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REVIEW ARTICLE
published: 18 March 2014
doi: 10.3389/fpsyg.2014.00226
Conceptual and empirical problems with game theoretic
approaches to language evolution
Jeffrey Watumull 1* and Marc D. Hauser 2
1Department of Theoretical and Applied Linguistics, University of Cambridge, Cambridge, UK
2Risk-Eraser, West Falmouth, MA, USA
Edited by:
Andrea Moro, Institute for Advanced
Study of Pavia (IUSS), Italy
Reviewed by:
Juan M. Toro, ICREA – University
Pompeu Fabra, Spain
Ur Shlonsky, Université de Genève,
Switzerland
*Correspondence:
Jeffrey Watumull, Department of
Theoretical and Applied Linguistics,
University of Cambridge, Sidgwick
Avenue, Cambridge CB3 9DA, UK
e-mail: jw647@cam.ac.uk
The importance of game theoretic models to evolutionary theory has been in formulating
elegant equations that specify the strategies to be played and the conditions to be satisfied
for particular traits to evolve. These models, in conjunction with experimental tests of
their predictions, have successfully described and explained the costs and benefits of
varying strategies and the dynamics for establishing equilibria in a number of evolutionary
scenarios, including especially cooperation, mating, and aggression. Over the past decade
or so, game theory has been applied to model the evolution of language. In contrast to the
aforementioned scenarios, however, we argue that these models are problematic due to
conceptual confusions and empirical difficiences. In particular, these models conflate the
comptutations and representations of our language faculty (mechanism) with its utility in
communication (function); model languages as having different fitness functions for which
there is no evidence; depend on assumptions for the starting state of the system, thereby
begging the question of how these systems evolved; and to date, have generated no
empirical studies at all. Game theoretic models of language evolution have therefore failed
to advance how or why language evolved, or why it has the particular representations and
computations that it does. We conclude with some brief suggestions for how this situation
might be ameliorated, enabling this important theoretical tool to make substantive empirical
contributions.
Keywords: language evolution, evolutionary game theory, communication, universal grammar, models, theoretical
INTRODUCTION
Modeling has played a fundamental role in evolutionary biology,
including the development of simple yet elegant equations that
make predictions about the conditions for the evolution of altru-
ism (Hamilton’s equation: C <rB, C =cost of the behavior,
r=degree of genetic relatedness, B =benefit of the behavior)
to more complicated equations that explore the dynamics of dif-
ferent selection pressures in the context of different population
sizes and migration rates. A fundamental approach for model-
ing the evolution of behavior is the game theoretic perspective
developed by Maynard Smith (1982). Borrowing from economics,
Maynard Smith readily saw that a number of significant interac-
tions in animals, including fighting, mating, and predator–prey
interactions could be modeled as games, clarifying the costs and
benefits of different strategies, and the time course for estab-
lishing equilibrium, among other issues. This approach not only
helped clarify many important conceptual problems, but helped
with the design of empirical experiments centered on these behav-
iors. Over the past three decades, game theoretic models have
made fundamental contributions to our understanding of coop-
eration in humans and other animals, with models closely tied
to empirical tests (Doebeli and Hauert, 2005). Game theoretic
models have also been developed to understand the evolution of
language. But, we argue, these models have not contributed to
conceptual clarity and nor have they been tied to any empiri-
cal tests. As such, they have not illuminated our understanding
of how language evolved or why it has the particular represen-
tational and computational structure that it does. This state of
affairs can, however, be remedied, a point that we return to in our
conclusion.
GAME THEORETIC MODELS
By “evolution of language” or “language evolution” we mean the
biological evolution of the neurocognitive system of linguistic
competence – the system of representations and computations
that enables our syntax, semantics, phonology, and the interfaces
between them. Given the limitations of comparative research and
the paucity of evidence from paleoarcheology and genetics for
this system, it would seem that game theoretic modeling could
be one of the best (or only viable) approaches to understand-
ing the evolution of language. As a formal system of rules and
representations, language could be formalized and understood
within a more general abstract model of evolution. The merits
of such a model would be many: the explicitness and manip-
ulability of conditions and relations generating consequences to
exploring the robustness and empirical plausibility of the modeled
system. With such clarification, researchers could then investi-
gate how closely nature actually approximates these idealizations.
Indeed it was the expectation of such benefits in the domain
of population genetics that motivated Lewontin (1961) to build
evolutionary game theory on the mathematical foundations estab-
lished by Fisher (1930),von Neumann and Morgenstern (1944),
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Watumull and Hauser Game theory and language evolution
among others. As Lewontin noted, the behaviors of idealized
agents – humans and nonhumans (e.g., animals, bacteria, plants,
genes, etc.) – engaged in competition are governed by or mea-
sured against general rational principles that necessarily determine
winning/losing strategies in specific idealized circumstances. The
classic models identified rigorously formulable and empirically
verifiable stable strategies approximated by different organisms.
This contrasts with modern models, which simulate the “dynamic”
evolution of populations of strategies rather than strategy-using
individuals.
DEFINITIONS AND DISTINCTIONS
Dynamic computational simulations generate insights insofar as
the simulated system is rigorously defined in an abstract math-
ematical theory. For instance, the important game theoretic
simulations on the evolution of cooperation run by Axelrod and
Hamilton (1981) were based on mathematically idealized sce-
narios of animal conflict (Maynard Smith and Price, 1973) and
reciprocation (Hamilton, 1964;Trivers, 1971). Such mathematical
foundations are nonexistent in computational models of the evo-
lution of language for the simple reason that most of language has
yet to be sufficiently idealized and mathematized. For those aspects
of language that have been adequately formalized, game theoretic
models of syntax (Ristad, 1993) and genetic algorithms as acquisi-
tion mechanisms (Clark and Roberts, 1993) have been successful
in explaining properties of the design of the language faculty, with
no pretense to explain its use in behaviors. This, we submit, is
the correct approach logically, theoretically, and methodologi-
cally. Logically, identifying the mechanism, even if not understood
completely, must precede and direct investigation of its functions.
Theoretically,if we are interested in the biological basis of linguistic
competence, language needs to be modeled as a property of indi-
viduals, which are subject to biological evolution, not as a set of
strategies, which are not. Moreover, as some have argued, the use
of language is ancillary to its design (Chomsky, 2013). Method-
ologically, there are virtually infinitely many uses of language so
that zooming in on one is in some sense arbitrary and zooming
out to all is impractical. And of course as a mechanism evolves, its
uses can change (Gould and Vrba, 1982). Nevertheless evolution-
ary simulations of language have all but exclusively modeled use.
In particular, these models assume that the language phenotype
emerges in the dynamics of communication. This assumption, we
suggest, is unfounded.
LANGUAGE AND COMMUNICATION
Language cannot, and should not be reduced to communication.
Even if it could, however, the computational model would be
vacuous pending a mathematical theory of communication. Shan-
non’s (1948) mathematical theory of communication is a start,
but the explanatory power and formal beauty of that theory is in
its abstraction from meaning so as to define and quantify infor-
mation. This information theoretic notion of communication is
obviously important to – though obviously far from sufficient
for – understanding linguistic communication, and it is not the
notion assumed in evolutionary simulations of language. In these
models, the transmission of meaning is the raison d’être of com-
munication; game theoretically, agents receive positive payoffs for
successful communication of referents (Nowak and Komarova,
2001). This is problematic because there is no mathematical the-
ory of communication in this sense to be modeled; nor is this sense
sufficient to encompass our communicativeuse of language, which
is boundless: “We inform, we request, we persuade, we interrogate,
we orate, and sometimes we just schmooze” (Pinker, 2007). There
are simply too many strategies to model: agents communicate to
trade knowhow (Pinker and Bloom, 1990), deceive (Dawkins and
Krebs, 1978), negotiate social relations (Dunbar, 1996), to list but
a few. Many such uses surely were adaptive, although establishing
this empirically for our hominin ancestors is surely impossible,
for we cannot travel back to listen (or look) in. Computer mod-
els of these strategies show how they could have proliferated,
but whether this corresponds to reality is unknown and prob-
ably unknowable for the simple reason that there are no viable
empirical tests. Furthermore, and fundamentally, none of these
uses explains the emergence of the system to be so used. In short, it
may be that“computer models are good for demonstrations of how
different uses of language provide benefit – but they are not much
good for proving why and how language evolved” (Livingstone,
2003).
A game theoretic model – verified experimentally – can, for
instance, successfully demonstrate the costs/benefits of particular
pragmatic acts (Lee and Pinker, 2010), but nothing so theoretically
rigorous and empirically robust has been formulated for language
in general, and in particular, for the underlying competence of
representations and computations. Importantly, we do not know
how canalized (genetically, epigenetically, anatomically) the evolu-
tion of this machinery was, so that game theory – which assumes
a sizable set of possibilities – may be largely inapplicable. This
fact has prevented modeling attempts to explain the evolution of
language.
FLAWS IN THE STANDARD GAME THEORY MODEL OF
LANGUAGE EVOLUTION
A standard game theoretic model of language (Nowak and
Komarova, 2001;Nowak et al., 2002) is formatted as a set of matri-
ces. The first “competence” matrix defines a language Lasasetof
sound-meaning associations. This is already questionable because
linguistic competence is not a set of structures but rather the mech-
anism generative of such structures (Watumull, 2012). Two more
matrices, Pand Q, represent “performance,”w ith Pthe set of prob-
abilities that a speaker of LIuses sound jto communicate meaning
i, and Qthe set of probabilities that a hearer with knowledge of LJ
(not necessarily distinct from LI) understands sound jas mean-
ing i. Needless to say, the specification of these probabilities is
arbitrary (and biases the outcomes) and empirically empty absent
any testable mapping to reality. It is also questionable to stipulate
the fidelity of transmission of meaning as the purpose of commu-
nication and language (the metric of its “success”) for there are
as many models – many of which are formally and empirically
solid (Pinker et al., 2008) – showing ambiguity to be a success-
ful communicative strategy built into our pragmatic competence.
And, to reiterate, the equation of communication with language
is a conflation of function with mechanism: playing any of these
games presupposes the linguistic machinery to be explained in the
evolutionary theory.
Frontiers in Psychology |Language Sciences March 2014 |Volume 5 |Article 226 |2
Watumull and Hauser Game theory and language evolution
Returning to the standard model, σis defined (over all pos-
sible meanings) as the probability that sound jdoes in fact
communicate meaning i. Again, no empirical basis is given for
specifying one probability rather than another; different proba-
bilities yield different but equally (im)plausible – hence equally
(un)interesting – results. The final probability that a speaker of LI
produces a sound jdecoded with meaning iby hearer with LJis
defined aIJ =ijσpijqij. From this foundation, the game theo-
retic payoff between LIand LJis defined as FIJ =1/2(aIJ +aJI).
The “communicative payoff ” of LIis thus FII =aII . The com-
municative payoff is a number kbetween 0 and 1, k<1 if the
signal is ambiguous or in some way impoverished. The higher
the communicative payoff of a language, the higher its “fitness”
in that a language is transmitted generation to generation in pro-
portion to its communicative payoff. But, since fitness applies
to biological entities, not sound-meaning pairs, this method-
ological approach is highly questionable. In these models, more
offspring are born to parents with more successful languages.
However, this presupposes the evolution of an acquisition device
enabling sophisticated imitation, which we know is unique to
humans among primates (Petkov and Jarvis, 2012). So once
again, the models might demonstrate how systems proliferate, but
not how they emerged – the fundamental question of language
evolution.
Finally, following Chomsky (1965) and Gold (1967),someof
these models do accept the need to explain the evolution of the
genetic components of grammar, but mistake “the crucial ques-
tion” to be “what makes a population of speakers converge to a
coherent grammatical system. In other words, what are the con-
ditions (grammar) has to fulfill for a population of individuals to
evolve coherent communication?” (Nowak and Komarova, 2001).
These are the wrong questions for modeling the evolution of the
language faculty. Rather, we must ask what emerged in the brain to
enable the representational and computational bases of language?
This question is distinct from that of the conditions this system had
to satisfy to be learnable, usable, and ultimately, genetically fixated
in a population. Communication was probably very important
in the fixation process, but as with work on animal communica-
tion (Hauser, 1996), we need extensive empirical studies to even
approach understanding.
CONCLUSION
In constrast to the substantial contribution of evolutionary game
theory to understanding cooperation, mating behavior, and
aggression, its contribution to understanding language evolution
has been substantially less. This is due to its (1) failure to distin-
guish between the mechanisms that constitute language and how
such mechanisms enable communicative expression; and its (2)
inability to generate a single empirical study to either support or
reject its predictions or assumptions. Given that we lack organisms
or situations in which such tests could be carried out, we suggest
that it will be exceedingly difficult for game theory to advance
our understanding of how language evolved, why it was designed
with its particular representations and computations, and what
selection pressures led to such design features. We cannot endorse
the proliferation of game theory models to understand the evo-
lution of language until a clear empirical agenda is established,
and until the target of inquiry is the evolution of our biologi-
cal capacity for language as opposed to one of its functions in
communication. In this light, we suggest that future attempts to
model language evolution from a game theoretic perspective focus
on understanding its computations and representations, includ-
ing why some formats or generative procedures might win out
over others, and how different language acquisition devices might
compete, with the goal of attaining optimal competences in the
knowledge acquired and expressed. Though empirical verifica-
tion of such models will be challenging, once the right models
are created, the different strategies may well be deployed in arti-
ficial agents via simulation. These results would at least add
to the plausibility of the theoretical predictions of game theory
modeling.
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Conflict of Interest Statement: The authors declare that the research was conducted
in the absence of any commercial or financial relationships that could be construed
as a potential conflict of interest.
Received: 08 December 2013; accepted: 28 February 2014; published online: 18 March
2014.
Citation: Watumull J and Hauser MD (2014) Conceptual and empirical problems
with game theoretic approaches to language evolution. Front. Psychol. 5:226. doi:
10.3389/fpsyg.2014.00226
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