The firm allows the sales rep set the price the marketplace

University of Houston

Dissertation Chair:

Niladri Syam

Associate Professor of Marketing and Entrepreneurship

Tong Lu

Assistant Professor of Accountancy and Taxation

Table of Contents

1. Introduction

2. 1. Overview of the Model Page 20

   2. Model Derivation Page 23

3. Experimental Essay on Price Delegation to the Salesforce: Does Price Delegation Actually Arise as an Equilibrium Strategy?

   1. Empirical Essay Overview Page 32

4. Discussion of the Contribution Page 49

1. Introduction

The market environment that I focus on is listed below. First, I assume that firms function in a competitive environment (an example of a recent study that focuses on competition is Syam, Ruan and Hess 2005). For analytic ease, I consider a duopoly decision game. Second, each firm maintains a salesforce which serves as the channel between the firm and the customers. The third condition assumes the traditional moral hazard issue present in principal-agent models (Basu et al. 1985). This refers to the situation in which the principal aims to motivate the agent to behave in a profit-maximizing manner, but the agent shows a natural tendency to shirk. As a result, the solution of the problem is for the principal to design a compensation contract that enables the agent to have incentives that align directly with the principal’s interest. The fourth condition, which is common of principal-agent models, is that the principal receives a noisy signal of the agent’s effort. For instance, in the personal selling scenario, the principal does not observe effort but rather sales. Since effort is related to sales, the principal receives a noisy assessment of the sales effort put forth by the agent. The fifth market condition assumes information symmetry between the firms and agents. Information symmetry in the delegation literature denotes that the firms and agents have the exact same information about the demand conditions (i.e. customers). On the contrary, the standard information asymmetry condition involves agents that possess superior knowledge of the customers. Given these market conditions, I consider when price delegation constitutes an equilibrium strategy.

Although the delegation decision has been examined in the extant marketing literature, there is some confusion over when price delegation is optimal and when it is not. In the presence of information asymmetry, price delegation is intuitively optimal because the salesperson possesses a better understanding of the customer and can ultimately set a more appropriate price. The firm on the other hand, is forced to make a probabilistic estimate of the demand conditions and choose the price that maximizes the expected profits. Hence, it is fairly accepted that price delegation is the optimal strategy for firms (Lal 1986 and Joseph 2001). Mishra and Prasad (2004), (2005) find a contrary result: as long as the firm offers a contract that reveals private information about the sales agent’s demand conditions, firms should not delegate the pricing decision. The intuition is that the firm can utilize the contract to extract the informational advantage of the salesperson.

Weinberg’s (1975) article sparks the first approach explaining how the firm and sales rep respond to price delegation. His model specifies that price delegation results in price discounts. Hence, the concern is that the sales representatives will bestow the customer too much of a discount which would then correspond to lower profits for the firm. This precise problem arises when the compensation is based on sales revenue and not gross margin. When compensated on sales, Weinberg shows that the salesperson will charge a price that is too low. This particular finding garners attention because most sales companies with some form of price delegation compensate on sales.

The price delegation literature continues with the lone empirical paper, Stephenson, Cron and Frazier (1979). This article surveys companies in multiple industries to assess how differential levels of price delegation (low, medium or high) lead to higher company performance via gross margins, sales rep contribution, sales, sales growth and return on assets. The study finds that the industries exhibiting the lowest degree of price delegation perform the best. In particular, firms with a low degree of price delegation have the highest gross margins and sales growth.

Mishra and Prasad (2005) consider price delegation in a competitive scenario with both information symmetry and asymmetry. Their major finding is that regardless of the information scenario competition does not cause delegation to be the equilibrium strategy. With the information asymmetry scenario, they use the contract theory approach which was used in the 2004 paper to demonstrate that the results extend to the competitive case. The information symmetry scenario constitutes an interesting finding. As long firms are allowed to choose contracts beyond the standard linear compensation package (salary plus commission) and firms are able to design alternative contracts for when delegation is selected and when centralized pricing strategy is chosen, firms can always design a contract that allows centralized pricing to be at least as good as delegation. Although the finding provides an interesting theoretical result, the practical nature of these compensation plans are not well defined. For instance, the type of compensation plan that the authors present in the paper includes salary plus commission and also a commission on price. As a result, the managerial implications of Mishra and Prasad (2005) are limited.

A second stream of literature that relates closely to price delegation is the channels of distribution literature (e.g. McGuire and Staelin 1983, Coughlan 1985 and Moorthy 1988). In the channels literature, a manufacturer considers the appropriate channel structure for distributing their product. The seminal article in this stream of research is McGuire and Staelin (1983). In their seminal paper, firms choose between two channel structures: a vertically integrated channel (centralized) and a franchised channel (decentralized). Furthermore, Mcguire and Staelin (1983) show that the centralized channel structure is always an equilibrium. However, they accordingly show that the decentralized channel is also an equilibrium for a sufficient level of product substitutability. Coughlan (1985) maintains McGuire and Staelin’s (1983) findings and further show supporting empirical evidence that the decentralized channel arises more readily with closely substitutable products. Similarly, Moorthy (1988) investigate further to examine when decentralization arises as the equilibrium channel structure.

(1) q_i(p_i,e_i,p_3-i,e_3-i) = h − p_i + θ_pp_3-i + e_i − θ_se_3-i + δ, for i =  1, 2,

where h is the demand intercept, θ_p is the cross-price effect, θ_s is the cross effort effect and δ is a common random shock to the demand system. Although a fairly common demand specification (McGuire and Staelin 1983 propose a similar version of this demand without the effort variables and the common shock), this specification has a couple of noteworthy problems. First, the demand function is fundamentally a reduced-form which arises from a customer’s utility maximization. As a result, the parameters of the demand function are actually a more complex combination of the utility function parameters. Second, the category demand increases with an increase in the cross price effect θ_p. Bhardwaj (2001) interprets θ_p as solely a measure of the degree of competition between the two brands, but clearly it captures more than just the intensity of price competition. Truth be told, θ_p also captures the customer’s inherent preference (attractiveness) for the product category.

Figure 1: Graphical Illustration of Products Being Closer Substitutes and the Tradeoffs Made by the Customer

Given this problem, I will review the propositions presented in Bhardwaj (2001) and discuss confounding explanations of the results. Proposition 1 states “In the symmetric Nash equilibrium under price delegation, the prices, the effort levels, and the commissions increase as price competition becomes more intense and decrease as effort competition becomes more intense.” Similarly, the first part of Proposition 2 states “In the symmetric Nash equilibrium under no-price delegation, the prices, the effort levels, and the commission increase as price competition becomes more intense but decrease as effort competition becomes more intense.” Since Propositions 1 & 2 are consistent with each other, I will refer to both propositions concurrently.

Propositions 1 & 2 are quite surprising because price competition leads to price increases in the marketplace. This goes directly against the classic theory of competition provided in the Hotelling model and the Bertrand pricing game. This surprising finding is solely an artifact of the demand specification (a similar finding is noted in the distribution channel literature by Ingene and Parry 2007 and Ingene, Taboubi and Zaccour, mimeo). In particular, the intensity of price competition simultaneously increases the customer’s affinity for both products which leads to a lift in the aggregate demand. Since the lift in aggregate demand confounds the findings, it is unclear if the model predictions hold true.

2.1 Overview of the Model

The model in this paper is quite similar to the model in Bhardwaj (2001). However, the difference is that I start from first principles and derive the demand for the marketplace products. This additional step allows for a demand curve with parameters that relate directly to the utility function of the customer. As a result, the model parameters are easier to interpret and the traditional thought-experiments can be conducted without any confounding factors. Specifically, I create a scenario that would allow us to analyze the game by determining how substitutability affects the delegation decision and correspondingly the prices, effort levels, commissions and salary.

where μ₁ and μ₂ represents how utility changes with increases in the consumption of the goods 1 and 2, λ is the marginal utility of the outside good (higher values indicate a higher utility for the outside good and consequently a lower utility for the two goods considered), ψ embodies the substitutability of the products (higher values correspond to closer substitutes), θ_s captures the impact of cross effort on the utility obtained from consuming a unit of the focal good (higher values suggest that the cross firm’s sales rep can more effectively alter the realized benefits of consuming the focal firm’s products). To further simplify the analysis, I will further assume that μ₁ = μ₂ = μ. With this simplification, the number of parameters is one more than that in Bhardwaj (2001). The added parameter is note worthy because my specification is a more general case of Bhardwaj (2001). More specifically, Bhardwaj (2001) is a special case of this utility specification.

Given this utility function, the customer decides the optimal assortment of products to purchase from the two firms subject to the budget constraint: M = p₁q₁ + p₂q₂ or q₀ = M – p₁q₁ + p₂q₂, where M is income. Substituting in for q₀ we rewrite Equation 4 as

(7) q_i = μ − λp_i − λψ(p_i−p_3-i) + e_i − θ_se_3 − i + δ,for i = 1,2.

At this point, I assume that there is a random component to unit sales and is common to both firms. Specifically, δ is a common random shock that arises due to the firm’s uncertainty about the customer’s affinity for the products where δ ~ N(0, σ_δ²). Note that this derived demand without the effort terms is the linear demand developed by Shubik and Levitan (1980). However, the addition of the effort variables allows this specification to be more relevant for situations involving salesforces with overlapping territories.

Now that we have obtained demand functions that come from first principles, we can then start to analyze the equilibrium behavior of the game. There are four possible equilibria. The first is the situation in which both firms delegate the pricing decision to the salesforce (Delegate/Delegate). The second involves both firms utilizing a centralized pricing strategy (Centralize/Centralize). The remaining equilibria are asymmetric where one firm delegates and the other centralizes (Delegate/Centralize) and vice versa (Centralize/Delegate). If delegation is selected, firm i maximizes the following optimization program

(9) $\underset{y_{i}\text{,α}_{i}}{\text{Max}}E\left\lbrack \left( y_{i} - c \right)q_{i} - \alpha_{i} \right\rbrack$

(12) $\underset{p_{i}\text{,y}_{i}\text{,α}_{i}}{\text{Max}}E\left\lbrack \left( y_{i} - c \right)q_{i} - \alpha_{i} \right\rbrack$

s.t.

Using the property that the expected utility in Equations 10, 11, 13 and 14 can be expressed in certainty equivalence (CE) terms, Equations 10, 13, 11 and 14 (11 and 14 are identical) become

(16) $\left( p_{i}\text{,e}_{i} \right) \in \text{argmax}\ \alpha_{i} + \left( p_{i} - y_{i} \right)q_{i} - e_{i}^{2} - \frac{1}{2}\left( p_{i} - y_{i} \right)^{2}\text{rσ}_{\delta}^{2}$,

(19) $\frac{\partial\text{EU}}{\partial e_{i}} = p_{i} - y_{i} - 2e_{i} \equiv 0$ and

(20) $\frac{\partial\text{EU}}{\partial p_{i}} = q_{i} - \left( p_{i} - y_{i} \right)\left\lbrack \lambda(1 + \psi) + \text{rσ}_{\delta}^{2} \right\rbrack \equiv 0$.

Similarly, substituting Equation 22 and solving for p_i as a function of y_i allows us to maximize Equation 21. The first order conditions become

(23) $\frac{\partial\pi_{i}}{\partial y_{i}} = \left( \frac{\partial p_{i}}{\partial y_{i}} - 1 \right)q_{i} + \left( p_{i} - y_{i} \right)\frac{\partial q_{i}}{\partial y_{i}} - 2e_{i}\frac{\partial e_{i}}{\partial y_{i}} - \left( p_{i} - y_{i} \right)\text{rσ}_{\delta}^{2}\left( \frac{\partial p_{i}}{\partial y_{i}} - 1 \right) \equiv 0\text{.}$

Note that D_DD is

(27) $\begin{matrix} D_{\text{DD}} = \text{2rσ}_{\delta}^{4}(2 + \psi) + \lambda(1 + \psi)^{2}\left\lbrack \text{2λ}(2 + \psi) - 1 \right\rbrack + \text{rσ}_{\delta}^{2}\left\lbrack \text{2λ}\left( \text{2ψ}^{2} + \text{7ψ} + 5 \right) - 2 - \psi \right\rbrack \\ \ + \theta_{s}(1 + \psi)\left( \text{rσ}_{\delta}^{2} + \lambda + \text{λψ} \right) \\ \end{matrix}$.

I set c=0 without loss of generality. Accordingly, I solve for e_i as a function of y_i. The equation for effort becomes

(29) $e_{i} = \frac{p_{i} - y_{i}}{2}$.

(32) $e_{\text{CC}}^{} = \frac{\mu^{3}}{2\lambda(2 + \psi)\left( 1 + 2\text{rσ}_{\delta}^{2} \right) + \theta_{s} - 1}$,

(33) $p_{\text{CC}}^{} = \frac{\text{2μ}\left( 1 + \text{rσ}_{\delta}^{2} \right)}{2\lambda(2 + \psi)\left( 1 + 2\text{rσ}_{\delta}^{2} \right) + \theta_{s} - 1}$,

Based on equations 24-26 and 32-34, we are able to answer the following question: How do the dual delegation/centralization equilibrium prices, efforts and the virtual marginal costs change with an increase the model parameters ψ, θ_s and λ?

Figure 4: Proposition 2

3. Does Price Delegation Actually Arise as an Equilibrium Strategy?

3.1 Empirical Essay Overview

Although there is an appropriate method to test the theory, the question still remains as to why it is important to test the price delegation theory. First of all, the game is complex with four players in unique roles (a quartet). Second, the model places very strong assumptions on the rationality of each player to generate the Nash equilibrium predictions. These assumptions restrict the firms and salespersons to be rational and their preferences to be defined specifically by the model. In other words, the players are not assumed to have other preferences that may confound the model predictions. For example, suppose that the brand manager decides to offer a higher commission rate to the sales rep with the anticipation that the sales rep will exert more effort. Will the sales rep put forth higher effort? What if the sales rep pays attention to other aspects of their role but neglects the commission rate? Will theory be supported? There are no guarantees since the question is an empirical question. Although theory is found to be supported in some experimental settings, the field of Behavioral Game Theory (Camerer 2003) begs to differ. In fact, numerous studies find that the traditional Nash equilibrium is not obtained in many empirical settings. Therefore, it is not a given that the theory will hold true in an empirical setting and for the theory to be applicable to managers it must be empirically validated.

The experiments are tailored to closely track the theory and will be used to test whether or not price delegation is an equilibrium strategy. In addition, I am also interested in the process by which the results are obtained. Therefore, there are two main hypotheses that I plan to test. The first hypothesis corresponds to how product substitutability affects the decision to delegate the pricing.

H1: As product substitutability increases, price delegation arises as the equilibrium strategy for both firms.

3.3 Experimental Design

To test the hypotheses, I design an experiment that contains three experimental cells. The first experimental cell (Condition 1) contains Low Product Substitutability and Low Cross Effort Responsiveness. The second (Condition 2) contains High Product Substitutability and Low Cross Effort Responsiveness. Finally, the third (Condition 3) involves High Product Substitutability and High Cross Effort Responsiveness. Note that the traditional 2x2 experimental design involves a fourth cell consisting of High Product Substitutability and High Cross Effort Responsiveness. Though the traditional 2x2 design is more complete, I am only interested in testing main effects for this study. In addition, the price delegation theory does not make a bold strategic prediction involving the fourth cell. As a result, I limit the analysis to three experimental cells.

The experimental design shown in Table 3 consists of the selected parameters: μ=100, r=.18 σ_δ²=5.56 and λ=1/2. For Condition 1 (ψ=2, θ_s=.1) and Condition 3 (ψ=4, θ_s=.9), the model prediction is a dual centralization equilibrium. For Condition 2 (ψ=4, θ_s=.1), the model prediction is a dual delegation equilibrium. These parameters were designed in the aforementioned manner.

Figures 6a-6g compare the variable means by round for the three conditions. There is some degree of learning which takes place during the experiments. Overall, decisions made in Rounds 1-10 tend to be higher than the decisions made in Rounds 11-20 and become more stable in the later rounds. Split-sample tests reveal the presence of learning. As a result, I run the statistical analyses for two sets of data. First, I use all 20 rounds of data and then I restrict the analysis to the final 10 rounds of data. The latter is done to analyze decisions when behavior is more stable.

Figure 6a: Delegation Frequency

Figure 6d: Fixed Wage

Figure 6g: Effort

Table 4 summarizes the mean levels of effort, price and the commission rates selected by participants where Mean-20 is for all 20 rounds of data and Mean-10 is for the last 10 rounds of data. First, we notice that effort by agents is significantly higher than the equilibrium prediction levels. Mean effort in C1, C2, C3 is significantly higher than their respective theoretical prediction (all with p=0.000). In C1 and C3, agents nearly double the level predicted by theory. Mean prices are roughly similar to the equilibrium predictions. T-tests reveal that prices in C1 are not significantly different from the theoretical prediction in Mean-20 (p=0.62), but are significantly lower than the theoretical prediction (p=0.04) in Mean-10. Prices in C2 and C3 are significantly higher in Mean-20 with p=0.000 and p=0.000, respectively. Similarly, prices in C2 and C3 are also significantly higher in Mean-10 with p=0.000 and p=0.000, respectively. For commission rates, we find a significantly lower commission rate in all conditions for both Mean-20 and Mean-10 (p=0.000).

We now proceed to formally test H1 and H2 using a probit model. The results of the test are presented in Table 5. For H1, we test whether increasing substitutability leads to an increase in the dual delegation selection. We find that the coefficient of the Condition 2 Dummy is not significant in either the 20 round or the final 10 round analysis (p=0.82 and p=0.12, respectively). Hence, I find that H1 is not supported. Although, I do not observe an increase in firms selecting a dual delegation strategy, it is still possible that firms may try delegation more than they had in Condition 1. Therefore, I examine whether there is a reduction in firms choosing the dual centralization strategy from Condition 1 to Condition 2 because any change requires at least one firm to select a delegation strategy. Based on the probit model, I find that the dual centralization equilibrium appears less readily when we compare Condition 1 to Condition 2. Hence, we conclude that delegation is more likely to be observed as substitutability increases. However, we do not find a change in the dual delegation behavior. For H2, I test whether increasing cross effort responsiveness leads to dual price centralization. From Table 5, I find a significant increase in the likelihood of observing the dual price centralization for the 20 round analysis (p=0.000) and significance at the 5% level with a one-tailed test for the 10 round analysis. Therefore, H2 is supported.

H1: H1 is not supported. As product substitutability increases, price delegation does not arise as the equilibrium strategy for both firms. Increases in substitutability do, however, lead to a higher tendency of at least one firm practicing price delegation.

For C1 and C3, I find that 81% and 83% of firms choose the dual centralization strategy, respectively, for the last 10 rounds. For all 20 rounds, I find that 79% and 80% choose dual centralization. These findings are consistent with the theoretical predictions. However, when we consider C2 the findings do not support theory. In fact, only 1% of quartets end up in the dual delegation equilibrium and 75% choose the dual centralization equilibrium for the final 10 rounds while 3% of quartets choose dual delegation and 67% choose dual centralization for all 20 rounds of the game. The question remains why firms continue to choose dual centralization when the equilibrium clearly dictates a dual delegation strategy.

To address this question, we focus on Condition 2 and show how behavior differs between delegation and centralization. As predicted by theory, prices are indeed higher under delegation than under centralization (p=0.000), but effort and the commission rate are no different (p=0.37 and p=0.58). We can ignore the fixed wage portion of compensation because the fixed wage does not produce any incentive effects. The fixed wage only affects the participation constraint. For delegation to be profitable and an equilibrium, agents should set higher prices and exert higher effort. However, a precursor to this scenario is that firms offer higher commission rates. Since firms do not offer a higher commission rate, delegation is susceptive to deviations to a centralized pricing strategy. Firms learn early on in the game that the commission rate is a rather sticky variable to alter and so effort does not change much. From the data, agents are willing to choose a higher price. Unfortunately, choosing delegation and having a higher price can hurt the focal firm because the competitor can easily swoop in with a lower price by sticking to a centralized pricing strategy and steal the market share. Had the firm offered a higher commission rate, the agent’s increased effort would act as a deterrent of deviating to a centralized pricing strategy. The firm’s ability to adjust the commission rate is a critical determinant of the price delegation equilibrium. From the experiment, commission rates are sticky and so centralized pricing arises as the equilibrium of the game.

Price delegation remains a fruitful avenue of research. I did not consider how information asymmetry affects the decision to delegate. This is a clear theoretical extension that is worth pursuing. Similarly, the fact that this paper is the first experimental test of the price delegation theory indicates that there is room for added empirical studies in this area. In particular, experimental tests of the optimality of price delegation in information asymmetric conditions would be of high interest to practitioners. Accordingly, the assessment of different compensation plans and their effect on the decision to delegate would also prove vastly important. Finally, considering various types of limited price delegation would also be an interesting and noteworthy extension. Although the price delegation literature began in 1975, the theory still contains many unanswered questions three decades later.

REFERENCES

Basu, Amiya K., Lal Rajiv, V. Srinivasan and Richard Staelin (1985), “Salesforce Compensation Plans: An Agency Theoretic Perspective,” Marketing Science, 4 (4), 267-291.

Bhardwaj, Pradeep (2001), “Delegating Pricing Decisions,” Marketing Science, 20 (2), 143-169.

——— (2007), “An Incentive-Aligned Mechanism for Conjoint Analysis,” Journal of Marketing Research, 44 (2), 214-223.

Dixit, Avinash (1979), “A Model of Duopoly Suggesting a Theory of Entry Barriers,” Bell Journal of Economics, 10 (1), 20-32.

Hansen, Ann-Kristin, Kissan Joseph and Manfred Krafft (2008), “Price Delegation in Sales Organizations: An Empirical Investigation,” Business Research, 1 (1), 94-104.

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Lal, Rajiv (1986), “Delegating Pricing Responsibility to the Salesforce,” Marketing Science, 5 (2), 159-168.

Lim, Noah and Teck H. Ho (2007), “Designing Price Contracts for Boundedly Rational Customers: Does the Number of Blocks Matter?” Marketing Science, 26 (3), 312-326.

——— and ——— (2005), “Delegating Pricing Decisions in Competitive Markets with Symmetric and Asymmetric Information,” Marketing Science, 24 (3), 490-497.

Moorthy, K. Sridhar (1988), “Strategic Decentralization in Channels,” Marketing Science, 7 (4), 335-355.

Staelin, Richard (2001), From Courtroom to Converse: My 30 Year Journey. American Marketing Association Publications.

Stephenson, P. Ronald, William L. Cron, and Gary L. Frazier (1979), “Delegating Pricing Authority to the Sales Force: The Effects on Sales and Profit Performance,” Journal of Marketing, 43 (2), 21-28.

This is an experiment in decision making. The instructions are simple, and if you follow them carefully and make good decisions, you could earn a considerable amount of money which will be paid to you. What you will earn partly depends on your decisions, partly on the decisions of others, and partly on chance. Do not look at the decisions of others. Do not talk during the experiment. You will be warned if you violate this rule. If you violate this rule twice, I will cancel the experiment immediately and your earnings will be $0.

There are 20+ participants in this experiment and there are a total of 60 decision rounds. In every decision round, you will be assigned to a group consisting of 4 participants. Your group assignment in each round has been randomly and anonymously determined. The random assignment also means that the set of 4 participants in your group changes every round. The 60 decision rounds are divided into three parts. Part 1 consists of rounds 1 to 20, Part 2 consists of rounds 21 to 40 and Part 3 consists of rounds 41 to 60.

1. Decide whether you or your Sales Representative will select the price of the product.

2. Choose the salary to pay to your Sales Representative (0 to 2000).

Profit = (1-Commission)*Price*Units – Salary.

Your earnings will be scaled and converted upon payment.

Income = Commission*Price*Units + Salary – Sales Call Costs

Note that commissions are paid on revenues. Attached to these instructions is Sheet 1.

Part 1:

Units = 100 + SalesCalls(Own) – .1*SalesCalls(Other) – 1.5*Price (Own) + 1*Price (Other) + Random Number

Units = 100 + SalesCalls(Own) – .9 *SalesCalls(Other) – 2.5*Price (Own) + 2*Price (Other) + Random Number

If the other sales rep rejects the contract, Units will be equal to

2. Sales Representatives will make their selections.

3. The computer will compute units sold, profits and income.