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Essays on Communication and Information in Game Theory.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Essays on Communication and Information in Game Theory./
Author:	Lim, Seunghwan.
Description:	1 online resource (108 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-04, Section: B.
Contained By:	Dissertations Abstracts International85-04B.
Subject:	Probability. -
Online resource:	click for full text (PQDT)
ISBN:	9798380470247

Essays on Communication and Information in Game Theory.
Lim, Seunghwan.

Essays on Communication and Information in Game Theory. - 1 online resource (108 pages)

Source: Dissertations Abstracts International, Volume: 85-04, Section: B.

Thesis (Ph.D.)--Stanford University, 2023.

Includes bibliographical references

In this dissertation, I investigate the role of information and communication in game theory. The dissertation consists of three chapters.The first chapter is co-authored with Takuo Sugaya, and we prove a folk theorem in two-player repeated games with public monitoring using the individual full-rank condition. The individual full-rank condition allows players to statistically distinguish a player's action holding fixed the other player's action. Under this condition, we may not be able to directly identify the pair of actions played in each period and punish the player who is likely to have deviated. We build an equilibrium where the players first coordinate on their actions, individually review the other player using noisy signals, and reward or punish the other player based on the history of signals and her own actions. One of the challenges of this construction is the problem of higher-order belief. The coordination and reviews are conducted through a noisy signal, and a player's optimal strategy depends in turn on the other player's belief about the coordinated strategy and her history of actions. This chain of beliefs can be extended indefinitely, and a strategy profile can easily be intractable, if not infeasible as an equilibrium. In this chapter, we use the idea of "keeping each other in the dark" to build strategies where the players can coordinate on their actions and review each other based on their own histories. The players intentionally mix noisy actions with their prescribed actions to cause the other player to think that miscoordination is most likely to have happened because of this noise. A player makes the other player indifferent among all actions after playing the noisy action too often, so the other player does not need to change his action although he detects miscoordination. In this setup, we only use the players' actions without public randomization or cheap-talk communication.The second chapter is about refinement in signaling games with cheap-talk communication. In many applications of signaling games, the sender can both play costly actions and send costless messages to the receiver. Introducing cheap-talk messages to the model can expand the set of equilibria in this game. Given a finite signaling game, I define a signaling game with cheap talk by adding costless messages to the sender's action space. I first find a finite message space that allows all possible equilibrium outcomes to be found in a tractable way, then define a forward-induction refinement of equilibria based on cheap-talk messages. Many forward-induction refinements use the idea that a type of sender can play an action and simultaneously make a speech about the subset oftypes to which she belongs. Different refinements arise based on different assumptions about which messages are credible to the receiver. I define a message called a strongly self-signaling set, which defines a binary partition over the type space such that for every type, the worst-case equilibrium payoff when the receiver believes that the type belongs to its own subset is larger than the best-case equilibrium payoff when the receiver believes otherwise. I argue that this message is credible when all types in the subset can be better off by sending this message because types in the other subset have no incentive to imitate this message. When there is no such strongly self-signaling subset, we say that the equilibrium is not vulnerable to a partitional message. I prove that, in every finite signaling game with cheap talk, there exists an equilibrium that is not vulnerable to a partitional message. We apply this refinement to various signaling games and compare them to other refinements, especially those implied by stability.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798380470247Subjects--Topical Terms:

667790
Probability.
Index Terms--Genre/Form:

554714
Electronic books.

Essays on Communication and Information in Game Theory.
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504 $a Includes bibliographical references
520 $a In this dissertation, I investigate the role of information and communication in game theory. The dissertation consists of three chapters.The first chapter is co-authored with Takuo Sugaya, and we prove a folk theorem in two-player repeated games with public monitoring using the individual full-rank condition. The individual full-rank condition allows players to statistically distinguish a player's action holding fixed the other player's action. Under this condition, we may not be able to directly identify the pair of actions played in each period and punish the player who is likely to have deviated. We build an equilibrium where the players first coordinate on their actions, individually review the other player using noisy signals, and reward or punish the other player based on the history of signals and her own actions. One of the challenges of this construction is the problem of higher-order belief. The coordination and reviews are conducted through a noisy signal, and a player's optimal strategy depends in turn on the other player's belief about the coordinated strategy and her history of actions. This chain of beliefs can be extended indefinitely, and a strategy profile can easily be intractable, if not infeasible as an equilibrium. In this chapter, we use the idea of "keeping each other in the dark" to build strategies where the players can coordinate on their actions and review each other based on their own histories. The players intentionally mix noisy actions with their prescribed actions to cause the other player to think that miscoordination is most likely to have happened because of this noise. A player makes the other player indifferent among all actions after playing the noisy action too often, so the other player does not need to change his action although he detects miscoordination. In this setup, we only use the players' actions without public randomization or cheap-talk communication.The second chapter is about refinement in signaling games with cheap-talk communication. In many applications of signaling games, the sender can both play costly actions and send costless messages to the receiver. Introducing cheap-talk messages to the model can expand the set of equilibria in this game. Given a finite signaling game, I define a signaling game with cheap talk by adding costless messages to the sender's action space. I first find a finite message space that allows all possible equilibrium outcomes to be found in a tractable way, then define a forward-induction refinement of equilibria based on cheap-talk messages. Many forward-induction refinements use the idea that a type of sender can play an action and simultaneously make a speech about the subset oftypes to which she belongs. Different refinements arise based on different assumptions about which messages are credible to the receiver. I define a message called a strongly self-signaling set, which defines a binary partition over the type space such that for every type, the worst-case equilibrium payoff when the receiver believes that the type belongs to its own subset is larger than the best-case equilibrium payoff when the receiver believes otherwise. I argue that this message is credible when all types in the subset can be better off by sending this message because types in the other subset have no incentive to imitate this message. When there is no such strongly self-signaling subset, we say that the equilibrium is not vulnerable to a partitional message. I prove that, in every finite signaling game with cheap talk, there exists an equilibrium that is not vulnerable to a partitional message. We apply this refinement to various signaling games and compare them to other refinements, especially those implied by stability.
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538 $a Mode of access: World Wide Web
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