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Playing for RealGame Theory$
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Ken Binmore

Print publication date: 2007

Print ISBN-13: 9780195300574

Published to Oxford Scholarship Online: May 2007

DOI: 10.1093/acprof:oso/9780195300574.001.0001

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 Cutting a Deal

 Cutting a Deal

Chapter:
(p.493) 17 Cutting a Deal
Source:
Playing for Real
Author(s):

Ken Binmore (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780195300574.003.0017

This chapter examines noncooperative bargaining models and links them with cooperative bargaining concepts in accordance with the Nash program. Following a discussion of what matters in real-life bargaining, the case in which commitment is possible is studied using the Nash Demand Game. It is shown that a Nash equilibrium of the smoothed version of the Nash Demand Game implements the Nash bargaining solution. Nash threat games are then considered with an application to collusion in Cournot models. The case in which commitment is impossible is considered. Rubinbstein's bargaining model is introduced using one-stage and two-stage Ultimatum Games to set the scene. Rubinstein's theorem that his model has a unique subgame-perfect equilibrium is proved. The outcome is shown to converge on an asymmetric version of the Nash bargaining solution when the time interval between successive proposals becomes sufficiently small. The chapter ends with a discussion of common mistakes in applying the theory.

Keywords:   John Nash, Nash program, implementation theory, Nash Demand Game, Nash Threat Game, collusion, Ultimatum Game, Ariel Rubinstein, Rubinstein bargaining model

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