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A Dynamic Game under Ambiguity: Repeated Bargaining with Interactive Learning

A Dynamic Game under Ambiguity: Repeated Bargaining with Interactive Learning
A Dynamic Game under Ambiguity: Repeated Bargaining with Interactive Learning
Conventional Bayesian games of incomplete information are limited in their ability to represent complete ignorance of an uninformed player about an opponent's private information. Using an illustrative example of repeated bargaining with interactive learning, we analyze a dynamic game of incomplete information that incorporates a multiple-prior belief system. We consider a game in which a principal sequentially compensates an agent for his effort on a novel experiment --- a Poisson process with unknown hazard rate. The agent has knowledge to form a single prior over the hazard rate, but the principal has complete ignorance, represented by the set of all plausible prior distributions over the hazard rate. We propose a new equilibrium concept --- Perfect Objectivist Equilibrium --- in which the principal infers the agent's prior from the observed history of the game via maximum likelihood updating. The new equilibrium concept embodies a novel model of learning under ambiguity in the context of a dynamic game. The unique (Markov) equilibrium outcome determines a unique bargaining solution. The underlying Markov Perfect Objectivist Equilibria are all belief-free, in sharp contrast to Markov Perfect Bayesian Equilibria, which hinge on subjective pretense of knowledge and predict a continuum of equilibrium outcomes.
University of Southampton
Besanko, David
f883b3af-f490-4125-b05e-5a047a56d8e2
Tong, Jian
8109179b-ff1d-483e-9ee0-bf3f96cda71b
Wu, Jianjun
b5d3072d-431a-4650-9d04-9ce11d7c3a93
Besanko, David
f883b3af-f490-4125-b05e-5a047a56d8e2
Tong, Jian
8109179b-ff1d-483e-9ee0-bf3f96cda71b
Wu, Jianjun
b5d3072d-431a-4650-9d04-9ce11d7c3a93

Besanko, David, Tong, Jian and Wu, Jianjun (2012) A Dynamic Game under Ambiguity: Repeated Bargaining with Interactive Learning Southampton, GB. University of Southampton 60pp.

Record type: Monograph (Working Paper)

Abstract

Conventional Bayesian games of incomplete information are limited in their ability to represent complete ignorance of an uninformed player about an opponent's private information. Using an illustrative example of repeated bargaining with interactive learning, we analyze a dynamic game of incomplete information that incorporates a multiple-prior belief system. We consider a game in which a principal sequentially compensates an agent for his effort on a novel experiment --- a Poisson process with unknown hazard rate. The agent has knowledge to form a single prior over the hazard rate, but the principal has complete ignorance, represented by the set of all plausible prior distributions over the hazard rate. We propose a new equilibrium concept --- Perfect Objectivist Equilibrium --- in which the principal infers the agent's prior from the observed history of the game via maximum likelihood updating. The new equilibrium concept embodies a novel model of learning under ambiguity in the context of a dynamic game. The unique (Markov) equilibrium outcome determines a unique bargaining solution. The underlying Markov Perfect Objectivist Equilibria are all belief-free, in sharp contrast to Markov Perfect Bayesian Equilibria, which hinge on subjective pretense of knowledge and predict a continuum of equilibrium outcomes.

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More information

Published date: 10 January 2012
Organisations: Economics

Identifiers

Local EPrints ID: 207857
URI: https://eprints.soton.ac.uk/id/eprint/207857
PURE UUID: 710ca22d-6fbf-4d63-9b86-5514a282b958
ORCID for Jian Tong: ORCID iD orcid.org/0000-0001-9367-4853

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Date deposited: 18 Jan 2012 15:19
Last modified: 04 Oct 2018 00:33

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Contributors

Author: David Besanko
Author: Jian Tong ORCID iD
Author: Jianjun Wu

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