# Repeated Games with Incomplete Information

@inproceedings{Renault2009RepeatedGW, title={Repeated Games with Incomplete Information}, author={J{\'e}r{\^o}me Renault}, booktitle={Encyclopedia of Complexity and Systems Science}, year={2009} }

Glossary and Notation I. Definition of the Subject and its Importance II. Strategies, Payoffs, Value and Equilibria III. The standard model of Aumann and Maschler IV. Vector Payoffs and Approachability V. Zero-sum games with lack of information on both sides VI. Non zero-sum games with lack of information on one side VII. Non-observable actions VIII. Miscellaneous IX. Future directions Bibliography

## 356 Citations

On a Markov Game with One-Sided Information

- Mathematics, EconomicsOper. Res.
- 2010

We apply the average cost optimality equation to zero-sum Markov games by considering a simple game with one-sided incomplete information that generalizes an example of Aumann and Maschler [Aumann,…

On a Markov Game with One-Sided Incomplete Information

- Mathematics, Economics
- 2009

We apply the average cost optimality equation to zero-sum Markov games, by considering a simple game with one-sided incomplete information that generalizes an example of Aumann and Maschler (1995).…

Optimal strategies in repeated games with incomplete information: the dependent case

- Mathematics, Economics
- 2014

Using the duality techniques introduced by De Meyer (1996a, 1996b), De Meyer and Marino (2005) provided optimal strategies for both players in finitely repeated games with incomplete information on…

A Note on the Evaluation of Information in Zero-Sum Repeated Games

- Economics, Computer Science
- 2010

Communication and Cooperation in Repeated Games

- Economics
- 2017

We study the role of communication in repeated games with private monitoring. We first show that without communication, the set of Nash equilibrium payoffs in such games is a subset of the set of…

Knowing the Informed Player's Payoffs and Simple Play in Repeated Games

- Economics
- 2021

We revisit the classic model of two-player repeated games with undiscounted utility, observable actions, and one-sided incomplete information, and further assume the informed player has…

On a Continuous-Time Game with Incomplete Information

- MathematicsMath. Oper. Res.
- 2009

For zero-sum two-player continuous-time games with integral payoff and incomplete information on one side, the authors show that the optimal strategy of the informed player can be computed through an…

Repeated games with incomplete information and discounting

- Economics
- 2014

Abstract. We analyze discounted repeated games with incomplete information, such that the players' payoffs depend only on their own type (known-own payoff case). We describe an algorithm for finding…

The Comparison of Information Structures in Games: Bayes Correlated Equilibrium and Individual Sufficiency

- Economics
- 2013

We de…ne and characterize a notion of correlated equilibrium for games with incomplete information, which we call Bayes correlated equilibrium: The set of outcomes that can arise in Bayes Nash…

Games with Incomplete Information in Continuous Time and for Continuous Types

- Economics, MathematicsDyn. Games Appl.
- 2012

It is proved that the value function of this game is solution of an auxiliary optimization problem over a set of measure-valued processes and characterized as the viscosity solution of a special type of a Hamilton–Jacobi equation.

## References

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Introduction and Examples.- Games with Incomplete Information.- Repeated Games with Lack of Information on One Side.- Repeated Games with Lack of Information on Both Sides.- Stochastic Games.-…

3-player repeated games with lack of information on one side

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This work studies the existence of uniform equilibria for three-player repeated games with lack of information on one side and perfect observation and finds that for larger spaces of states, a completely revealing or joint plan equilibrium always exists.

Nonzero-Sum Two-Person Repeated Games with Incomplete Information

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Characterization of all equilibria of nonzero-sum two- person repeated games with incomplete information, in the standard one-sided information case, and the concept of a bi-martingale is introduced.

Stochastic Games with a Single Controller and Incomplete Information

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Stochastic games with incomplete information on one side are studied, and it is proved that if the informed player also controls the transitions, the game has a value, whereas if the uninformed player controls the transition, the max-min value as well as the min-max value exist, but they may differ.

Nonzero-Sum Two-Person Repeated Games with Incomplete Information and Known-Own Payoffs

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This paper deals with repeated games with incomplete information, where the uninformed player has complete knowledge of his own payoffs. This is a specific case of Hart′s model. We provide a…

Repeated Games, Duality and the Central Limit Theorem

- Mathematics, EconomicsMath. Oper. Res.
- 1996

Dual games are introduced that allow for the analysis of the “Markovian” behavior of the uninformed player, and to explicitly compute his optimal strategies, to explain the appearance of the normal density in the n-1/2-term of the asymptotic expansion of vn as a consequence of the Central Limit Theorem.

Equilibria in repeated games of incomplete information: The general symmetric case

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Abstract. Every two person repeated game of symmetric incomplete information, in which the signals sent at each stage to both players are identical and generated by a state and moves dependent…

Optimal strategies in repeated games with incomplete information

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The paper results in the construction of an optimal strategy for the uninformed player in the infinitely repeated game.

The Value of Two-Person Zero-Sum Repeated Games the extensive case

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The purpose of this article is to extend the results of J. F.Mertens and S.Zamir, The Value of Two-Person Zero-Sum Repeated Games with Lack of Information on Both Sides (Intern. Journal of Game…

Existence of optimal strategies in Markov games with incomplete information

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The existence of a value and optimal strategies is proved for the class of two-person repeated games where the state follows a Markov chain independently of players’ actions and at the beginning of…