EDITORS: Benz, Anton; Jaeger, Gerhard; Van Rooij, Robert
TITLE: Game Theory and Pragmatics
PUBLISHER: Palgrave Macmillan
Eric McCready, Department of English Language and Literature,
Aoyama Gakuin University
This book is the first book-length collection of papers available on the
rapidly developing field of game-theoretic pragmatics, which uses
techniques from game theory to characterize pragmatic phenomena.
This collection includes 10 papers. The first, by the editors, is an
introduction to game theory for linguists; since game-theoretic analysis
involves techniques from utility and decision theory, the authors begin
by giving a brief introduction to these areas, and move directly into a
discussion of classical game theory. The chapter closes with the
basics of evolutionary game theory. The chapter is extremely clear
and aimed directly at linguists, and the reader that follows the
discussion here is well-equipped to read the majority of the papers in
the rest of the volume; conversely, the reader without something
roughly equivalent to the background given in this chapter will have
trouble understanding what is going on.
The second chapter, 'Saying and Meaning: Cheap Talk and
Credibility', by Robert Stalnaker, considers the notion of credibility in
communication by making use of signalling games. Stalnaker provides
a way of characterizing credibility within this class of games and
connects this characterization to the Gricean notion of intention in
communication. This paper has several typos, most non-serious; the
only one that caused real problems for me was a missing reference (to
a paper by Robert Farrell), which was unfortunate. The reason for
bringing this up is that it was atypical for the volume, which was in
general nearly free of editing errors.
Next is Prashant Parikh's contribution, 'Pragmatics and Games of
Partial Information.' In it, Parikh discusses his games of partial
information as an extension of signalling games. He also suggests, in
the latter part of his chapter, that these games can be used to model
how solution concepts are selected (because in some situations
certain equilibria may be better than others); this selection process
might be modelled as a sequence of games, culminating in the game
that models actual utterance interpretation.
The fourth chapter, Nicholas Allott's 'Game Theory and
Communication,' discusses some assumptions of game-theoretic
pragmatics from the perspective of relevance theory. Allott takes
Parikh's (e.g. 2001) analysis as a starting point and argues that
augmenting it with certain concepts of relevance theory improves the
predictions of the model and also gives it broader application.
The above chapters are theoretical in nature and are largely
concerned with foundational issues. The following chapters concern
themselves with particular linguistic phenomena, and so are in a
sense more empirically oriented. Chapter 5, by Robert van Rooij and
Merlijn Sevenster, provides an analysis of 'risky speech', speech
which is risky in the sense that it admits misunderstanding. Examples
are underspecified utterances (extensively considered also by Parikh)
and indirect speech acts, where the literal content is largely divorced
from what the speaker intends the hearer to recover. The authors
analyze such utterances by introducing a notion of risky play which
comes with a cost. The end of the chapter extends this analysis to
Chapter 6, entitled 'Pragmatic Reasoning, Defaults and Discourse
Structure,' is by Nicholas Asher and Madison Williams. [I should note
for the record that one of these authors supervised my dissertation. --
EMcC] These authors explore the question of how the pragmatic
inferences stemming from semantic information develop: why do we
reason about utterances in just the way we do? The answer, for the
authors, comes in a dynamic coordination that arises through multiple
game iterations. The way coordination is 'agreed' on is modelled in a
dynamic version of Variable Frame Theory (Bacharach 1993).
Next, Anton Benz's chapter is on 'Utility and Relevance of Answers.'
Benz begins by laying out the typology of question answers:
exhaustive answers, mention-some answers, and partial answers. He
then provides a game-theoretic model for calculating the utility of a
given answer; in this model, no notion of relevance must be assumed.
Instead, agents are assumed to work to maximize expected payoffs:
i.e. they are Bayesian utility maximizers. Benz then shows
(convincingly in my view) that relevance-based measures cannot be
sufficient to model answerhood. The basic reason is that pure
relevance measures (at least as formulated up to now in the linguistic
literature) make reference only to the preferences of a single agent.
This is a very suggestive and interesting result.
In Chapter 8 Kris de Jaegher discusses 'Game-Theoretic Grounding.'
Here, de Jaegher shows that the basic notion of grounding (Traum
1994) can be given a game-theoretic characterization; he does this by
making use of a simple communication game called the electronic mail
game. This game introduces a coordination problem which agents can
then work to solve. de Jaegher then shows that the various equilibria
of (his variant of) this game corresponds to the different sorts of
grounding shown to exist by Traum. This result is formally proved in
the final section.
Chapter 9 'A Game Theoretic Approach to the Pragmatics of Debate'
by Jacob Glazer and Ariel Rubenstein describes what one would
guess from the title. Specifically, Glazer and Rubenstein set out to
explain what strategies are used by listeners to judge the winner of a
debate. The authors first show that the form of the argument makes a
difference; second, they show that no method is foolproof. The end of
the paper makes a specific connection to language, showing that the
strategy space depends in part on the form of the language used to
specify the solutions.
The last paper in the volume is 'On the Evolutionary Dynamics of
Meaning-Word Associations' by Tom Lenaerts and Bart de Vylder.
This chapter is the only one that makes use of evolutionary game
theory (EGT). Here it is used to show how particular meanings can be
fixed to particular signals, in the context of an experiment involving a
sequence of 'naming games' in which one player picks a signal from a
given set to describe a meaning and the other player tries to recover
the meaning. The authors show that, given the right kind of replicator
equations, meanings are consistently associated with signals in a
successful way. This chapter requires more mathematical
sophistication than the others, which is perhaps a result of the use of
EGT. The reader with no experience of game theory (or without
proficiency in calculus) might have a difficult time understanding some
of the exposition, even after reading the introductory chapter. I think
this is the only chapter that has this property, again probably because
of the use of EGT.
This book can only be described as exciting. The game-theoretic
approach to pragmatics is an extremely interesting and useful one,
and is one that is really only beginning to be explored in detail. But
one can already find analyses of such phenomena as Gricean
inference and exhaustification within the framework; this sort of data
has in the past resisted formalization, but serious progress is being
made. One of the reasons this book is welcome is therefore that it
collects the state of the art (or at least a large subset thereof) into a
single place. One other reason is the introduction: for people without a
background in game theory, which is probably most linguists, it is
extremely useful to have an introduction to game theory around that
takes the concerns of linguists into account. Another nice feature of
the introduction is that it is almost completely self-contained: unlike, for
instance, game theory texts aimed at economists, no special
background in mathematics is assumed beyond an understanding of
basic formal logic. Thus the book is worth acquiring for the
introduction alone. But I don't mean to sell the papers short by any
means. They all present interesting results, as one can gather from
the summaries above, although these results come on a number of
different levels. As one might expect from an emerging field of study,
there is not yet a consensus about what the basic conceptualization of
the field should be; the first papers in the volume perhaps speak to
these concerns more than they do to the analysis of empirical data.
From this perspective the middle group of papers might be more
useful for the working pragmaticist. But I would recommend this book
very highly to anyone interested in this recent approach to pragmatics,
or to formal accounts of pragmatic phenomena in general.
Bacharach, M. 1993. Variable universe games. In K. Binmore, A.
Kirman and P. Tani, eds., Frontiers of Game Theory, Cambridge MA:
Parikh, P. 2001. The Use of Language. Stanford: CSLI.
Traum, D. R. 1994. A Computational Theory of Grounding in Natural
Language Conversation. Ph.D Thesis, University of Rochester.