Why would a big retailer refuse to collaborate on manufacturer SPIFF programs?

Abstract

Big retailers that carry a large assortment of products rely on knowledgeable salespeople to provide purchase advice to customers and match customers with suitable products. Interestingly, big retailers vary in their policies regarding whether to allow their salespeople to receive manufacturer SPIFF (Sales Person Incentive Funding Formula) payments, which motivate salespeople advising at no cost of the retailer. In this study, we investigate a big retailer’s incentive to block manufacturer SPIFF programs, which has the consequence of demotivating salespeople from advising customers, from the perspective of vertical channel interactions. We scrutinize a big retailer’s decision to maximize its profit through managing its channel interactions with upstream manufacturers offering horizontally differentiated products, customers uncertain about true fits with competing products, and its salesperson who can match customers with suitable products through offering purchase advice. Our analysis shows that motivating the salesperson to advise customers is profitable for the retailer only if the such advising has moderate effectiveness in matching consumers and suitable products, and only in this case would the retailer collaborate on manufacturer SPIFF programs. Otherwise, salesperson advising hurts retailer profit and the big retailer benefits from blocking manufacturer SPIFF programs. Our study reveals the interesting theoretical insight that the incentives of a big retailer and upstream manufacturers to motivate sales advising reside in their incentives to battle for a more favorable channel status.

Appendix

Proof of Lemma 1

The retailer has three options of pricing strategies: p₁ < p₂, p₁ = p₂, and p₁ > p₂. When p₁ < p₂, the retailer’s profit function is $\pi _{R}^{N}(p_{1}<p_{2})=\alpha (p_{1}-w_{1})-(1-\alpha )r$. The retailer’s optimal prices can be solved as {p₁ = V, p₂ > V}, which leads to the maximized profit of $\pi _{R}^{N\ast }(p_{1}<p_{2})=\alpha (V-w_{1})-(1-\alpha )r$. Similarly, we can solve the case when p₁ > p₂ . Lastly, when p₁ = p₂ = p, the retailer’s profit function is $\pi _{R}^{N}(p_{1}=p_{2})=\frac {1}{2}\alpha (2p-w_{1}-w_{2})-(1-\alpha )r$. The retailer optimally charges p₁ = p₂ = V, which leads to the maximized profit of $\pi _{R}^{N}(p_{1}=p_{2})=\frac {1}{2}\alpha (2V-w_{1}-w_{2})-(1-\alpha )r$. Comparing $\pi _{R}^{N\ast }(p_{1}<p_{2})$, $\pi _{R}^{N\ast }(p_{1}=p_{2})$, and $\pi _{R}^{N\ast }(p_{1}>p_{2})$, we obtain Lemma 1. □

Proof of Lemma 3

The retailer has three options of pricing strategies: p₁ < p₂, p₁ = p₂, and p₁ > p₂. We discuss the three strategies respectively.

First, if the retailer charges p₁ < p₂, its profit function is

$$ {\pi_{R}^{A}}(p_{1}<p_{2})=\!\left\{ \begin{array}{ccc} \alpha (p_{1}-w_{1})+s\alpha (1-\alpha )(p_{2}-w_{2}) & if & p_{2}\geq \frac{ e}{s\alpha (1-\alpha )m_{M2}}\&p_{1}<p_{2}\leq V \\ \alpha (p_{1}-w_{1})-(1-\alpha )r & if & \begin{array}{c} p_{2}<\frac{e}{s\alpha (1-\alpha )m_{M2}}\&p_{1}<p_{2}\leq V \\ \text{ or }p_{1}\leq V<p_{2}. \end{array} \end{array} \right. $$

(17)

The retailer optimally charges the highest possible prices for the two products, that is,

$$ \left\{ \begin{array}{ccc} p_{1}=V-\varepsilon ,p_{2}=V & if & m_{M2}\geq \frac{e}{s\alpha (1-\alpha )V} \&w_{1},w_{2}\leq V \\ p_{1}=V,p_{2}>V & if & m_{M2}<\frac{e}{s\alpha (1-\alpha )V}\&w_{1}\leq V- \frac{1-\alpha }{\alpha }r. \end{array} \right. $$

(18)

This strategy leads to the retailer’s maximized profit of

$$ {\pi_{R}^{A}}(p_{1}<p_{2})=\left\{\! \begin{array}{ccc} \alpha (V-w_{1})+s\alpha (1-\alpha )(V-w_{2}) & if & m_{M2}\geq \frac{e}{ s\alpha (1-\alpha )V}\&w_{1},w_{2}\leq V \\ \alpha (V-w_{1})-(1-\alpha )r & if & m_{M2}<\frac{e}{s\alpha (1-\alpha )V} \&w_{1}\leq V-\frac{1-\alpha }{\alpha }r. \end{array} \right. $$

(19)

Similarly, if the retailer charges p₁ > p₂, its maximized profit can be derived as

$$ {\pi_{R}^{A}}(p_{1}>p_{2})=\left\{\! \begin{array}{ccc} s\alpha (1-\alpha )(V-w_{1})+\alpha (V-w_{2}) & if & m_{M1}\geq \frac{e}{ s\alpha (1-\alpha )V}\&w_{1},w_{2}\leq V \\ \alpha (V-w_{2})-(1-\alpha )r & if & m_{M1}<\frac{e}{s\alpha (1-\alpha )V} \&w_{2}\leq V-\frac{1-\alpha }{\alpha }r. \end{array} \right. $$

(20)

Lastly, when the retailer charges the same price for the two products, p₁ = p₂ = p, its profit function is

$$ {\pi_{R}^{A}}(p_{1}=p_{2}=p)=\left\{\! \begin{array}{ccc} \alpha (p-w_{i})+s\alpha (1-\alpha )(p-w_{j}) & if & \frac{e}{s\alpha (1-\alpha )\frac{m_{M1}+m_{M2}}{2}}\leq p\leq V \\ \frac{1}{2}\alpha (2p-w_{1}-w_{2})-(1-\alpha )r & if & p<\frac{e}{s\alpha (1-\alpha )\frac{m_{M1}+m_{M2}}{2}}\&p\leq V. \end{array} \right. $$

(21)

The retailer’s optimal pricing strategy can be derived as p₁ = p₂ = V, if $\left \{\frac {m_{M1}+m_{M2}}{2}\right .$ $\left .\geq \frac {e}{s\alpha (1-\alpha )V} \&w_{1},w_{2}\leq V\right \}$ or if $\ \left \{\frac {m_{M1}+m_{M2}}{2}<\frac {e}{s\alpha (1-\alpha )V}\&w_{1},w_{2}<V-\frac {1-\alpha }{\alpha }r\right \}$, which renders the retailer profit of

$$ {\pi_{R}^{A}}(p_{1}=p_{2}) = \left\{\! \begin{array}{ccc} \frac{1}{2}(\alpha +s\alpha (1 - \alpha ))(2V - w_{1} - w_{2}) & if &\! \frac{ m_{M1}+m_{M2}}{2}\geq \frac{e}{s\alpha (1-\alpha )V}\&w_{1},w_{2}\leq V \\ \frac{1}{2}\alpha (2V - w_{1}-w_{2}) - (1 - \alpha )r & if &\! \frac{m_{M1}+m_{M2}}{2 }\!<\!\frac{e}{s\alpha (1-\alpha )V}\&w_{1},w_{2}\!<\!V - \frac{1-\alpha }{\alpha }r. \end{array} \right. $$

(22)

Given the wholesale prices for the two products, w₁ and w₂, the retailer decides which pricing strategy to take (p₁ < p₂, p₁ = p₂ , or p₁ > p₂). We consider the following conditions.

• (i) m_M1 = m_M2 = m_M. In this case, the retailer’s optimal pricing strategy is similar as in subgame N. In particular, if w_i < w_j (i, j = 1,2,i ≠ j), the retailer optimally charges p_i < p_j:

  $$ \left\{ \begin{array}{ccc} p_{i}^{A\ast }=V-\varepsilon ,\text{ }p_{j}^{A\ast }=V & if & m_{M}\geq \frac{e}{s\alpha (1-\alpha )V}\&w_{i}<w_{j}\leq V \\ p_{i}^{A\ast }=V,\text{ }p_{j}^{A\ast }>V & if & m_{M}\!<\!\frac{e}{s\alpha (1-\alpha )V}\&w_{i}\leq V-\frac{1-\alpha }{\alpha }r\&w_{i}<w_{j}. \end{array} \right. $$

  (23)

  And if w_i = w_j, the retailer optimally charges $p_{i}^{A\ast }=p_{j}^{A\ast }=V$, if $\{m_{M}\geq \frac {e}{s\alpha (1-\alpha )V}$ & w_i = w_j ≤ V } or if $\ \left \{m_{M}<\frac {e}{s\alpha (1-\alpha )V}~\&~ w_{i}=w_{j}\leq V-\frac {1-\alpha }{\alpha }\right \}$.

• (ii) m_M1 < m_M2. In this case, we consider the following conditions.

  • (ii.a) $m_{M1}\geq \frac {e}{s\alpha (1-\alpha )V}$: The retailer optimally charges $\{p_{i}^{A\ast }=V-\varepsilon ,$ $p_{j}^{A\ast }=V\}$ if w_i < w_j ≤ V, and charges $p_{i}^{A\ast }=$ $p_{j}^{A\ast }=V$ if w_i = w_j ≤ V.

  • (ii.b) $m_{M2}<\frac {e}{s\alpha (1-\alpha )V}$: The retailer optimally charges $\{p_{i}^{A\ast }=V,$ $p_{j}^{A\ast }>V\}$ if $w_{i}\leq V-\frac { 1-\alpha }{\alpha }r\&w_{i}<w_{j}$, and charges $p_{i}^{A\ast }=$ $p_{j}^{A\ast }=V$ if $w_{i}=w_{j}\leq V-\frac {1-\alpha }{\alpha }$.

  • (ii.c) $m_{M1}<\frac {e}{s\alpha (1-\alpha )V}\leq m_{M2}$: The retailer has two strategic options. The retailer can charge $\{p_{1}^{A\ast }=V-\varepsilon ,$ $p_{2}^{A\ast }=V\}$ and obtain a profit of α(V − w₁) + sα(1 − α)(V − w₂); alternately, the retailer can charge $\{p_{1}^{A\ast }>V,$ $p_{2}^{A\ast }=V\}$ and obtain a profit of α(V − w₂) − (1 − α)r. It can be proved that the former strategy is more profitable given w₁,w₂ ≤ V.

• (iii) m_M1 > m_M2. This case is symmetric to case (ii) and the retailer’s optimal pricing strategies can be derived following a similar approach.

  Summarizing the above discussion, we obtain Lemma 3.

□

Proof of Eq. 8

• (i) We first consider the case when the two manufacturers offer the same SPIFF rate m_M1 = m_M2 = m_M. We consider the following conditions.

  • (i.a) $m_{M}\geq \frac {e}{s\alpha (1-\alpha )V}$: Manufacturer i(i = 1,2)’s profit function is

    $$ \pi_{Mi}^{A}=\left\{ \begin{array}{ccc} \alpha (w_{i}-m_{M}V) & if & w_{i}<w_{j}\leq V \\ \frac{1}{2}(\alpha +s\alpha (1-\alpha ))(w_{i}-m_{M}V) & if & w_{i}=w_{j}\leq V \\ s\alpha (1-\alpha )(w_{i}-m_{M}V) & if & w_{j}<w_{i}\leq V. \end{array} \right. $$

    (24)

    Each manufacturer can guarantee a demand of sα(1 − α) by charging the highest possible wholesale price of V. The manufacturer’s equilibrium profit is thus $\pi _{Mi}^{A\ast }=s\alpha (1-\alpha )(1-m_{M})V$. By undercutting its rival’s wholesale price, a manufacturer can obtain a demand of α. Therefore, the lowest wholesale price $\underline {w}$ a manufacturer is willing to charge satisfies $(\underline {w}-m_{M}V)\alpha =$ sα(1 − α)(1 − m_M)V, that is, $\underline {w}=s(1-\alpha )(1-m_{M})V+m_{M}V$. In equilibrium, each manufacturer i(i = 1,2) randomizes its wholesale price over $w_{i}^{A\ast }\in \lbrack s(1-\alpha )V+m_{M}V,V+m_{M}V]$. The distribution function of ${w_{i}^{A}}$ can be derived from

    $$\begin{array}{@{}rcl@{}} &&s\alpha (1-\alpha )(w_{i}-m_{M}V)+(1-F(w_{i}))(\alpha \!-s\alpha (1-\alpha ))(w_{i}-m_{M}V)\\&=&s(1-\alpha )(1-m_{M})V. \end{array} $$

  • (i.b) $m_{M}<\frac {e}{s\alpha (1-\alpha )V}$: Manufacturer i’s profit function is

    $$ \pi_{Mi}^{A}=\left\{ \begin{array}{ccc} \alpha (w_{i}-m_{M}V) & if & w_{i}<w_{j}\leq V-\frac{1-\alpha }{\alpha }r \\ \frac{1}{2}\alpha (w_{i}-m_{M}V) & if & w_{i}=w_{j}\leq V-\frac{1-\alpha }{ \alpha }r \\ 0 & if & w_{i}>w_{j}. \end{array} \right. $$

    (25)

    In this case, each manufacturer keeps undercutting its rival’s wholesale price until it is no more profitable to do so. Therefore, the optimal wholesale price is $w_{i}^{A\ast }=m_{M}V$, which renders the manufacturer profit of $\pi _{Mi}^{A\ast }= 0$.

• (ii) We then consider the case when the two manufacturers offer different SPIFF rates m_M1 < m_M2. We consider the following conditions.

  • (ii.a) $m_{M1}>\frac {e}{s\alpha (1-\alpha )V}$: Manufacturer i(i = 1,2)’s profit function is

    $$ \pi_{Mi}^{A}=\left\{ \begin{array}{ccc} \alpha (w_{i}-m_{Mi}V) & if & w_{i}<w_{j}\leq V \\ \frac{1}{2}(\alpha +s\alpha (1-\alpha ))(w_{i}-m_{Mi}V) & if & w_{i}=w_{j}\leq V \\ s\alpha (1-\alpha )(w_{i}-m_{Mi}V) & if & w_{j}<w_{i}\leq V. \end{array} \right. $$

    (26)

    Each manufacturer can guarantee a demand of sα(1 − α) by charging the highest possible wholesale price of V. Manufacturer i’s equilibrium profit is thus $\pi _{Mi}^{A\ast }=s\alpha (1-\alpha )(1-m_{Mi})V$ . By undercutting its rival’s wholesale price, a manufacturer can obtain a demand of α. Therefore, the lowest wholesale price $\underline {w}_{i}$ a manufacturer is willing to charge satisfies $(\underline {w}-m_{Mi}V)\alpha =$ sα(1 − α)(1 − m_Mi)V, that is, $\underline {w}_{i}=s(1-\alpha )(1-m_{Mi})V+m_{Mi}V$. Clearly, $\underline {w}_{1}<\underline {w}_{2}$. Therefore, manufacturer 1 can charge a wholesale price slightly lower than $\underline {w}_{2}$ and get the demand of α . The two manufacturers’ equilibrium profits are thus

    $$\begin{array}{@{}rcl@{}} \pi_{M1}^{A\ast } \!&=&\!\alpha (\underline{w}_{2} - m_{M1}V) = \alpha (s(1 - \alpha )(1 - m_{M2})V + (m_{M2} - m_{M1})V)\text{, and}\\ \end{array} $$

    (27)
    $$\begin{array}{@{}rcl@{}} \pi_{M2}^{A\ast } &=&s\alpha (1-\alpha )(\underline{w}_{2}-m_{M2}V)=\alpha (s(1-\alpha )(1-m_{M2})V. \end{array} $$

    (28)

    That is, the manufacturer 2 that offers a higher SPIFF rate ends up with a lower profit.

    In equilibrium, both manufacturers randomize their wholesale prices over [$\underline {w}_{2},V$]. The distribution function of manufacturer 1’s wholesale prices F₁ can be derived from

    $$\begin{array}{@{}rcl@{}} &&{}s\alpha{\kern-.5pt}(1\! -\!\alpha {\kern-.5pt}){\kern-.5pt}({\kern-.5pt}w_{2}\! -\! m_{M2}V{\kern-.5pt})\! +\! ({\kern-.5pt}1\! -\! F_{1}{\kern-.5pt}({\kern-.5pt}w_{2}{\kern-.5pt}){\kern-.5pt}){\kern-.5pt}({\kern-.5pt}\alpha - s\alpha {\kern-.5pt}({\kern-.5pt}1 - \alpha {\kern-.5pt}){\kern-.5pt}){\kern-.5pt}({\kern-.5pt}w_{2}\! -\! m_{M2}V{\kern-.5pt})\\ &=&s\alpha (1-\alpha )(\underline{w}_{2}-m_{M2}V). \end{array} $$

    The distribution function of manufacturer 2’s wholesale price F₂ can be derived from

    $$\begin{array}{@{}rcl@{}} &&s{\kern-.5pt}\alpha{\kern-.6pt}({\kern-.6pt}1\! -\! \alpha {\kern-.6pt}){\kern-.6pt}({\kern-.6pt}w_{1}\! -\! m_{M1}{\kern-.6pt}V{\kern-.6pt})\! +\! ({\kern-.6pt}1 \! -\! F_{2}{\kern-.6pt}({\kern-.6pt}w_{1}{\kern-.6pt}){\kern-.6pt}){\kern-.6pt}({\kern-.6pt}\alpha \! -\! s{\kern-.5pt}\alpha {\kern-.6pt}(1\! -\! \alpha{\kern-.6pt}){\kern-.6pt}){\kern-.6pt}({\kern-.6pt}w_{1}\! -\! m_{M1}{\kern-.6pt}V{\kern-.6pt})\\ &&=\alpha (\underline{w}_{2}-m_{M1}V). \end{array} $$

  • (ii.b) $m_{M1}<\frac {e}{s\alpha (1-\alpha )V}<m_{M2}$: Manufacturer i(i = 1,2)’s profit function is

    $$ \left\{\!\! \begin{array}{ccc} \pi_{M1}^{A}\! =\! \alpha ({\kern-.5pt}w_{1} - m_{M1}V{\kern-.5pt}){\kern-.5pt},{\kern-.5pt}\pi_{M2}^{A}=s\alpha {\kern-.5pt}({\kern-.5pt}1 - \alpha {\kern-.5pt}){\kern-.5pt}({\kern-.5pt}w_{2} - m_{M2}{\kern-.5pt}V{\kern-.5pt}) & if & w_{1},w_{2}\leq V \\ \pi_{M1}^{A}\! =\! \alpha ({\kern-.5pt}w_{1}\! -\! m_{M}V{\kern-.5pt}),\pi_{M2}^{A}\! =\! 0 & if & w_{1}\!{\kern-.5pt} <{\kern-.5pt}\! V\! -\! \frac{ (1-\alpha )r}{\alpha }\&w_{2}{\kern-.5pt}\! >\!{\kern-.5pt} V \\ \pi_{M2}^{A}\! =\! 0,\pi_{M1}^{A}\! =\! \alpha (w_{1}\! -\! m_{M}V) & if & w_{1}\! >\! V\&w_{2}\! <\! V\! -\! \frac{(1-\alpha )r}{\alpha } \\ \pi_{M1}^{A}\! =\! \pi_{M2}^{A}\! =\! 0 & if & w_{1},w_{2}>V. \end{array} \right. $$

    (29)

    No manufacturer has incentive to undercut its rival’s wholesale prices and in equilibrium, $w_{1}^{A\ast }=w_{2}^{A\ast }=V$. The manufacturers’ equilibrium profits are thus $\pi _{M1}^{A\ast }=\alpha (1-m_{M1})V$ and $\pi _{M2}^{A\ast }=s\alpha (1-\alpha )(1-m_{M2})V$ respectively. Again, manufacturer 2 that offers a higher SPIFF rate ends up with a lower profit.

  • (ii.c) $m_{M1}<\frac {e}{s\alpha (1-\alpha )V}$: Manufacturer i’s profit function is

    $$ \pi_{Mi}^{A}=\left\{ \begin{array}{ccc} \alpha (w_{i}-m_{Mi}V) & if & w_{i}<w_{j}\leq V-\frac{(1-\alpha )r}{\alpha } \\ \frac{1}{2}\alpha (w_{i}-m_{Mi}V) & if & w_{i}=w_{j}\leq V-\frac{(1-\alpha )r }{\alpha } \\ 0 & if & w_{i}>w_{j}\text{ }. \end{array} \right. $$

    (30)

    Each manufacturer has incentive to undercut its rival’s wholesale price until it is not profitable to do so. The lowest wholesale price $\underline {w }_{i}$ a manufacturer is willing to charge satisfies $\underline {w}_{i}=m_{Mi}$. Clearly, $\underline {w}_{1}<\underline {w}_{2}$. Therefore, manufacturer 1 can charge a wholesale price slightly lower than $\underline {w }_{2}$ and get the demand of α. The two manufacturers’ equilibrium profits are thus $\pi _{M1}^{A\ast }=\alpha (m_{M2}-m_{M1})V$ and $\pi _{M2}^{A\ast }= 0$. Therefore, manufacturer 2 that offers a higher SPIFF rate ends up with a lower profit.

    Summarizing the above discussion, we obtain Eq. 8.

□

Proof of Proposition 1

From Eq. 8, we obtain that the manufacturers have incentive to undercut each other’s SPIFF rate. This undercutting stops when $m_{M1}^{A\ast }=m_{M2}^{A\ast }=\frac {e}{s\alpha (1-\alpha )V}$. The manufacturer’s equilibrium profit is thus $\pi _{M1}^{A\ast }=$ $\pi _{M2}^{A\ast }=s\alpha (1-\alpha )(1-\frac {e}{s\alpha (1-\alpha )V})V$. □

Proof of Proposition 2

The retailer’s maximized profit in subgame N when it does not allow SPIFF is given by $\pi _{R}^{N\ast }=\alpha V-(1-\alpha )r$, and the retailer’s maximized profit in subgame A when it allows SPIFF is given by $\pi _{R}^{A\ast }=(\alpha -s\alpha (1-\alpha ))(1-\frac {e}{s\alpha (1-\alpha )V} )V$. Comparing $\pi _{R}^{N\ast }$ and $\pi _{R}^{A\ast }$, it is easy to obtain that $\pi _{R}^{N\ast }>\pi _{R}^{A\ast }$ if $s<\underline {s}$ or $s> \overline {s}$. □