Haggling over substitutes

doi:10.1016/j.jet.2003.09.002

Journal of Economic Theory

Volume 117, Issue 2, August 2004, Pages 217-245

https://doi.org/10.1016/j.jet.2003.09.002 Get rights and content

Abstract

Using a model of substitutable goods I determine generic conditions on tastes which guarantee that fixed prices are not optimal: the fully optimal tariff includes lotteries. That is, a profit maximising seller would employ a haggling strategy. We show that the fully optimal selling strategy in a class of cases requires a seller to not allow themselves to focus on one good but to remain haggling over more than one good. This throws new light on the selling strategies used in diverse industries. These insights are used to provide a counter-example to the no lotteries result of McAfee and McMillan (J. Econ. Theory 46 (1988) 335).

References (12)

R McAfee et al.
Multidimensional incentive compatibility and mechanism design
J. Econ. Theory
(1988)
J-C Rochet
A necessary and sufficient condition for rationalizability in a quasi context
J. Math. Econ.
(1987)
M Armstrong
Multiproduct nonlinear pricing
Econometrica
(1996)
Y Bakos et al.
Bundling information goodspricing, profits and efficiency
Manage. Sci.
(1999)
A Manelli et al.
Bundling as an optimal selling mechanism for a multiple-good monopolist
(2001)
R McAfee et al.
Multiproduct monopoly, commodity bundling, and correlation of values
Quart. J. Econ.
(1989)

There are more references available in the full text version of this article.

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Haggling over substitutes

Abstract

J. Econ. Theory

J. Math. Econ.

Multiproduct nonlinear pricing

Econometrica

Bundling information goodspricing, profits and efficiency

Manage. Sci.

Bundling as an optimal selling mechanism for a multiple-good monopolist

Multiproduct monopoly, commodity bundling, and correlation of values

Quart. J. Econ.