Buyer power and mutual dependency in a model of negotiations

• DOI: http://doi.org/10.1111/1756-2171.12261
• Author: Roman Inderst,Joao Montez
• Date: 01 March 2019
• Published date: 01 March 2019

RAND Journal of Economics

Vol.50, No. 1, Spring 2019

pp. 29–56

Buyer power and mutual dependency in a

model of negotiations

Roman Inderst∗

and

Joao Montez∗∗

We study bilateral bargaining between several buyers and sellers in a framework that allows

both sides, in case of a bilateral disagreement, flexibility to adjust trade with each of their other

trading partners and receive the gross benefit generated by each adjustment. A larger buyer pays

a higher per-unit price when buyers’ bargaining power in bilateral negotiations is sufficiently

low, and a lower price otherwise. An analogous result holds for sellers. These predictions, and

the implications of different technologies,are explained by the fact that size is a source of mutual

dependency and not an unequivocal source of power.

1. Introduction

We develop a bargaining model where several buyers negotiate bilaterally with several

sellers of substitute goods, which have convex costs. Transfers and quantities are determined by

the ability of buyers to relocate purchases across sellers, and of sellers to relocate sales across

buyers, in case of a bilateral disagreement. Specifically, the two parties in disagreement can

optimally adjust their bilateral transactions with each of their other counterparties while changing

the transfer to exactly reflect the changes in costs or benefits of that counterparty. Next to a

foundation that builds on the axiomatic (asymmetric) Nash bargaining solution, we introduce a

strategic game that generates these adjustments endogenously as reasonable inside options.

This model is applied to a question that has become increasingly important for researchers

in industrial organization, as well as antitrust and business strategy practitioners, namely, whether

size is alwaysan advantage in negotiations, and more generally,the impact of market concentration

on negotiated terms of trade. Consistent with most of the literature, in our model, a larger buyer

obtains a lowerper-unit (or average) price if there is a single seller or if adjustments are unfeasible.

We explain, however, that this result does not necessarily extend to those often more realistic

situations with multiple sellers and adjustments in trade. Here, our approach reveals that size

∗University of Frankfurt; inderst@finance.uni-frankfurt.de.

∗∗University of Lausanne and CEPR; joao.montez@unil.ch.

We are grateful to the Editor, DavidMyatt, and three anonymous referees. We also thank the participants at numerous

conferences and seminars. The online appendix is available in https://sites.google.com/site/jvmontez/.

C2019, The RAND Corporation. 29

30 / THE RAND JOURNAL OF ECONOMICS

tends to increase both buyer and seller dependency by worsening the alternative options of both

sides when they seek to adjust what they trade in case of disagreement, which as explained next,

can become an advantage or a disadvantage.

Disagreement of a seller with a large buyer displaces a large fraction of the potential demand

and leaves a seller with few alternative buyers to replace its sales. Instead, a disagreement with a

small buyer displaces a small fraction of demand and leaves the seller with many alternatives to

turn to. In this sense, a seller is more dependent on a larger buyer. However, increasing marginal

costs also render it relatively more costly for other sellers to accommodate a larger increase

in production, and so it is equally more expensive for a large buyer to try to make up for a

(off-equilibrium) shortfall when relocating its demand to other sellers of substitute goods. In this

sense, a larger buyer is also more dependent on each individual seller.This second counter vailing

effect of size seems to have been largely overlooked by the literature.

With multiple sellers, the two conflicting effects of buyer size coexist and size becomes

a source of mutual dependency, not an unequivocal source of power.1This demonstrates, in a

stylized model that shuts down other explanations, a potential new mechanism for why size may

not necessarily yield a better bargaining outcome to a firm conducting multiple bilateral bargains.

In our model, the effect of size on buyer dependency dominates, and a larger buyer pays higher

per-unit prices, if and only if the bilateral bargaining powerof sellers is sufficiently high. So size

and bilateral bargaining power are complements. Analogous results hold with respect to the size

of sellers.

Mutual dependency also explains why the impact of size depends crucially on the extent

to which technology allows for adjustments in case of bilateral disagreement. This suggests

that practitioners and empiricists should take into account the technological specificities of the

industry as a determinant of bargaining power,such as existing capacity constraints and the extent

to which sellers are able to accommodate large-scale switching(e.g., by utilizing existing capacity

more extensively at a reasonable cost).

By supporting the view that large purchase volumes are not per se conclusiveof the existence

of buyer power, in the sense of better terms of trade, our model provides conceptual guidance for

policy and business strategy where buyer power has become increasingly topical.2

First, by changing the focus from size per se to ease of substitution and dependency, it

seems to formalize concerns that have previously been expressed informally, for example, in the

European Commission’s guidelines on horizontal mergers and in recent sector inquiries. For in-

stance, in the mentioned guidelines, buyer power is defined as “the bargaining strength that the

buyer has vis-`

a-vis the seller in commercial negotiations due to its size, its commercial signifi-

cance to the seller and its ability to switch to alternative suppliers.” This definition highlights that,

in addition to size, an assessment of buyer power needs to take into account two additional con-

siderations: the consequences to the supplier from losing a particular buyer, and the consequences

to the buyer from losing a particular supplier.

Second, the model’s predictions accord well with the view taken in several influential court

cases where, following inquiries with business experts, doubts were cast on the presumption

that larger buyers should be able to negotiate lower per-unit prices. For example, in Hutchi-

son/RCPM/ECT (2001) container terminal operators (sellers) argued that large carriers (buyers)

had significant leverage in negotiations. Yet the European Commission argued to the contrary,

stating that switching opportunities were limited for the largest carriers as “there is currently

a limited number of terminal operators able to accommodate the largest vessels being used”

by which “it becomes economically more difficult for the (larger) carrier to switch ports for

a significant portion of its cargo.” In another case, concerning toilet tissue and kitchen towels

1Note that, when there is a single seller, all buyers are completelydependent on that seller regardless of their size,

thus, the second effect is absent, and a larger buyer then pays a lower per-unit price.

2Recent evidence from the UK retailing sector and the US pharmaceutical industry suggests that size alone is no

guarantee to obtain discounts (see, for instance, Sorensen, 2003; Competition Commission UK, 2008; Ellison and Snyder,

2010; Grennan, 2013).

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The RAND Corporation 2019.