A Nash Threats Folk Theorem for Repeated Games with Local Monitoring PDF Download
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Author: Krittanai Laohakunakorn
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Languages : en
Pages : 0
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We study sequential equilibrium payoffs of a repeated game with local interaction and local monitoring. An undirected network determines both the interaction and the monitoring structure. When players do not discount the future, a sequentially rational Nash threats folk theorem holds without any restrictions on the network structure. To prove this result, we construct strategies that support as a sequential equilibrium any payoff vector which is a convex combination (with rational weights) of stage game payoffs and is such that each player is strictly better off than under a Nash equilibrium of the stage game. No form of communication or coordination device is required. On the other hand, when players discount the future, the folk theorem cannot hold in our setting unless further restrictions are made either on payoffs or the network structure.
Author: Krittanai Laohakunakorn
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ISBN:
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Languages : en
Pages : 0
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Book Description
We study sequential equilibrium payoffs of a repeated game with local interaction and local monitoring. An undirected network determines both the interaction and the monitoring structure. When players do not discount the future, a sequentially rational Nash threats folk theorem holds without any restrictions on the network structure. To prove this result, we construct strategies that support as a sequential equilibrium any payoff vector which is a convex combination (with rational weights) of stage game payoffs and is such that each player is strictly better off than under a Nash equilibrium of the stage game. No form of communication or coordination device is required. On the other hand, when players discount the future, the folk theorem cannot hold in our setting unless further restrictions are made either on payoffs or the network structure.
Author: George J. Mailath
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Category : Game theory
Languages : en
Pages : 40
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Author: Johannes Hörner
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Languages : en
Pages : 0
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Languages : en
Pages :
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Author: Drew Fudenberg
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Languages : en
Pages :
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Author: Julio González Díaz
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Languages : en
Pages : 11
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Author: Dilip Abreu
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Category : Game theory
Languages : en
Pages : 11
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Author: Benjamin Bernard
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Category : Game theory
Languages : en
Pages : 184
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This thesis treats continuous-time models of repeated interactions with imperfect public monitoring. In such models, players do not directly observe each other's actions and instead see only the impacts of the chosen actions on the distribution of a random signal. Often, there are two reasons why this signal imperfectly reflects the chosen actions: (a) information is continuously available but it is noisy, or (b) events are observable but occur only at intermittent occasions. In a continuous-time setting, these two different types of information can be cleanly distinguished, where Brownian motion is used to model noise in the continuous information and Poisson processes indicate the arrival of informative events with an intensity that depends on players' actions. The first major result of this thesis is a folk theorem for continuous-time repeated games even when players receive only noisy information about past play. The folk theorem gives sufficient conditions such that players achieve asymptotic efficiency as they get arbitrarily patient. Because more outcomes are sustainable in equilibrium when more information is observed, this result also applies when players receive both aforementioned types of imperfect information. In the proof, we restrict ourselves to strategies that are adjusted only at identical copies of certain stopping times. This has two important implications: (1) despite the possibility of switching actions infinitesimally fast, players do not need to do so to attain asymptotic efficiency, and (2) continuous-time equilibria can be attained as limits of equilibria in discrete-time repeated games where the length of the time period is random, rather than fixed. The other main result of this thesis is a characterization of all payoffs that are attainable in equilibrium in such games with two finitely patient players. Relating optimal actions and incentives to the boundary of the equilibrium payoff set, we obtain a differential equation describing the curvature of the set at almost every point. The equilibrium payoff set is obtained from an iterative procedure, which is similar to that known for discrete-time repeated games but leads to an explicit characterization in our setting. Our result shows that the two types of information have drastically different impacts on the equilibrium payoff set. This is due to the fundamental difference in which the two types of information are used to provide incentives: while the continuous information can be used only to transfer value between players, the discontinuous information may be used to transfer or destroy value upon the arrival of an infrequent event. The quantitative nature of the result makes it possible to precisely measure the impact of abrupt information on the efficiency of players' payoffs in equilibrium. Thus, one can compare the value of additional information to the cost of procuring or providing it, which may lead to interesting applications in mechanism design and information disclosure.
Author: James W. Friedman
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Category :
Languages : en
Pages :
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Author: Olivier Compte
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Category :
Languages : en
Pages : 16
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Much of the repeated game literature is concerned with proving Folk Theorems. The logic of the exercise is to specify a particular game, and to explore for that game specification whether any given feasible (and individually rational) value vector can be an equilibrium outcome for some strategies when agents are sufficiently patient. A game specification includes a description of what agents observe at each stage. This is done by defining a monitoring structure, that is, a collection of probability distributions over the signals players receive (one distribution for each action profile players may play). Although this is simply meant to capture the fact that players don't directly observe the actions chosen by others, constructed equilibria often depend on players precisely knowing these distributions, somewhat unrealistic in most problems of interest. We revisit the classic Folk Theorem for games with imperfect public monitoring, asking that incentive conditions hold not only for a precisely defined monitoring structure, but also for a ball of monitoring structures containing it. We show that efficiency and incentives are no longer compatible.
