Toward a Theory of Discounted Repeated Games with Imperfect Monitoring

Abreu, Dilip; Pearce, David; Stacchetti, Ennio

doi:10.2307/2938299

Cited by 984 publications

(889 citation statements)

References 18 publications

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“…The second major thrust involved the development of sophisticated repeated game-theoretic models of strategic interaction, which began with Shubik (1959), culminating in the major contributions of Fudenberg and Maskin (1986), Abreu et al (1990), Fudenberg et al (1994), Piccione (2002), Ely and Välimäki (2002), Bhaskar and Obara (2002) and others. While there is no question but these models have strongly advanced our understanding of the theory of social cooperation, the very fact these contributions prove "folk theorems" that sustain full-dimensional open sets of sequential equilibria virtually assure that these models will have poor dynamic qualities.…”

Section: Resultsmentioning

confidence: 99%

“…A quite different approach was needed to extend this to imperfect public information. The key step here was provided by the dynamic programming method of Abreu, Pearce and Stacchetti (1990), culminating in the definitive paper by Fudenberg, Levine and Maskin (1994) (hereafter FLM), who show that close to full cooperation can be attained for sufficiently patient agents, provided only that the information structure is sufficiently rich to detect accurately which agents appear to have defected (I say "appear" because the signal may be inaccurate). In this section I will outline the FLM analysis as applied to the model of cooperation laid out above and show why it does not solve the problem of cooperation.…”

Section: Cooperation Of Self-interested Agents With Publicmentioning

confidence: 99%

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Modeling cooperation among self-interested agents: a critique

Gintis

2004

The Journal of Socio-Economics

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Section: Resultsmentioning

confidence: 99%

Section: Cooperation Of Self-interested Agents With Publicmentioning

confidence: 99%

Modeling cooperation among self-interested agents: a critique

Gintis

2004

The Journal of Socio-Economics

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“…Examples of such games go back to Rubinstein (1979), Rubinstein andYaari (1983), andRadner (1985) with reference to principal-agent models and by Green and Porter (1984) with reference to oligopoly. More systematic analyses of games with imperfect public monitoring have been provided by Abreu et al (1990, , and Tomala (1998). These papers focus on perfect public equilibria, namely, equilibria in which each player uses only strategies that depend on the public signal and not on her private history.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore all these papers consider repeated games without discounting. Abreu et al (1990) consider pure strategy equilibria, keep the discoungt factor fixed, and do not analyze convergence theorem. impose a pair-wise identifiability condition that is not satisfied by our game.…”

Section: Introductionmentioning

confidence: 99%

Discounted and finitely repeated minority games with public signals

Renault¹,

Scarlatti²,

Scarsini³

2008

Mathematical Social Sciences

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We consider a repeated game where at each stage players simultaneously choose one of two rooms. The players who choose the less crowded room are rewarded with one euro. The players in the same room do not recognize each other, and between the stages only the current majority room is publicly announced, hence the game has imperfect public monitoring. An undiscounted version of this game was considered by Renault et al. (2005), who proved a folk theorem. Here we consider a discounted version and a finitely repeated version of the game, and we strengthen our previous result by showing that the set of equilibrium payoffs Hausdorff-converges to the feasible set as either the discount factor goes to one or the number of repetition goes to infinity. We show that the set of public equilibria for this game is strictly smaller than the set of private equilibria.

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“…More precisely, what do calibration (or estimation) results mean in the presence of in the presence of multiple equilibrium? 2 For example, say one perturbs the counterfactual parameter comparable to the old RE at the initial set of parameters? How about comparing the approximate RE under the new counterfactual parameters?…”

Section: Introductionmentioning

confidence: 99%

Which recursive equilibrium?

Mirman

Morand²,

Reffett

2010

Proceedings of the Behavioral and Quantitative Game Theory: Conference on Future Directions

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For simple versions of the Cass-Diamond growth model where the fundamental welfare theorems of economics fail, we prove the set of minimal state space recursive equilibrium (RE) is large, with multiple RE existing in multiple subclasses of functions. This situation remains the true even when uniqueness results are known, for both OLG and in…nity-lived agent versions of the model. This implies the set of Generalized Markov equilibrium (GME) is also large. We also provide explicit iterative procedures from computing particular RE in each subclass, with some procedures globally stable from a topological persective for particular RE when their domains are restricted. All iterative methods are order stable relative to perturbations of deep parameters. Finally, we construct an simple economy where existing correspondence-based methods for computing GME fails, and propose a new method that computes the set of GME as minimal state spaceWe thank Subir Chakrabarti, Ramu Gopolan, Takashi Kamihigashi, Rajnesh Mehra, Adrian Peralta-Alva, Ed Prescott, Manuel Santos, Yiannis Vailakis, × ukasz Woźny, and especially, Robert Becker for helpful discussions, as well as seminar participants at IU-PUI, ASU, and EWGET-2012 at Exeter for their helpful comments. Manjira Datta and Kevin Re¤ett thank the Center d'Economie de la Sorbonne (CES) and the Paris School of Economics for graciously arranging their visits during the Spring terms of both 2011 and 2012.y Manjira Datta, Department of Economics, Arizona State University; Leonard J. Mirman, Department of Economics, University of Virginia; Olivier F. Morand, Department of Economics, University of Connecticut; Kevin Re¤ett, Department of Economics, Arizona State University. We are in the process of rewriting this paper, so do not recirculate, as errors, types, etc. may remain; rather write the corresponding author at Kevin.Re¤ett@asu.edu for the most recent version. 1 RE using …xed points of the expanded set of state variables. Our results point to the complicated nature of the RE approximation problem even in simple macro models.

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Toward a Theory of Discounted Repeated Games with Imperfect Monitoring

Cited by 984 publications

References 18 publications

Modeling cooperation among self-interested agents: a critique

Modeling cooperation among self-interested agents: a critique

Discounted and finitely repeated minority games with public signals

Which recursive equilibrium?

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