Econometrica: Jan 1999, Volume 67, Issue 1

Cooperation in Repeated Games When the Number of Stages is not Commonly Known

https://doi.org/10.1111/1468-0262.00003
p. 45-64

Abraham Neyman

It is shown that an exponentially small departure from the common knowledge assumption on the number of repetitions of the prisoners' dilemma already enables cooperation. More generally, with such a departure, any feasible individually rational outcome of any one‐shot game can be approximated by a subgame perfect equilibrium of a finitely repeated version of that game.

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Supplemental Material

Supplement to "Dynamic Product Positioning in Differentiated Product Markets: The Effect of Fees for Musical Performance Rights on the Commercial Radio Industry"

This file contains 4 Appendices.  Appendix A lists the variables in the state space, while Appendices B-D contain details of the methods used to estimate and solve the model.

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Supplement to "Inference on Counterfactual Distributions"

This zip file contains the data and programs for the empirical application.  A brief guide to the content of the folder is given in the README.PDF file.

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Supplement to "Inference on Counterfactual Distributions"

This supplement material contains the proof of he validity of bootstrap confidence bands for counterfactual functionals, a numerical comparison of quantile and distribution regression estimators, additional empirical results, and details about the variance decomposition of the composition effect.

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Supplement to "Optimal Taxes on Fossil Fuel in General Equilibrium"

This document covers numerically solved versions of the model and can be viewed as a robustness check on the main results.

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Supplement to "Dynamic Financial Constraints: Distinguishing Mechanism Design from Exogenously Incomplete Regimes"

In this appendix we formulate, solve, and estimate two additional mechanism design models: a model with unobserved capital and investment and a model with hidden output.

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Supplement to "How Responsive is Investment in Schooling to Changes in Redistributive Policies and in Returns?"

This supplement contains tables not found within the manuscript.

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Supplement to "How Responsive is Investment in Schooling to Changes in Redistributive Policies and in Returns?"

This zip file contains the replication files for the results reported in the online appendix.

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Supplement to "How Responsive is Investment in Schooling to Changes in Redistributive Policies and in Returns?"

This zip file contains the replication files for the results reported in the paper tables..

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Supplement to "GMM with Many Weak Moment Conditions"

This supplement provides proofs for the paper.

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Supplement to "Public vs. Private Offers in the Market for Lemons"

Extensions of the proofs found in the paper.

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Supplement to "What Happens When Wal-Mart Comes to Town: An Empirical Analysis of the Discount Retailing Industry"

This zip file contains data and programs for replication.

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Supplement to "Liquidity in Asset Markets with Search Frictions"

In this appendix we generalize the stochastic process for preference shocks.

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Supplement to "What Drives Media Slant? Evidence from U.S. Daily Newspapers"

PDF file containing supplemental appendix with additional analysis, tables and figures.

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Supplement to "Identification and Estimation of a Discrete Game of Complete Information"

This appendix specializes the arguments for identification to the two by two game.

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Supplement to "Identification and Estimation of a Discrete Game of Complete Information"

A zip file containing data and programs for the paper.

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Supplement to "An Equilibrium Theory of Learning, Search and Wages"

PDF file containing complete proofs of the lemmas and theorems presented in the paper.

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Supplement to "Estimating the Technology of Cognitive and Noncognitive Skill Formation"

An appendix containing proofs for the manuscript.

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Supplement to "Estimating the Technology of Cognitive and Noncognitive Skill Formation"

A zip file containing replication files for the paper.

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Supplement to "Incentive Problems with Unidimensional Hidden Characteristics: A Unified Approach"

This appendix provides formal proofs of Lemmas 2.7-2.9 in the text of the paper.

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Supplement to "The Effects of Health Insurance and Self-Insurance on Retirement Behavior"

Technical appendices with details of the methodology and data, along with additional results.

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Supplement to "The Effects of Health Insurance and Self-Insurance on Retirement Behavior"

Replication files for the manuscript, first stage.  This archive addresses the dataset and the life-cycle profiles that are used in the structural model.

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Supplement to "The Effects of Health Insurance and Self-Insurance on Retirement Behavior"

Replication files for the manuscript, second stage.  This archive addresses the structural estimation procedure and the policy simulations.

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Supplement to "A Structural Evaluation of a Large-Scale Quasi-Experimental Microfinance Initiative"

This zip file contains the replication files for the manuscript.

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Supplement to "Risk Sharing in Private Information Models with Asset Accumulation: Explaining the Excess Smoothness of Consumption"

A zip file containing the manuscript's replication files.

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Supplement to "Risk Sharing in Private Information Models with Asset Accumulation: Explaining the Excess Smoothness of Consumption"

This document contains two main sections which correspond to Appendix B and Appendix C in the main text.  In the first section we formally derive the closed forms presented in Sections 3.2 and 3.3 in the main text.  In the second section, we derive the expression for the bias in the variance induced by the use of a pseudo-panel (such as the one we consider in our estimations).

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Supplement to What Drives Media Slant? Evidence from U.S. Daily Newspapers

Zip file containing supplemental data and programs (approximately 40MB)

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Supplement to "Ambiguity, Learning, and Asset Returns"

This technical appendix describes the numerical method used to solve the model in the paper.

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Supplement to "Ambiguity, Learning, and Asset Returns"

A zip file containing the replication files for the manuscript.

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Supplement to "Bounds on Elasticities with Optimization Frictions: A Synthesis of Micro and Macro Evidence on Labor Supply"

A PDF file containing proofs and meta-analysis appendices for the manuscript.

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Supplement to "Bounds on Elasticities with Optimization Frictions: A Synthesis of Micro and Macro Evidence on Labor Supply"

This zip file contains the replication files for the manuscript.

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Supplement to "Contract Pricing in Consumer Credit Markets'

This zip file contains the replication files for the manuscript.

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Supplement to "Contract Pricing in Consumer Credit Markets"

This appendix provides a more detailed analysis of a parameterized version of the consumer model presented in Section 4.1.  It also illustrates some of the theoretical properties of the model and shows that the model can incorporate features observed in the data. Third, it shows the calibrated parameters of the model to match several key moments in data and further explores the features of the model.  Finally, it reports how well this model can be approximated by the linearized version in Section 4.3 of the paper.

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Supplement to "Contract Pricing in Consumer Credit Markets"

This appendix describes the details associated with the estimation of the model described Sections 4 and 5 of the paper. 

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Supplement to "Constrained Efficiency in the Neoclassical Growth Model with Uninsurable Idiosyncratic Shocks"

This zip file contains replication files for the manuscript

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Supplement to "Identification and Inference in Ascending Auctions with Correlated Private Values"

This supplement contains a full description of the estimators and their properties for the application in the paper.

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Supplement to "Identification and Inference in Ascending Auctions with Correlated Private Values"

This zip file contains the replication files for the manuscript.

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Supplement to "The Lucas Orchard"

This PDF contains the online appendix.

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Supplement to "The Lucas Orchard"

This zip file contains Mathematica notebooks that calculate the integral formulas in the two-, three-, and N-tree cases.

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Supplement to "The 2007 Subprime Market Crisis Through the Lens of European Central Bank Auctions for Short-Term Funds"

This zip file contains the replication files for the manuscript.

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Supplement to "The 2007 Subprime Market Crisis Through the Lens of European Central Bank Auctions for Short-Term Funds"

Description of the Iterative Algorithm, institutional background, results from the Long Term Refinancing Operations.

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Supplement to "Contract Structure, Risk Sharing, and Investment Choice"

This PDF contains the instructions for the joint liability game with imperfect monitoring (complete experimental instructions are contained in the replication files) and Figure A1.

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Supplement to "Contract Structure, Risk Sharing, and Investment Choice"

This file contains the replication files for the manuscript.

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Supplement to "Dynamic Product Positioning in Differentiated Product Markets: The Effect of Fees for Musical Performance Rights on the Commercial Radio Industry"

This zip file contains MATLAB code used to estimate and solve the model.  The file also contains data that can be used to estimate the parameters, although the share and revenue data has been permuted in accordance with my agreement with the company providing the data.

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