Nancy L. Schwartz Lecture ECONOMICS AND LANGUAGE ARIEL RUBINSTEIN Delivered May 27, 1998, at the Kellogg Graduate School of Management Northwestern University 2001 Sheridan Road Evanston, Illinois NANCY L. SCHWARTZ A dedicated scholar and teacher, Nancy Schwartz was the Morrison Professor of Decision Sciences, Kellogg’s first female faculty member appointed to an endowed chair. She joined Kellogg in 1970, chaired the Department of Managerial Economics and Decision Sciences and served as director of the school’s doctoral program until her death in 1981. Unwavering in her dedication to academic excel- lence, she published more than 40 papers and co-authored two books. At the time of her death she was associate editor of Econometrica, on the board of editors of the American Economic Review and on the governing councils of the American Economic Association and the Institute of Management Sciences. The Nancy L. Schwartz Memorial Lecture series was established by her family, colleagues and friends in tribute to her memory. The lectures pres- ent issues of fundamental importance in current economic theory. 1 ARIEL RUBINSTEIN Ariel Rubinstein is the Salzberg Chair professor of economics at Tel-Aviv University, where he has been teaching since 1990, and a professor of eco- nomics at Princeton University, where he has been teaching since 1991. He received his Ph.D. in eco- nomics from the Hebrew University in 1979, with earlier degrees in mathematics and economics from the same institution. His past teaching and research affiliations include The Hebrew University, Nuffield College (Oxford), Bell Laboratories, the London School of Economics, the University of Chicago, the University of Pennsylvania, Columbia University, New York University, and the Russell- Sage Foundation. Professor Rubinstein is a Fellow of the Israeli Academy of Sciences and of the Econometric Society, and a foreign honorary member of the American Academy of Arts and Sciences and of the American Economic Association. He has delivered major invited lectures at universities and congresses around the world including the Walras-Bowley Lecture of the Econometric Society, and has served as editor for a large number of publications includ- ing Econometrica, Journal of Economic Theory, Review of Economic Studies, and Games and Economic Behavior. An author of three books and more than 60 research papers, Professor Rubinstein is one of the world’s leading researchers in the areas of econom- ics and game theory. He has done path-breaking work on dynamic strategic interaction, bargaining, interactive epistemology, and bounded rationality, and his papers are published in the leading journals of economics, decision theory and applied mathe- matics. 2 ACKNOWLEDGEMENTS Parts of this lecture are based on my Churchill Lectures delivered at Cambridge, England, in May 1996, and which will eventually be published by Cambridge University Press. Chapter 2 of this lec- ture is based on Rubinstein (1996) and Chapter 3 is based on Glazer and Rubinstein (1997). I would like to thank Kobi Glazer for permitting me to use our joint paper for this lecture and to Ehud Kalai and Bart Lipman for their comments. TABLE OF CONTENTS Chapter One: Economics and Language . .4 1.1 A Personal Note 1.2 Economics and Language Chapter Two: The Functionality of Properties of Binary Relations . .7 2.1 Binary Relations 2.2 Indication-friendliness 2.3 Informativeness Chapter Three: Strategic Considerations in Pragmatics . .14 3.1 Grice’s Principles and Game Theory 3.2 Debates 3.3 A Model References . .24 3 ECONOMICS AND LANGUAGE Chapter One: Economics and Language 1.1 A Personal Note The psychologist Joel Davitz once wrote: “I suspect that most research in the social sciences has roots somewhere in the personal life of the researcher, though these roots are rarely reported in published papers.” (Davitz, 1976). The first part of this state- ment is definitely true about this lecture. Although I work in several fields in economics and game the- ory, all my academic research has been motivated by my childhood desire to understand the way that people argue. In high school, I wanted to study logic. The main reason was that I thought that it would be useful for the political debates, which I was planning to be involved in or in the legal bat- tles against evil, which I hoped to conduct after becoming a solicitor. Unfortunately, I became neither a lawyer nor a politician. In the meantime, I came to understand that logic is not a very useful tool in those areas in any case…. But I continued to explore formal models of game theory and economic theory, never sustaining any desire to predict human behavior, never wishing to anticipate the stock prices, and never having illusions about capturing all of reality in one tiny model. I simply kept being interested in the arguments people bring in debates and in the reasons motivating decisions. And, I am still puz- zled, even fascinated, by the magic of the links between the formal language of the mathematical models and natural language. This brings me to the subject of this lecture, “Economics and Language.” 1.2 Economics and Language The title of the lecture may be misleading. The caption “economics and language” is somewhat 4 “attractive” but it is also vague. As a heading, it cov- ers many different subjects that I will not raise here. For example, I will not talk about the language of decision-makers. When decision-makers make deliberate choices, they often formulate their judg- ments and decisions in words. Were I to speak on this domain, I would present an investigation of the assumption that decision-makers formulate their considerations by using some language. This is a particularly attractive assumption when the “decision maker” is a collective of individuals but it is also appealing when we refer to a decision-maker as an individual. The formalization of this assump- tion requires the tools of mathematical logic. The analytical task would be to identify the constraints on the set of preferences induced from natural restrictions on the language used by the decision- maker to define his preferences. For example, such constraints make the lexicographic preferences much more appealing when compared to a stan- dard textbook consumer’s utility function, such as log(x1+1)x2. But today, I leave this subject aside. And I will not talk about the language of econom- ics. Much can be said about the rhetoric of eco- nomic theory and game theory. An economic model is not just a mathematical model. It is a com- bination of a mathematical model and an interpre- tation. The investigation of the language we use for attaching interpretations to economic models is, in my opinion, of much interest. If I were to discuss this subject here, I would try to argue that the rhet- oric of game theory is actually misleading in creat- ing an impression that it is much more “useful” than it actually is. In particular, I would try to per- suade you that basic game theoretical notion of “strategy” is modeled in a way quite different from what is suggested by its meaning in natural language and that the term “solution” carries a deterministic flavor which is not appropriate. But, I will not discuss here the “language of eco- nomic agents” and nor the “language of econom- ics.” I will make do with topics within a research 5 domain, which is probably far away from tradi- tional economics: “economics about language.” Why would economic-type thinking be relevant to some linguistic issues? Economic theory is an attempt to explain regularities in human interac- tion and the most fundamental nonphysical regu- larity in human interaction is our natural language. In economic theory we have studied, quite care- fully, issues concerning the design of social systems; language is partially a mechanism of communica- tion. Economics tries to explain social institutions as regularities derived from optimizing certain functions which they serve; one can try to use this method regarding language as well. In this lecture I will try to demonstrate what we, economists, can do in this area by presenting two short investiga- tions in which we use “economic” reasoning to address linguistic issues. And before starting, I owe my audience an apology. Browsing through the literature while preparing these lectures, I came across a short article written by Jacob Marshack called, “Economics of Language” (Marschak, 1965). The article starts with a description of a discussion between engi- neers and psychologists regarding the design of the communication system of a small fighter plane. After the presentation, Marschak states: “The pres- ent writer…apologizes to those of his fellow econ- omists who might prefer to define their field more narrowly, and who would object to…identification of economics with the search of optimality in fields extending beyond, though including, the produc- tion and distribution of marketable goods.” He then continues: “Being ignorant of linguistics, he apologizes even more humbly to those linguists who would scorn the designation of a simple dial- and-buttons systems a language.” I believe that like Marschak, I am not really apologizing to econo- mists…but like Marschak, I do feel apologetic toward linguists and philosophers of language because my knowledge of this territory is much too limited. 6 Chapter Two: The Functionality of Properties of Binary Relations 2.1 Binary Relations A binary relation on a set Ω specifies a connection between elements within Ω. Such binary relations are common in natural language. For example, “person x knows person y,” “tree x is to the right of tree y,” “picture x is similar to picture y,” “chair x and chair y have the same color” and so on. I will avoid binary relations like “Professor x works for university y” or “the social security number of x is y,” which specify “relationships” between elements which naturally belong to two distinct sets.