Beliefs and private monitoring

Christopher Phelan; Andrzej Skrzypacz

doi:10.1093/restud/rds009

Beliefs and private monitoring

Christopher Phelan, Andrzej Skrzypacz

Economics (Twin Cities)

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

This paper develops new recursive, set based methods for studying repeated games with private monitoring. For any finite-state strategy profile, we find necessary and sufficient conditions for whether there exists a distribution over initial states such that the strategy, together with this distribution, form a correlated sequential equilibrium (CSE). Also, for any given correlation device for determining initial states (including degenerate cases where players' initial states are common knowledge), we provide necessary and sufficient conditions for the correlation device and strategy to be a CSE, or in the case of a degenerate correlation device, for the strategy to be a sequential equilibrium. We also consider several applications. In these, we show that the methods are computationally feasible, and how to construct and verify equilibria in a secret price-setting game.

Original language	English (US)
Article number	rds009
Pages (from-to)	1637-1660
Number of pages	24
Journal	Review of Economic Studies
Volume	79
Issue number	4
DOIs	https://doi.org/10.1093/restud/rds009
State	Published - Oct 2012

Bibliographical note

Funding Information:
Acknowledgment. The authors thank V. Bhaskar, Peter DeMarzo, Glenn Ellison, Larry Jones, Michihiro Kandori, Narayana Kocherlakota, David Levine, George Mailath, Stephen Morris, Ichiro Obara, Larry Samuelson, Itai Sher, Ofer Zeitouni, seminar participants at the Federal Reserve Bank of Minneapolis, the Harvard/MIT joint theory seminar, Stanford University, Iowa State University, Princeton University, the University of Chicago, the University of Minnesota, University College London, the London School of Economics and the 2006 meetings of the Society for Economic Dynamics, and three anonymous referees for helpful comments as well as the excellent research assistance of Songzi Du, Kenichi Fukushima, and Roozbeh Hosseini. Financial assistance from National Science Foundation grant number 0721090 is gratefully acknowledged. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

Keywords

Private monitoring
Repeated games

Access

10.1093/restud/rds009

OpenUrl availability

Full text

Cite this

@article{1727c42d58904d87b59670aac2f20aa3,

title = "Beliefs and private monitoring",

abstract = "This paper develops new recursive, set based methods for studying repeated games with private monitoring. For any finite-state strategy profile, we find necessary and sufficient conditions for whether there exists a distribution over initial states such that the strategy, together with this distribution, form a correlated sequential equilibrium (CSE). Also, for any given correlation device for determining initial states (including degenerate cases where players' initial states are common knowledge), we provide necessary and sufficient conditions for the correlation device and strategy to be a CSE, or in the case of a degenerate correlation device, for the strategy to be a sequential equilibrium. We also consider several applications. In these, we show that the methods are computationally feasible, and how to construct and verify equilibria in a secret price-setting game.",

keywords = "Private monitoring, Repeated games",

author = "Christopher Phelan and Andrzej Skrzypacz",

note = "Funding Information: Acknowledgment. The authors thank V. Bhaskar, Peter DeMarzo, Glenn Ellison, Larry Jones, Michihiro Kandori, Narayana Kocherlakota, David Levine, George Mailath, Stephen Morris, Ichiro Obara, Larry Samuelson, Itai Sher, Ofer Zeitouni, seminar participants at the Federal Reserve Bank of Minneapolis, the Harvard/MIT joint theory seminar, Stanford University, Iowa State University, Princeton University, the University of Chicago, the University of Minnesota, University College London, the London School of Economics and the 2006 meetings of the Society for Economic Dynamics, and three anonymous referees for helpful comments as well as the excellent research assistance of Songzi Du, Kenichi Fukushima, and Roozbeh Hosseini. Financial assistance from National Science Foundation grant number 0721090 is gratefully acknowledged. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.",

year = "2012",

month = oct,

doi = "10.1093/restud/rds009",

language = "English (US)",

volume = "79",

pages = "1637--1660",

journal = "Review of Economic Studies",

issn = "0034-6527",

publisher = "Oxford University Press",

number = "4",

}

TY - JOUR

T1 - Beliefs and private monitoring

AU - Phelan, Christopher

AU - Skrzypacz, Andrzej

N1 - Funding Information: Acknowledgment. The authors thank V. Bhaskar, Peter DeMarzo, Glenn Ellison, Larry Jones, Michihiro Kandori, Narayana Kocherlakota, David Levine, George Mailath, Stephen Morris, Ichiro Obara, Larry Samuelson, Itai Sher, Ofer Zeitouni, seminar participants at the Federal Reserve Bank of Minneapolis, the Harvard/MIT joint theory seminar, Stanford University, Iowa State University, Princeton University, the University of Chicago, the University of Minnesota, University College London, the London School of Economics and the 2006 meetings of the Society for Economic Dynamics, and three anonymous referees for helpful comments as well as the excellent research assistance of Songzi Du, Kenichi Fukushima, and Roozbeh Hosseini. Financial assistance from National Science Foundation grant number 0721090 is gratefully acknowledged. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.

PY - 2012/10

Y1 - 2012/10

N2 - This paper develops new recursive, set based methods for studying repeated games with private monitoring. For any finite-state strategy profile, we find necessary and sufficient conditions for whether there exists a distribution over initial states such that the strategy, together with this distribution, form a correlated sequential equilibrium (CSE). Also, for any given correlation device for determining initial states (including degenerate cases where players' initial states are common knowledge), we provide necessary and sufficient conditions for the correlation device and strategy to be a CSE, or in the case of a degenerate correlation device, for the strategy to be a sequential equilibrium. We also consider several applications. In these, we show that the methods are computationally feasible, and how to construct and verify equilibria in a secret price-setting game.

AB - This paper develops new recursive, set based methods for studying repeated games with private monitoring. For any finite-state strategy profile, we find necessary and sufficient conditions for whether there exists a distribution over initial states such that the strategy, together with this distribution, form a correlated sequential equilibrium (CSE). Also, for any given correlation device for determining initial states (including degenerate cases where players' initial states are common knowledge), we provide necessary and sufficient conditions for the correlation device and strategy to be a CSE, or in the case of a degenerate correlation device, for the strategy to be a sequential equilibrium. We also consider several applications. In these, we show that the methods are computationally feasible, and how to construct and verify equilibria in a secret price-setting game.

KW - Private monitoring

KW - Repeated games

UR - http://www.scopus.com/inward/record.url?scp=84867765449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867765449&partnerID=8YFLogxK

U2 - 10.1093/restud/rds009

DO - 10.1093/restud/rds009

M3 - Article

AN - SCOPUS:84867765449

SN - 0034-6527

VL - 79

SP - 1637

EP - 1660

JO - Review of Economic Studies

JF - Review of Economic Studies

IS - 4

M1 - rds009

ER -

Beliefs and private monitoring

Abstract

Bibliographical note

Keywords

Access

OpenUrl availability

Other files and links

Fingerprint

Cite this