Abstract
In this paper we study the relationship between a firm (hotel) and a service platform (Ctrip.com). We start with a newsvendor hotel facing two kinds of customers. D-customers order the room directly from the hotel front desk; C-customers order the room through Ctrip.com. Ctrip.com charges the hotel while introducing its members to the hotel. The hotel decides how many rooms are allotted to Ctrip.com to achieve optimal profit. We consider the situation where one party’s demand cannot be observed by another, and study the commonly used wholesale price contract. Interestingly, the contract can always coordinate the system. We then investigate the influence of bargaining power on the profit division under situations where Ctrip.com and hotel, respectively, dominate the system, and find that increasing (or decreasing) a party’s bargaining power without considering the other does not necessarily benefit (or damage) the first party. Further, we discuss how the parties choose dominance and appropriate bargaining power to make a trade-off for better cooperation. An interesting phenomenon is that bargaining power for each party can be identical when any party dominates the system. We also propose a threshold at which the wholesale price contracts can always be the Pareto optimal for the channel.
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Acknowledgements
The authors thank the editor and anonymous reviewers for several insightful comments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 71371008 and 71001093), Major International (Regional) Joint Research Projects (Grant No. 71110107024), the National Natural Science Foundation of China for Innovative Research Groups (Grant No. 71121061) and Major Program (Grant No. 71090400/71090401) of Natural Science Foundation of China.
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Appendix
Appendix
Explaining and proofs
Explaining of function (1)
Assuming the quantity of allocated rooms is Q, then the remainder is K−Q. D h and D t are the demand of D-customers and C-customers respectively. Obviously, there may be four different situations: (1)K−Q⩾D h ,Q⩾D t ; (2)K−Q⩾D h ,Q<D t ; (3)K−Q<D h ,Q⩾D t ; (4)K−Q<D h ,Q<D t . Therefore, the integrated system’s profit function is
Π c (Q)=(p h −c v )D h −c u (K−Q−D h )+(p t −c v )D t −c u (Q−D t ) if (1) is established;
OrΠ c (Q)=(p h −c v )(K−Q)+(p t −c v )D t −c u (Q−D t ) if (2) is established;
OrΠ c (Q)=(p h −c v )D h −c u (K−Q−D h )+(p t −c v )Q if (3) is established;
OrΠ c (Q)=(p h −c v )(K−Q)+(p t −c v )Q if (3) is established.
So we have
Proof of Lemma 1
For
Taking derivative of Π c (Q) gives
Obviously, Π′ c (Q) is continuous and decreasing in Q.
-
a)
If Π′ c (0)⩽0, then we know Π c (Q) has a unique maximizer and 0 is the unique solution.
-
b)
If Π′ c (0)>0, since Π′ c (K)=−(p t −c v +c u )F t (K)−(p h −p t )<0. Therefore, Π c (Q) is quasi-concave and has a unique maximizer. □
Together we know Π c (Q)has a unique maximizer.
Proof of Lemma 2
For Π h (Q)=(p h −c v +c u )[∫0 K−Q xf h (x)dx+∫ K−Q +∞ (K−Q)f h (x)dx]−c u (K−Q)+WQ, and Π t (Q)=(p h −c v +c u )[∫0 Q xf t (x)dx+∫ Q +∞ Qf t (x)dx]−c u Q−wQ.
The first-order condition Π′ h (Q)=0 yields
Similarly, the first-order condition Π′ t (Q)=0 yields
Obviously, Π h (Q) and Π t (Q) have a unique maximizer. □
Proof of Proposition 1
-
i)
The derivative of Q h with respect to w gives (dQ h )/(dw)=(1)/(p h −c v +c u )(1)/(f h (K−Q))>0, so Q h is increasing in w.
-
ii)
The derivative of Q t with respect to w gives(dQ t )/(dw)=−(1)/(p t −c v +c u )(1)/(f t (Q))<0, Q t is decreasing in w.
-
iii)
Let w*=(p t −c v )−(p t −c v +c u )F t (Q c ). From the first-order condition (A1), we know (p t −c v )−(p t −c v +c u )F t (Q c )=(p h −c v )−(p h −c v +c u )F h (K−Q c ), then we have w*=(p h −c v )−(p h −c v +c u )F h (K−Q c ). If w<w*, from (A2) we know Q h <Q c , and from (A3), we know Q t >Q c , thus, Q t >Q c >Q h . Similarly, if w>w*, we have Q t <Q c <Q h . Besides, Q t =Q c =Q h when w=w*. □
Proof of Proposition 2
-
i)
The derivative of Π t (w) with respect to w gives
Thus, Π t (w) is decreasing in w.
-
ii)
The derivative of Π h (w) with respect to w gives
If w⩽w*, Q t ⩾Q c and (p h −c v +c u )F h (K−Q)−(p h −c v −w)⩽0, from (i) we know (dQ t )/(dw)<0, then we have
If w=p
t
−c
v
, notice from (ii) in Proposition 1, we know Q
t
=0, then, we have 
. Since F
h
(K)=(p
h
−c
v
−w
2)/(p
h
−c
v
+c
u
), then we have 
. We can see that (dΠ
t
(w))/(dw) is continuous, so there exists w
3∈(w*, p
t
−c
v
) such that 
. Together we know the result is correct. -
iii)
From the proof of Lemma 1, we know Π c is increasing in Q for Q⩽Q c and decreasing in Q for Q>Q c . Recall from (ii) in Proposition 1 that Q is decreasing in w and Q=Q c for w=w*. This implies that Π c (w) is increasing in w for w⩽w* and decreasing in w for w>w*. □
If w=p
t
−c
v
, notice from (ii) in Proposition 1, we know Q
t
=0, then, we have 
. Since F
h
(K)=(p
h
−c
v
−w
2)/(p
h
−c
v
+c
u
), then we have 
. We can see that (dΠ
t
(w))/(dw) is continuous, so there exists w
3∈(w*, p
t
−c
v
) such that 
. Together we know the result is correct.Proof of Proposition 3
The derivative of Π h (w) and Π t (w) with respect to w are given, respectively, by
The proofs are similar to that of Proposition 2 and omitted. □
Proof of Lemma 5
From (i) of Proposition 3, we know that Π h b(w*)>Π h b(w 2)=Π h o, then we have Π h a(w*)>Π h b(w*)>Π h o. For Π h a(0)=0<Π h o, besides, recall from (ii) of Proposition 2 that Π h a(w) is increasing in w for w⩽w*, then, we know that there exists a threshold w l <w* such that Π h a(w)⩽Π h o for every w⩽w l . □
Proof of Lemma 6
The proof is similar to that of Lemma 5 and is omitted. □
Proof of Lemma 7
The reasonable scope of bargaining power is [w l ,p t −c v ]. Recall from (i) and (ii) of Proposition 2 that both Π t a(w) and Π h a(w) are decreasing in w for w 3<w⩽p t −c v . This implies the set (w 3, p t −c v ] is not the set of Pareto optimal wholesale price contracts. However, there exists no alternative such that some firm is strictly better off and no firm is worse off for every w∈[w l , w 3]. □
Proof of Lemma 8
The proof is similar to that of Lemma 7 and is omitted. □
Proof of Lemma 9
From (ii) of Proposition 2, we know that w 3>w*, from (ii) of Proposition 3, we know that w 4<w*. So we have w 4<w*<w 3. □
Proof of Proposition 6
For w 3>w*, from Proposition 1, we know Q t (w 3)≠Q h (w 3), then Π h a(w 3)<Π h b(w 3). From (ii) of Proposition 2, we know that Π h a(w 3)>Π h a(w*)=Π h b(w*). Further, recall from (i) of Proposition 3 that Π h b(w) is increasing in w, then, we know that there exists a threshold w o∈(w*, w 3) such that Π h b(w o)=Π h a(w 3). □
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Zhang, J., Zha, Y., Yue, X. et al. Dominance, bargaining power and service platform performance. J Oper Res Soc 67, 312–324 (2016). https://doi.org/10.1057/jors.2015.44
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DOI: https://doi.org/10.1057/jors.2015.44