Bargaining under Liquidity Constraints: Unified Strategic Foundations of the Nash and Kalai Solution

Tai-Wei Hu; Guillaume Rocheteau

doi:10.1016/j.jet.2020.105098

Bargaining under Liquidity Constraints: Unified Strategic Foundations of the Nash and Kalai Solution

Tai-Wei Hu^*, Guillaume Rocheteau^*

^*Corresponding author for this work

School of Economics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

11 Citations (Scopus)

105 Downloads (Pure)

Abstract

We provide unified strategic foundations for the Nash (1950) and Kalai (1977) solutions in the context of negotiations under liquidity constraints. We propose an N-round game where in each round a seller and a buyer with limited payment capacity negotiate a bundle of divisible goods, where bundle sizes can vary across rounds, according to Rubinstein's (1982) alternating-offer game. The game implements the Nash solution if N=1 and the Kalai solution if N=∞ and bundle sizes are infinitesimal. If N is set by one player ex ante, the buyer chooses N=1 while the seller chooses N=∞. We endogenize liquidity constraints and show they binds for all N<∞, even when there is no cost in holding liquidity.

Original language	English
Article number	105098
Number of pages	45
Journal	Journal of Economic Theory
Volume	189
Early online date	24 Jul 2020
DOIs	https://doi.org/10.1016/j.jet.2020.105098
Publication status	Published - 24 Jul 2020

Keywords

bargaining with an agenda
Nash program
bargaining solution

Access to Document

10.1016/j.jet.2020.105098

Full-text PDF (author’s accepted manuscript)
This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://doi.org/10.1016/j.jet.2020.105098 . Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 538 KBLicence: CC BY-NC-ND

Handle.net

Persistent link

Professor Tai-Wei Hu
- taiwei.hubristol.acuk
- School of Economics - Professor of Economics
Person: Academic

Cite this

@article{86d3d2ced5a6449d8d3ee328b671a556,

title = "Bargaining under Liquidity Constraints: Unified Strategic Foundations of the Nash and Kalai Solution",

abstract = "We provide unified strategic foundations for the Nash (1950) and Kalai (1977) solutions in the context of negotiations under liquidity constraints. We propose an N-round game where in each round a seller and a buyer with limited payment capacity negotiate a bundle of divisible goods, where bundle sizes can vary across rounds, according to Rubinstein's (1982) alternating-offer game. The game implements the Nash solution if N=1 and the Kalai solution if N=∞ and bundle sizes are infinitesimal. If N is set by one player ex ante, the buyer chooses N=1 while the seller chooses N=∞. We endogenize liquidity constraints and show they binds for all N<∞, even when there is no cost in holding liquidity.",

keywords = "bargaining with an agenda, Nash program, bargaining solution",

author = "Tai-Wei Hu and Guillaume Rocheteau",

year = "2020",

month = jul,

day = "24",

doi = "10.1016/j.jet.2020.105098",

language = "English",

volume = "189",

journal = "Journal of Economic Theory",

issn = "0022-0531",

publisher = "Academic Press",

}

TY - JOUR

T1 - Bargaining under Liquidity Constraints

T2 - Unified Strategic Foundations of the Nash and Kalai Solution

AU - Hu, Tai-Wei

AU - Rocheteau, Guillaume

PY - 2020/7/24

Y1 - 2020/7/24

N2 - We provide unified strategic foundations for the Nash (1950) and Kalai (1977) solutions in the context of negotiations under liquidity constraints. We propose an N-round game where in each round a seller and a buyer with limited payment capacity negotiate a bundle of divisible goods, where bundle sizes can vary across rounds, according to Rubinstein's (1982) alternating-offer game. The game implements the Nash solution if N=1 and the Kalai solution if N=∞ and bundle sizes are infinitesimal. If N is set by one player ex ante, the buyer chooses N=1 while the seller chooses N=∞. We endogenize liquidity constraints and show they binds for all N<∞, even when there is no cost in holding liquidity.

AB - We provide unified strategic foundations for the Nash (1950) and Kalai (1977) solutions in the context of negotiations under liquidity constraints. We propose an N-round game where in each round a seller and a buyer with limited payment capacity negotiate a bundle of divisible goods, where bundle sizes can vary across rounds, according to Rubinstein's (1982) alternating-offer game. The game implements the Nash solution if N=1 and the Kalai solution if N=∞ and bundle sizes are infinitesimal. If N is set by one player ex ante, the buyer chooses N=1 while the seller chooses N=∞. We endogenize liquidity constraints and show they binds for all N<∞, even when there is no cost in holding liquidity.

KW - bargaining with an agenda

KW - Nash program

KW - bargaining solution

U2 - 10.1016/j.jet.2020.105098

DO - 10.1016/j.jet.2020.105098

M3 - Article (Academic Journal)

SN - 0022-0531

VL - 189

JO - Journal of Economic Theory

JF - Journal of Economic Theory

M1 - 105098

ER -

Bargaining under Liquidity Constraints: Unified Strategic Foundations of the Nash and Kalai Solution

Abstract

Keywords

Access to Document

Handle.net

Fingerprint

Profiles

Professor Tai-Wei Hu

Cite this