According to M. Schwind ( 2007), the efficiency and equity of this DP form is also highly dependent on the bargaining agents' talent.To avoid all the price bargaining problems, researchers started to build electronic bargaining tables and systems.Bargaining is any process through which the players try to reach an agreement.This process is typically time-consuming and involves the players making offers and counteroffers to each other (Muthoo, 1999).Here are two options stated: the possibility not to reach agreement or reaching it after a costly delay.

Zone of agreement
M. Schwind (2007), M. Bichler et al., (2003), K. Chatterjee and W. Samuelson (1983), P.V. Balakrishnan and J. Eliashberg (1995), R. Wang (1995), N.L. Stokey and R.E.Lucas (1989) and other dynamic economics researchers assume that DP is an effective method to reach the optimal agreement stage.Bargaining is an inherently dynamic process; for instance, a low-ball early offer by the buyer will affect the course of the whole bargaining interaction.Any estimation must incorporate these dynamic considerations, and techniques for the analysis of dynamic games have become available only recently.We should note that buyers and sellers have different future outcomes if trade occurs.Sellers are professional traders and always return to the market and begin bargaining with a fresh buyer at the conclusion of a successful or unsuccessful trade.Buyers, on the other hand, are temporary participants in the market.Upon completion of a successful sale, they exit the market permanently.However, if bargaining with a given seller fails to result in trade, the buyer seeks out another seller (Keniston, 2011) W.F. Samuelson (2006) argues that bargaining inevitably produces tension between the forces of competition and cooperation.To reach a mutually beneficial agreement, both sides (here buyer and seller) must cooperate.An overlap between the maximum purchase price that the buyer is willing to pay and the minimum sell price that the seller is willing to accept, the pair is said to possess a Zone of Agreement or Zone of Possible Agreement.A graphical representation of a zone of agreement is given in Fig. 4. If the negotiators are successful, they will come to an agreement somewhere within this range, and thus both come out better than they would have had they gone elsewhere.If, on the other hand, the maximum buy and minimum sell prices do not overlap, then no agreement zone exists (Usunier, 2002;Samuelson, 2006).We state that the Zone of Agreement is the DP fluctuation zone where the buyer and the seller are looking for the mutually beneficial agreement point.In this view, we agree with T. Alfredson and A. Cungu (2008) that the relative power of each party affects their ability to secure their individual goals through bargaining.Structural theories offer varying definitions of power.For example, power sometimes is defined as the ability to win or, alternatively, as the possession of 'strength' or 'resources'.
We assume that the bargaining process is tacit in the sense that the buyer and the seller can communicate only by making a price over that directly affects their payoffs.We refer to K.M. Murnighan's (1992) "tacit bargaining" definition as "bargaining in which communication is incomplete or impossible".Put this way, any set of terms falling inside the zone of agreement can be supported as an equilibrium outcome.
Our approach is supported by D.E.Keniston (2011): at the beginning of the game, sellers decide once and for all whether to enter the market by comparing the expected returns to the trader profession with some exogenous external option.In contrast, a new round of buyers enters the market each period to replace those that have traded in the past period and exited the market.Entering buyers first decide whether to participate or not in the market; if not, they exit and are replaced in the next period.Buyers who do select to participate remain in the market until they have successfully completed the trade.
Via the dynamic process, the parties will arrive at some final outcome; however, the multitude of equilibrium outcomes makes it difficult to predict to which one.Clearly the final outcome depends significantly on the bargainers' expectations -expectations that are modified via the offers exchange and counteroffers during the bargaining (Fig. 5).
The optimal agreement zone is the most desirable point to be reached by both sides (see the grey plot in Fig. 5).In some sense, bargaining ceases when expectations converge, at a point where neither side can expect the other to concede further.Then, either an agreement is signed or, if the sides stubbornly hold to conflicting expectations, a disagreement follows (Samuelson, 2006).

Methods
In this paper, we suggested to analyze DP as a bargaining form.For this reason, the DP model was formed and tested in the real business environment -the international retail The research stages are as follows: identification of the most significant DP forming factors and justification of the corresponding parameters; construction of an econometric model to evaluate DP setting; verification and justification of the model.The created econometric model integrated the demand and supply factor groups that met the economic logic related with the DP setting formation.
Forming the DP model, first it is necessary to select and justify the determinants and their reflective indicators.For this purpose, expert survey was selected as the instrument to obtain judgments from experts about the importance of DP-forming factors.This questionnaire was directed to get the priority weight of each factor used for ranking the DP-forming factors.The methodology used is Analytic Hierarchy Process (AHP).The factors here should be rated by the method of a pairwise comparison where the preference of one factor over the other is given a numeric value (scale 1-3-5-7-9).The method brigives the possibility of a qualitative evaluation to be transformed into quantitative evaluation.The comparison result is a square matrix P = ||p ij || (i, j = 1, …, m).

The comparison matrix mathematical expression:
The research stages are as it follows: identification of the most significant DP forming factors and justification of corresponding parameters; construction of an econometric model to evaluate DP setting; verification and justification of the model.The created econometric model integrated the demand and supply factors groups that they meet economic logic related with the DP setting formation.
Forming the DP model, firstly need to select and justify determinants and their reflective indicators.For this purpose expert survey was selected as instrument to obtain judgments from experts about the importance of DP forming factors.This questionnaire was directed to get the priority weight of the each factor used for ranking DP forming factors.The methodology used is Analytic Hierarchy Process (AHP).The factors here should be rated by method of a pair-wise comparison where the preference of a factor over the other is given a numeric value (scale 1-3-5-7-9).The method brings the possibility the qualitative evaluation to be transformed into quantitative evaluation.The comparison result is a square matrix P =�� �� �(i, j = 1, …, m).
Comparison matrix mathematical expression: More than 10 international experts were interviewed in 2012 December -2013 April.
Due to existence of categorical variables was decided to use the general linear model (GLM).In fact, it is the ordinary linear regression and analysis of variance models compound that allows instead of the explanatory variables to use the quantitative and qualitative variables and their various interactions.The application of GLM model and optimization methods were selected in this paper, because they allow to determine and identify the impact of factors and implement the DP setting model idea in a real business environment in order to maximize the retail trade company revenue.

1.1
More than ten international experts were interviewed in 2012 December -2013 April.The first phase was carried out in a pilot study to determine the adequacy of the study and to verify measuring instruments and adapted procedures.The survey data were computed by the "Make It Decision Rational Tool" program.As a result authors evaluated the main DP forming factors: f n -inventory level, BrAssort n -partial assortment effect, PLC itproduct lifecycle, SEASw -seasonality, COO it -origin country, PD it -product discount, QA it -product quality, Brand it -brand attractiveness (for more, see Deksnyte, Lydeka, 2012Lydeka, , 2013)).
Due to existence of categorical variables it was decided to use the general linear model (GLM).In fact, it is the ordinary linear regression and analysis of a variance models' compound that allows, instead of the explanatory variables, to use the quantitative and qualitative variables and their various interactions.The application of the GLM model and optimization methods were selected in this study, because they allow to determine and identify the impact of the factors and to implement the DP setting model idea in a real business environment in order to maximize the retail trade company revenue.
the regular -static pricing setting.The static price in the control group often leads to delays: as analyzed above, in our experiment case the lowest price limit had no such effect as in the DP case (Fig. 7).
The empirical results show that the old / slow selling inventory can reduce the overall organization profitability when the total assets increase due to investments in stocks.As a result, the decline in asset turnover, the lack of working capital and thus the opportunity to invest in other, more profitable, asset class will be limited.These problems often cause the company to seek additional investment sources.
In assessing the amount of stock sold in both experimental groups, the DP case resulted in a +2% (+55 units) higher number of units sold.According to the international retail companies group XYZ statistics, the total category turnover, taking the results of the experimental group increased from 4.21 to 4.24.Thus, the experimental results show that the DP effected the inventory management efficiency.Based on this reasoning, we conclude that the DP reduces the risk of excess inventory.
In DP research studies, an integral part of the debate is the effect on organization profit.B.P. Reagan (1982), L. Weatherford, and S. Bodily (1992), V. Aguirregabiria (1999), I. Yeoman et al. (1999), M. Fleischmann et al. (2004) identify DP as one of the factors influencing the performance of an organization, emphasizing the impact on company profit.An experimental study confirmed that DP leads to sales growth, inventory management efficiency, but not in all cases; the profit was obtained as compared with the control product group (Figs. 8,9).Experiment results in this study have shown that the product lifecycle indicator is statistically significant and identifies obsolete inventory which would weaken the position of the variable in question.The product quality 13 optimal price set.A rare case in which this can be achieved using the regular -static pricing setting.Static price results in control group often leads to delays: as analyzed above in our experiment case -the lowest price limit had no effect as in DP case (Fig. 7.).

FIG.7. Experiment and control groups, comparison based on average price variation
Source: compiled by authors based on international retail companies group XYZ data.
Empirical results show that the old/slow selling inventory can reduce the overall organization profitability when total assets increased due to investments in stocks.As a result, the decline in asset turnover, the lack of working capital and in this way the opportunity to invest in other, more profitable asset class will be limited.These problems often cause the company to seek additional investment sources.
In assessing the amount of stock sold in both experimental groups, DP case resulted in a higher number of units sold -+2% (+55 units).According to the international retail companies group "XYZ" statistics, total category turnover, taking the results of the experimental group increased from 4.21 to 4.24.Thus, the experimental results show that the DP effected inventory management efficiency.Based on this reasoning we conclude that DP reduces the risk of excess inventory.

Conclusions
In the literature and in organizations' practice, more and more attention is paid to the price setting based on the current product demand-and-supply conditions -the DP and its modelling.Appropriate price setting still remains a very challenging task requiring the organization's knowledge not only about their operating costs, but also the possibility to understand the DP-affecting product demand and supply parameters.
The bargaining mechanism itself is a vast literature subject, but the relations between DP and bargaining are rarely purified in practice.While the majority of DP researchers assume that buyers and sellers are uncertain as to each other's valuations for the good, we state that DP is a concept where two parties bargain over a surplus split as the difference between the total surplus and the sum of their reservation utilities.
The DP concept analysis states that up to now in the literature there has been no unanimous and widely used DP definition.In this paper, the authors have defined DP as bargaining form and as a dynamic price regulation for consumers, evaluating the ability of the current product demand / supply parameters to maximize the revenue.Using DP, the seller dynamically over time and in response to parameters such as a product demand and supply adjusts the product prices.
This paper contributes to the field of research on DP analyzed as a bargaining form in which the existing analyses are more often empirical and multinational.It suggests that the Zone of Agreement is the DP fluctuation zone where the buyer and the seller look for a mutually beneficial agreement point.The relative power of each party affects their ability to secure their individual goals through bargaining.
Following the methodology of our research, we propose to use the AHP method for the identification of DP-forming factors and GLM modelling to assess DP efficiency.
The results of our research indicate that in comparing the dynamic and regular (static) prices, the experimental study has shown that DP leads to sales growth, inventory management efficiency, but not in all cases: the profit was lower as compared with the control product group.The greater number of successful bargains in the DP case has indicated that the DP is a successful tacit bargaining practice.Via the dynamic process, parties will arrive at some final outcome, bBut the multitude of equilibrium outcomes makes it difficult to predict at which one.The final outcome depends significantly on the bargainers' expectations -expectations that are modified via the exchange of offers and counteroffers during the bargaining.

FIG. 7 .
FIG.7.Experiment and control groups, comparison based on average price variationSource: compiled by authors based on the international retail companies group XYZ data.

TABLE 1 . Dynamic price application areas and results 1
Source: compiled by authors.