Payoff uncertainty, bargaining power, and the strategic sequencing of bilateral negotiations

TL;DR: In this article, the authors investigate the sequencing choice of a buyer who negotiates with the sellers of two complementary objects with uncertain payoffs and identify the first and second-mover advantages for the sellers.

Abstract: This article investigates the sequencing choice of a buyer who negotiates with the sellers of two complementary objects with uncertain payoffs. The possibility of inefficient trade may generate strict sequencing preference. The buyer begins with the weaker seller if the sellers have diverse bargaining powers and with the stronger one if both sellers are strong bargainers. This sequencing is likely to increase the social surplus. Moreover, the buyer may find it optimal to raise her own acquisition cost by committing to a minimum purchase price or outsourcing. The first- and second-mover advantages for the sellers are also identified.

Summary

1 Introduction

• When both sellers are strong bargainers, the buyer’s concern for aggressive pricing shifts to the last seller.
• The authors paper belongs to a growing literature on one-to-many bargaining, and complements several papers that address the issue of optimal bargaining sequence without payoff uncertainty.
• In Section 5, the authors show that the buyer’s expected payoff may decrease with her own bargaining power and examine the two procurement policies alluded to above.

2 The Model

• An employer often has to interview a job candidate to determine the match value; a home-owner frequently needs to consult with a contractor for a customized project; and a real-estate developer may require access to the construction history of a land parcel from the landowner.
• It is also conceivable that αi may simply reflect the intrinsic bargaining ability of the seller vis-à-vis the buyer.
• Having obtained the two prices pi and pj , and ascertained her valuations v i and vj , the buyer decides which goods to purchase (if any).
• Thus, the authors call any equilibrium inefficient if it involves less than joint purchase with a positive probability.

2.1 Discussion of the Assumptions

• The authors keep each buyer-seller bargaining simple to better focus on sequencing; nevertheless, their one-shot bargaining can be a good approximation of applications in which the buyer has a short time to acquire the goods, or else the trade opportunity is lost.
• But, such a “monotonic” incentive would then lead to the 12For instance, for many customized goods and services such as home re-modeling and landscaping, contractors give a free price estimate to which the customer needs to respond in a short-time period.
• 6 full disclosure of pi, much like in the literature on signaling a verifiable quality, e.g., Grossman (1981).
• Perhaps, what is more important is that sellers know the sequence.
• The authors envision environments where any meeting between the buyer and sellers is highly visible or publicized, or it can be easily inferred by the sellers from the calendar time.

3 Equilibrium Characterization

• The authors characterize the equilibrium prices for a fixed negotiation sequence.
• Recall, however, that the authors break ties in favor of social efficiency.
• This requires a price coordination with seller j.
• Note also that as the likelihood of having a low-value product j, qj, increases, seller j’s price decreases; but seller i’s price is increasing in qj only when αj is large due to the coordination incentive.

4 Strategic Sequencing

• A key observation from Proposition 2 is that for a fixed sequence of negotiations, the sellers’ bargaining powers and the buyer’s payoff uncertainty each influence equilibrium prices.
• Since, under an efficient trade, the extra surplus due to complementarity is captured by the sellers unless the buyer proposes in both negotiations, the buyer is indifferent to the sequence.
• The authors next finding uncovers how the buyer’s sequencing choice depends on the sellers’ bargaining powers.
• The buyer strictly prefers to start negotiations with seller 1 because, being followed by a strong rival, seller 1 has an equilibrium incentive to coordinate prices by lowering his own.
• 19 According to part (b), even though the buyer is not maximizing the social surplus per se, her sequencing choice increases it.

5 Benefits of Being a Weak Buyer

• Up to now, two robust insights have emerged from their analysis.
• First, the buyer cares about the negotiation sequence when equilibrium trade is inefficient and at least one seller is a powerful bargainer.
• The answer to this question can indeed be affirmative.
• Proposition 6 implies that it may sometimes be in the buyer’s best interest to limit her own bargaining power vis-à-vis the sellers.
• Consistent with their model, these authors define buyer power as “the bargaining strength that a buyer has with respect to the suppliers with whom it trades.”.

5.1 Minimum Purchase Price

• One reason why the sellers may price aggressively in their model is that in equilibrium, the buyer always makes the lowest price offer, namely the marginal-cost, 0.
• In particular, it may entice the leading seller to disregard price coordination with the follower and target the buyer’s entire surplus of 1 instead.
• It is evident that any positive payment by the buyer will allow the sellers to earn positive profits regardless of who makes the offer while reducing the buyer’s own payoff.
• Note that an upfront commitment to w > 0 is crucial here, because, once the leading seller lowers his price offer, the buyer has a strict incentive to lower her offer to 0 in the second negotiation whenever she proposes.
• In the same vein, large employers might favor minimum wage regulations when hiring new employees.

5.2 The Make-or-Buy Decision

• A critical decision for many industrial buyers is whether to make inputs internally or outsource them from independent suppliers.
• If two complementary inputs are required, as in the present setting, the following result shows that the buyer may optimally outsource an input even if it could be costlessly provided inhouse.
• Second, the authors know from Proposition 1 that two powerful suppliers would have the greatest incentives to coordinate and lower their prices.
• In contrast, in their model, a single firm outsources production to raise its own cost for an input to receive a favorable deal from the other supplier of a complementary input.

6 First- vs. Second-Mover Advantages for Sellers

• So far the authors have focused on the buyer’s preference over the negotiation sequence since she is the central agent who initiates the negotiations.
• It is, however, conceivable that the sellers will also have a preference.
• In particular, if, all else equal, the sellers expect a higher profit from being the first to negotiate with the buyer than being the second, then they may actively solicit the buyer’s business by offering a discount for the right to be the first.
• Otherwise, there will be a second-mover advantage since the follower can then have a significant chance to claim the buyer’s entire surplus if the buyer ends up proposing in the first negotiation.
• It is worth comparing their observations from Proposition 9 with those from the standard duopoly theory in which the sellers are price-setters, i.e, α → 1.

7 Concluding Remarks

• Unlike the standard consumer theory, the buyer is not a simple price-taker in many real examples; rather she is a powerful agent who actively negotiates the price with the sellers.
• The authors first set of results have revealed that to the extent that equilibrium trade is efficient, the buyer will be neutral to the sequence.
• The authors believe that this efficiency reasoning is also the driving force behind the similar “indifference” findings in the literature.
• In such cases, it would be interesting to determine the buyer’s incentive to invest in this information prior to negotiations given that her sequencing choice can signal her valuations to the sellers.

Figures

Figure 2: Sellers’ equilibrium prices (p∗i (si), p ∗ j (sj |si))

Figure 1: Timing and Information Structure

Full text

Electronic copy available at: http://ssrn.com/abstract=1904401
Payoff Uncertainty, Bargaining Power, and the
Strategic Sequencing of Bilateral Negotiations
July 20, 2011
ERID Working Paper Number 108
This paper can be downloaded without charge from
The Social Science Research Network Electronic Paper Collection:
http://ssrn.com/abstract=1904401
Silvana
Krasteva
Christopher
Timmins
Texas A&M University
Duke University

Electronic copy available at: http://ssrn.com/abstract=1904401
Payoff Uncertainty, Bargaining Power, and t he Strategic
Sequencing of Bilateral Negotiations
∗
Silvana Krasteva
Department of Economics
Texas A&M University
Allen 3054
College Station, TX 77843
E-mail: ssk8@tamu.edu
Huseyin Yildirim
Department of Economics
Duke University
Box 90097
Durham, NC 27708
E-mail: yildirh@econ.duke.edu
July 20, 2011
Abstract
This paper investigates the sequencing choice of a buyer who negotiates with the sellers
of two complementary objects with uncertain payoffs. We show that the seq uencing matters
to the buyer only when equilibrium trade can be inefficient. In this case, the buyer begins
with the less powerful seller if the sellers have sufficiently diverse bargaining powers. If,
however, both sellers are strong bargainers, then the buyer begins with the stronger of the
two. For either choice, the buyer’s sequencing (weakly) increases the social surplus. Our
analysis further reveals that it is sometimes optimal for the buyer to raise her own cost
of ac quisition to better manage the supplier competition. As such, we find that the buyer
may commit to paying the sellers a minimum pric e strictly above the marginal cost; and
that the buyer may outsource an input even though it can be made in-house. Finally, we
identify the first- and second-mover advantages in negotiations for the sellers.
JEL Classifications: C70, L23.
Keywords: negotiation, s e quencing, bargaining power, coordination.
∗
We thank Jim Anton,
¨
Ozlem Bedre-Defolie, Hanming Fang, Tracy Lewis, Leslie Marx, Debashis Pal, Curtis
Taylor and participants at various seminars for their helpful comments and suggestions. All errors are ours.
1

Electronic copy available at: http://ssrn.com/abstract=1904401
1 Introduction
In a variety of bargaining settings, a buyer sequentially negotiates with the sellers of com-
plementary objects. Examples include a shopping mall developer negotiating with several
landowners to assemble parcels of land; academic departments trying to recruit multiple faculty
members with complementary skills; a vaccine manufacturer bargaining with patent holders
of various antigens; and a home-owner dealing with multiple contractors for complementary
parts of a large project.
1
With sequential negotiations, a key s tr ategic choice for the buyer is th e sequence itself
because the sellers are likely to pr ice objects differently depending on the order. In this paper,
we investigate this sequ en cing choice by the buyer and its social efficiency consequences. While
doing so, we also discover that the buyer may sometimes be better off weakening her bargaining
power against the sellers. In particular, we identify an incentive for th e buyer to raise her own
cost of acquiring goods to better manage the supplier competition.
Our model consists of two sellers who own complementary objects and a buyer with unit
demands. While the buyer’s joint valuation is commonly known, her stand-alone valuations
are each independently drawn from a binary distribution.
2
In each bu yer-seller n egotiation,
one p layer makes a price offer with a pre-specified probability that reflects his/her relative
bargaining power. After receiving both price offers and ascertaining all her valuations in the
process, the buyer decides ex post which objects to purchase.
3
For a fixed sequence, there is a unique (perf ect Bayesian) equilibrium in our negotiation
game. In the special case of no payoff uncertainty, we show that the buyer is completely
1
Although, for concreteness, our examples will mostly relate to procurements, similar sequencing issues
also arise in other contexts such as international negotiations where one central country aims to sign bilateral
trade agreements with others, or build a coalition for an international mission (Sebenius 1996), and political
vote-buying where an interest group tries to secure endorsements of several legislators (Groseclose and Snyder
1996).
2
In particular, we assume that the buyer’s stand-alone payoffs are (at least initially) more uncertain than her
joint payoff. For example, a developer may be more uncertain about th e profitability of a smaller shopping mall
built on a subset of targeted parcels; an academic department may be more uncertain about the stand-alone
contributions of faculty candidates than their joint contributions to the department; a vaccine manufacturer
may be more uncertain ab out the effectiveness of the vaccine that uses only a subset of the antigens; and a
home-owner may be more uncertain about the use of a backyard porch without landscaping than with it. It is,
however, conceivable that the b uyer will resolve her payoff uncertainty as she meets with the sellers and learn
about the objects.
3
An ex post purchasing decision guarantees that the buyer does not incur a loss, and this assumption makes
most sense if the buyer is credit-constrained by the value of the project. For instance, in land acquisitions, it is
a common practice to secure an option on the prop erty at a nominal fee, that specifies a price and expiration
date (Poorvu 1999, pp. 151-3).
2

indifferent to the sequence because the sellers perfectly coordinate their prices in equilibriu m,
resulting in an efficient trade.
4
With a sufficient payoff uncertainty, however, equilibrium trade
can be inefficient. In such cases, we show that the buyer optimally begins with the weak seller
if one seller is weak and the other is a strong bargainer. If, on th e other hand, both sellers
are strong bargainers, then the b uyer begins with the stronger of the two. To understand
these observations, note that the buyer –not surp risingly– proposes to pay only the marginal
cost in each negotiation. Thus, the leading seller prices aggressively, if he is followed by a
weak seller who is unlikely to propose against the buyer and capture any surplus. To curb
this behavior, the buyer begins with the weak seller. When both sellers are strong bargainers,
the buyer’s concern for aggressive pricing shifts to the last seller. By leaving the weaker seller
of the two to be the last, the buyer minimizes the likelihood of a high price response in the
second negotiation in the event that the first one end s in her favor. In either case, we show
that the buyer’s sequencing (weakly) improves the social sur plus.
An interesting implication of our bargaining analysis is that the buyer is sometimes strictly
better off dealing with the sellers who have higher bargaining powers. The reason is that such
sellers anticipate the other to be more demanding against the buyer and become more concerned
about price coordination, leading them to lower prices. Put differently, the b uyer can sometimes
enhance her bargaining position by becoming weaker vis-`a-vis the sellers. This finding has two
important implications for procurement policies. First, the buyer may optimally adopt a
minimum purchase price by which she commits to paying the sellers a pr ice strictly above
their marginal costs even when she makes the offers; and second, the buyer who can internally
provide an input at the same cost as the outside seller may, nonetheless, choose to outsour ce
it. Under each policy, th e buyer weakens her bargaining power by raising her own cost of
acquiring the go ods in order to better manage the supplier competition.
5
We also examine the sellers’ preference for the negotiation sequence, as this may inform us
of their incentives to actively solicit the buyer’s business and even bid for the right to negotiate
at the desired order. Although the standard IO theory establishes a firs t-mover advantage for
price-setting duopolists selling complementary goods (e.g., Gal-Or 1985, and Dow rick 1986), a
second-mover advantage also emerges in our model with a powerful buyer. The reason is that
a powerful buyer is h ighly likely to secure a low price from the first negotiation, which leaves
4
Given complementarity, it is socially efficient for the buyer to purchase both units in our model.
5
This is a reminiscent of, but quite distinct from, the “handicapping” principle in procurement auctions
where the buyer commits to purchasing a single good from the high-cost supplier at times to induce a more
intense supplier competition (e.g., McAfee and McMillan 1989, and Lewis and Yildirim 2002).
3

a large surplus to the second negotiation.
Related Literature. Our paper belongs to a growing literature on on e-to-many bargain-
ing, and complements several papers that add ress the issue of optimal bargaining sequence
without payoff uncertainty. Among them, Marx and Shaffer (2007) show that with contingent
contracts, the buyer strictly prefers to negotiate first with the weaker seller in order to extract
rents from the stronger one. Absent contingent contracts (as with our model), however, the
buyer would be indifferent to the sequence in their setting. Xiao (2010) stu dies a complemen-
tary good setting with n on contingent contracts but with a pay-as-you-go sch eme. Like Marx
and Shaffer, he too finds that th e buyer is better off starting with the weaker seller, though only
to alleviate a “holdup” problem due to sunk payments for prior purchases. Such a problem
does not arise in our setting because the buyer decides on purchases after receiving all the p rice
offers. Li (2010) studies an infinite-horizon random-proposer model of complementary goods.
Given no payoff uncertainty, he sh ows that any sequencing is sustainable in equilibrium.
6
In
contrast, our model yields a unique equilibrium, and a strict sequencing preference. In two
related papers, Krasteva and Yildirim (2010), and Noe and Wang (2004) compare p ublic and
private negotiations, and note that the buyer is indifferent to the sequence u nder both types of
negotiations, th ough she may strictly randomize. We abstr act from privacy concerns h ere, and
show that with demand uncertainty, the buyer has a strict preference over the sequence.
7
In a
labor union-multiple firm framework, Marshall and Merlo (2004) examine the sequen cing issue
using “pattern bargaining” where the b uyer uses the contract agreed upon in the first negoti-
ation as a starting point of the second negotiation.
8
In their case with non-pattern sequential
negotiations, the buyer does not, however, care about the sequence. A similar indifference
result is obtained by Moresi et al. (2010) in a fairly general model of bilateral negotiations.
Without payoff uncertainty, our model would also result in the buyer’s indifference to the
sequence, wh ich we fur ther discuss below.
Our paper is also related to models of endogenous sequencing through sellers’ bidding for
positions, e.g., Arbatskaya (2007), and Marx and Shaffer (2010). While these papers uncover
either a firs t- or second-mover advantage for the sellers, our setting features th e presence of
both advantages depending on the degree of payoff uncertainty and the buyer’s bargaining
6
Both Li (2010) and Xiao (2010) build on Cai (2000) who assume homogenous sellers. See also Horn and
Wolinsky (1988), and St ole and Zwiebel (1996) who assume a fixed order of negotiations.
7
Note that this is not a simple “purification” argument for mixed strategies, because, under the present setup ,
Krasteva and Yildirim (2010) would imply that without any uncertainty, the ordering issue is inconsequential
under both public and private negotiations.
8
See also Banerji (2002).
4

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Payoff uncertainty, bargaining power, and the strategic sequencing of bilateral negotiations" ?

This paper investigates the sequencing choice of a buyer who negotiates with the sellers of two complementary objects with uncertain payoffs. The authors show that the sequencing matters to the buyer only when equilibrium trade can be inefficient. Their analysis further reveals that it is sometimes optimal for the buyer to raise her own cost of acquisition to better manage the supplier competition. As such, the authors find that the buyer may commit to paying the sellers a minimum price strictly above the marginal cost ; and that the buyer may outsource an input even though it can be made in-house. 

Q2. What are the future works in "Payoff uncertainty, bargaining power, and the strategic sequencing of bilateral negotiations" ?

In this paper, the authors have focused on the sellers of complementary goods, and included the possibility that the buyer can be uncertain of her valuations. Their first set of results have revealed that to the extent that equilibrium trade is efficient, the buyer will be neutral to the sequence. The authors believe that this efficiency reasoning is also the driving force behind the similar “ indifference ” findings in the literature. This commitment can manifest itself in the form of a procurement policy such as a minimum purchase price or the outsourcing of an input when it can be made in-house at the same cost.