Equilibrium opacity in ultimatum‐offer bargaining

• Author: Kai A. Konrad,Marcel Thum
• Date: 01 September 2020
• Published date: 01 September 2020
• DOI: http://doi.org/10.1111/jpet.12471

J Public Econ Theory. 2020;22:1515–1529. wileyonlinelibrary.com/journal/jpet

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1515

Received: 27 April 2020

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Accepted: 10 August 2020

DOI: 10.1111/jpet.12471

ORIGINAL ARTICLE

Equilibrium opacity in ultimatum‐offer

bargaining

Kai A. Konrad

1

|Marcel Thum

2

1

Max Planck Institute for Tax Law and

Public Finance, Marstallplatz 1, Munich,

Germany

2

Faculty of Business and Economics, TU

Dresden, Dresden, Germany

Correspondence

Kai A. Konrad, Max Planck Institute for

Tax Law and Public Finance, Marstallplatz

1, D‐80539 Munich, Germany.

Email: kai.konrad@tax.mpg.de

Abstract

We consider ultimatum bargaining between a seller

and a buyer of an asset. They know each other's va-

luation of the asset. Both can defer their decisions to

delegates. These delegates have opaque preferences.

Seller and buyer choose the opacity of their delegate.

For the seller's delegate this choice is restricted to a

random reservation price drawn from the set of

symmetric two‐point distributions around the seller's

true reservation price. The opacity choice of the

buyer's delegate is restricted to a random willingness‐

to‐pay drawn from the set of symmetric two‐point

distribution around the buyer's true willingness‐to‐

pay. We characterize the set of pure‐strategy equili-

bria in their delegation choices. Multiple equilibria

arise. Except for two corner solutions, both players

will exploit the strategy of opacity. A large set of ef-

ficient equilibria exist. For these, opacity choices do

not reduce the probability of transacting, but benefit

the buyer compared with the no‐delegation equili-

brium. We also study the robustness of the results

with respect to the player's ability to also resort to a

tougher delegate in addition to the opacity choice.

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