Home Address:
  388 Whitney Avenue, #2
  New Haven, CT 06511

Telephone: (203) 777-5532 (home)

Game Theory
Microeconomic Theory
Development Economics

Game Theory
Microeconomics
Development Economics

2003 (Oral): Microeconomics, Development Economics
2002 (Written): Microeconomic Theory (with distinction), Macroeconomic Theory (with distinction)

Common Knowledge of Language and Iterative Admissibility in Cheap Talk Games

Professor Stephen Morris (chair)
Professor Dino Gerardi
Professor Benjamin Polak

May 2006

M. Phil., Economics, Yale University, 2004
M.A., Economics, Yale University, 2003
B.A., Accounting (major) and Economics (minor), National Taiwan University, 2001

Dissertation Fellowship, Yale University, 2005
Cowles Foundation Prize, Yale University, Summer 2004
Sasacawa Fund Fellowship, Yale University, 2003–2004
Graduate Student Fellowship, Yale University, 2001–2005
Summer Fellowship, Yale University, 2002 and 2003

Teaching Assistant, Introductory Microeconomics, Yale University, Spring 2005

Professor Stephen Morris
Center for Advanced Studies in the Behavioral
   Sciences
75 Alta Road
Stanford, CA 94305
Phone: (650) 321-2052
Fax: (650) 321-2052
Email: smorris@princeton.edu

Professor Benjamin Polak
Department of Economics
Yale University
PO Box 208268
New Haven, CT 06520-8268
Phone: (203) 432-9926
Fax: (203) 432-2128
Email: benjamin.polak@yale.edu

Professor Dino Gerardi
Department of Economics
Yale University
P.O. Box 208281
New Haven, CT 06520-8281
Phone: (203) 432-6519
Fax: (203) 432-6167
Email: donato.gerardi@yale.edu

In standard economic analysis of communication, all messages are treated symmetrically in that labeling does not matter. Thus, language is irrelevant. Two messages can swap names with each other without changing the strategy set or the equilibrium outcome. However, if players speak the same language, convention offers a way to interpreting messages. For example, suppose a man and a woman have to choose between going to the opera or to the boxing game. The woman can send a message beforehand. It is natural that two messages "OPERA" and "BOXING" uttered in a serious manner are either taken by their literal meanings or ignored for strategic reasons. It is counter-intuitive that the message "OPERA" would indicate going to the boxing game while the message "BOXING" would indicate going to the opera.

This dissertation proposes the following general framework to incorporate language. First, we model as a direct restriction on players’ strategies. We call this new game a game with language. Second, we characterize the prediction under iterative deletion of weakly dominated strategies. The language restriction does not assume information transmission a priori. It eliminates only strategies that are a replica of another strategy up to name swapping. We show that every equilibrium outcome in the original game is also an equilibrium outcome in the game with language. However, we demonstrate that breaking the symmetry between messages, combined with iterative deletion of weakly dominated strategies, can eliminate some of the outcome multiplicities prevalent in cheap talk games.

Our approach differs from Rabin (1990), Farrell (1993) and Zapater (1997) who also take the stand that messages have literal meanings. They assume in general that the literal meaning is believed if it is credible while differ in the credibility criteria they propose. The behavioral assumptions they impose on players’ belief differ from game to game because credibility is a strategic concern. In contrast, this dissertation takes language as a universal phenomenon independent of the specifics of a game while imposes no strategic assumptions. Other than equilibrium selection, it provides a systematic and structural approach to understanding implications of different properties of language.

Chapter I: Iterative Admissibility and Common Knowledge of Language in a Sender-Receiver Game

The first chapter applies the general framework to a classic sender-receiver game á la Crawford and Sobel (1982) (C-S). The sender is the only player with one-dimensional private information. The receiver, upon receiving the message, takes a one-dimensional action, which affects the utility of both. The sender always prefers a slightly higher action than the receiver. Messages can be seen as recommendations, since the sender talks in an attempt to affect the behavior of the receiver. By equating message space with action space, similarities between pairs of messages can be compared because the action space is on the real line. Two observations of natural language usage are imposed as assumptions: (i) there always exists a natural expression to induce a certain action, if that action is indeed inducible by some message; (ii) messages that are more different from each other induce actions that are weakly more different.

To analyze this game, we first take the normal form approach to this multi-stage game. We find that if the players’ interests are sufficiently aligned, this procedure eliminates outcomes where not much information is transmitted. Under certain conditions, all equilibrium outcomes but the most informative one are eliminated.

We then show by an example that the normal form procedure might allow the receiver to take a sub-optimal action after receiving some messages. In this example, our procedure yields a unique informative outcome while babbling is the unique equilibrium in the original game. We propose weak sequential rationality with language and an extensive form procedure to resolve the tension between language, iterative deletion of weakly dominated strategies and sequential rationality. The key is that messages that induce the same action will be seen by the sender as the same and hence should be seen as the same by the receiver. We show that the limiting set is nonempty under this iterative procedure. As in the normal form procedure, we find that the extensive form procedure eliminates the less informative outcomes.

Chapter II: Coordination and Language—Self-Signaling vs. Self-committing

To gauge credibility of messages in cheap talk games with complete information, Farrell (1988) and Aumann (1990) propose self-committing and self-signaling respectively. A message is self-committing if the speaker would have an incentive to carry it out if it is believed. A message is self-signaling if the speaker wants it to be believed if and only if he plans to carry it out. Morris and Shin (2002) transform cheap talk games about intended action into cheap talk games about private information and formalize the intuition behind self-committing and self-signaling conditions.

The second chapter tries to shed light on this issue by assuming a pre-existing rich language. It deals with one-sided communication in a complete information game without any assumption on the existence of a linear order on the action space. However, if the language is rich enough, there exists a partial similarity relation on the messages space. For example, "Most important of all, don’t burn the house. Then try not to fight with your brother. Hopefully, you’ll do your homework" is closer to the message "Most important of all, don’t burn the house. Then try not to fight with your brother. Hopefully, you’ll practice the piano" than to the message "Burn the house". The two observations on language in the previous paper can then be imposed in a similar fashion on every subset of messages where similarities can be compared. This language combined with normal form iterative admissibility yields full communication and perfect coordination being the unique outcome in perfect coordination games. However, if the Sender’s preference over the Receiver’s actions does not depend on the Sender’s intended action, my solution concept does not eliminate any strategy pair. This supports Aumann’s idea that self-signaling messages would be believed but messages that are only self-committing do not guarantee coordination.