Publications
[2025] Philippe Schlenker, Christina Pawlowitsch, Luc H. Arnal, Keny Chatain, Lucie Ravaux, Robin Ryder, Ambre Salis, Shane Steinert-Threlkeld, Léo Wang, and Emmanuel Chemla: Ancestral meanings: A prelude to evolutionary animal linguistics. Linguistics and Philosophy. Published: 16 October 2025.
Abstract:
How did the very first meaning components arise in animals? Within a simple game-theoretic framework, we use standard notions of evolutionary stability to analyze the emergence of three meaning components: individual signals, nontrivial combinations, and pragmatic principles of competition among signals.
[2025] Josef Hofbauer and Christina Pawlowitsch:
The evolutionary dynamics of costly signaling. International Journal of Game Theory 54, Article 23. Published: June 3 2025. [Preprint]
Abstract:
The theory of costly signaling (Spence in Q J Econ 87:355–374, 1973) is a wellestablished paradigm in economics and theoretical biology, where it is also known as the Handicap Principle (Zahavi J Theor Biol 53:205–214, 1975). Nevertheless, while costly-signaling games have been extensively studied in classical game theory (focused on Nash equilibrium and its refinements), evolutionary dynamics in costly-signaling games are relatively unexplored. This paper gives a comprehensive account of evolutionary dynamics in two canonical classes of games with two states of nature, two signals, and two possible reactions to signals: a model with differential signaling costs (similar to Spence’s model) and a model with differential benefits from success (similar to Milgrom and Roberts’s in J Polit Econ 94:796–821, 1986, respectively Grafen’s J Theor Biol 144:517–546, 1990, model). We first use index theory to give a necessary condition for the dynamic stability of the equilibria in these games. Then, we study the replicator dynamics and the best-response dynamics. Along the way, we relate our findings to classical equilibrium refinements that test for the plausibility of beliefs off the equilibrium path.
[2025] Josef Hofbauer and Christina Pawlowitsch: Evolutionary dynamics of signals with type-specific payoff increments. Dynamic Games and Applications, Collection in Honor of Ross Cressman, March 2025, Vol. 15 (1).
Abstract:
This paper studies the replicator dynamics and the best-response dynamics of a signaling game with type-specific preferences over signals—a generalization of the beer-quiche game (Cho and Kreps in Q J Econ 102(2):179–221, 1987). When the prior probability of the high type is below the critical value at which player 2 is indifferent between accepting and not accepting, there is a unique, partially revealing equilibrium with partial pooling in the signal that the high type prefers.Under the replicator dynamics, this equilibrium is(Lyapunov)stable but not asymptotically stable. It is surrounded by periodic orbits each of which attracting a three-dimensional stable manifold from the interior of the state space. When the prior probability of the high type is above the critical value (the case usually considered), there are two equilibrium outcomes, each with pooling in one of the two signals. Under the replicator dynamics, the equilibrium outcome with pooling in the signal that the high type prefers is stable but not asymptotically stable. The equilibrium outcome with pooling in the signal that the low type prefers is unstable. Still, both components have basins of attraction with nonempty interior. The proofs use center manifold theory and chain recurrence. Throughout, results of the dynamic analysis are compared to equilibrium selection based on the intuitive criterion and index theory.
[2023] Antoine Billot and Christina Pawlowitsch: Introduction to the Special Issue of Revue Économique in Honor of Robert Aumann. Revue Économique 74: 505-510
[2021] Christina Pawlowitsch: Strategic manipulation in Bayesian Dialogues. Synthese 199: 11279-11303.
Abstract:
In a Bayesian dialogue two individuals report their Bayesian updated belief about a certain event back and forth, at each step taking into account the additional information contained in the updated belief announced by the other at the previous step. Such a process, which operates through a reduction of the set of possible states of the world, converges to a commonly known posterior belief, which can be interpreted as a dynamic foundation for Aumann’s agreement result. Certainly, if two individuals have diverging interests, truthfully reporting one’s Bayesian updated belief at every step might not be optimal. This observation could lead to the intuition that always truthfully reporting one’s Bayesian updated belief were the best that two individuals could do if they had perfectly coinciding interests and these were in line with coming to know the truth. This article provides an example which shows this intuition to be wrong. In this example, at some step of the process, one individual has an incentive to deviate from truthfully reporting his Bayesian updated belief. However, not in order to hide the truth, but to help it come out at the end: to prevent the process from settling into a commonly known belief—the “Aumann conditions”—on a certain subset of the set of possible states of the world (in which the process then would be blocked), and this way make it converge to a subset of the set of possible states of the world on which it will be commonly known whether the event in question has occurred or not. The strategic movement described in this example is similar to a conversational implicature: the correct interpretation of the deviation from truthfully reporting the Bayesian updated belief thrives on it being common knowledge that the announced probability cannot possibly be the speaker’s Bayesian updated belief at this step. Finally, the argument is embedded in a game-theoretic model.
[2020] Christina Pawlowitsch: Making see: a structural analysis of mathematical and in particular game-theoretic writing. Narrative. 28 (No. 3): 327-54.
Abstract:
“Narrative does not make us see,” Barthes proclaimed in 1966. Narrative, in Barthes’s analysis, does not refer to anything outside itself, but operates exclusively in the sphere of language, generating sense—signifiers, not things being signified. I use Barthes’s position to shed some light on mathematical writing. I develop the
hypothesis that mathematical writing, though it uses the form of narrative, is referring
to something—namely, mathematical objects—and hence relies on truth conditions
emanating from the things being referred to, which feeds back into how mathematicians use the narrative code. This investigation, on the one hand, extends the reach
of narrative analysis by bringing it to bear as a window into mathematical practice;
on the other hand, it brings out certain aspects of the tools of narrative analysis in
new ways. One of the central findings is that for mathematical writing, the Barthesian terms often work out “under reversed signs.” For example, in narrative fiction, as
Barthes says, everything is functional by definition. In mathematical writing, instead,
functionality has to hold as a necessary condition, which has the effect that in the end
everything is functional again. I further argue that the specific referential nature of
mathematical narrating leaves certain markers on the text—markers such as explicit
reference to the act of “seeing,” calls on the reader to get involved with the argument,
and a multiplicity of grammatically differently marked voices—which I document in
three articles that have become classics in game theory.
[2012] Michael L. Manapat, Christina Pawlowitsch, David G. Rand, Martin A. Nowak: Stochastic evolutionary dynamics resolve the Traveler's Dilemma. Journal of Theoretical Biology 303: 119-27.
Abstract:
Behavior in social dilemmas is often inconsistent with the predictions of classical game theory: people
(and a wide variety of other organisms) are more cooperative than might be expected. Here we consider
behavior in one such social dilemma, the Traveler’s Dilemma, that has received considerable attention
in the economics literature but is little known among theoretical biologists. The rules of the game are as
follows. Two players each choose a value between R and M, where 0oRoM. If the players choose the
same value, both receive that amount. If the players choose different values v1 and v2, where v1ov2,
then the player choosing v1 receives v1 þR and the player choosing v2 receives v1R. While the players
would maximize their payoffs by both choosing the largest allowed value, M, the Nash equilibrium is to
choose the smallest allowed value, R. In behavioral experiments, however, people generally choose
values much larger than the minimum and the deviation from the expected equilibrium decreases with
R. In this paper, we show that the cooperative behavior observed in the Traveler’s Dilemma can be
explained in an evolutionary framework. We study stochastic evolutionary dynamics in finite
populations with varying intensity of selection and varying mutation rate. We derive analytic results
showing that strategies choosing high values can be favored when selection is weak. More generally,
selection favors strategies that choose high values if R is small (relative to M) and strategies that choose
low values if R is large. Finally, we show that a two-parameter model involving the intensity of
selection and the mutation rate can quantitatively reproduce data that from a Traveler’s Dilemma
experiment. These results demonstrate the power of evolutionary game theory for explaining human
behavior in contexts that are challenging for standard economic game theory.
[2011] Christina Pawlowitsch, Panayotis Mertikopoulo, and Nikolaus Ritt: Neutral stability, drift, and the diversificationa of languages. Journal of Theoretical Biology 287: 1-12.
Abstract:
The diversification of languages is one of the most interesting facts about language that seek
explanation from an evolutionary point of view. Conceptually the question is related to explaining
mechanisms of speciation. An argument that prominently figures in evolutionary accounts of language
diversification is that it serves the formation of group markers which help to enhance in-group
cooperation. In this paper we use the theory of evolutionary games to show that language diversification on the level of the meaning of lexical items can come about in a perfectly cooperative world solely
as a result of the effects of frequency-dependent selection. Importantly, our argument does not rely on
some stipulated function of language diversification in some co-evolutionary process, but comes about
as an endogenous feature of the model. The model that we propose is an evolutionary language game in
the style of Nowak et al. (1999) [The evolutionary language game. J. Theor. Biol. 200, 147–162], which
has been used to explain the rise of a signaling system or protolanguage from a prelinguistic
environment. Our analysis focuses on the existence of neutrally stable polymorphisms in this model,
where, on the level of the population, a signal can be used for more than one concept or a concept can
be inferred by more than one signal. Specifically, such states cannot be invaded by a mutation for
bidirectionality, that is, a mutation that tries to resolve the existing ambiguity by linking each concept
to exactly one signal in a bijective way. However, such states are not resistant against drift between the
selectively neutral variants that are present in such a state. Neutral drift can be a pathway for a
mutation for bidirectionality that was blocked before but that finally will take over the population.
Different directions of neutral drift open the door for a mutation for bidirectionality to appear on
different resident types. This mechanism—which can be seen as a form of shifting balance—can explain
why a word can acquire a different meaning in two languages that go back to the same common
ancestral language, thereby contributing to the splitting of these two languages. Examples from
currently spoken languages, for instance, English clean and its German cognate klein with the meaning
of ‘‘small,’’ are provided.
[2008] Immanuel Bomze and Christina Pawlowitsch: One-third rules with equality:
second-order evolutionary stability conditions in finite populations. Journal of Theoretical Biology 254: 616-20.
Abstract:
The one-third law of evolutionary dynamics [Nowak et al. 2004. Emergence of cooperation and
evolutionary stability in finite populations. Nature 428, 246–650] describes a robustness criterion for
evolution in a finite population: If at an A-frequency of 1=3, the fitness of an A player is greater (smaller)
than the fitness of a B player, then a single A mutant that appears in a population of otherwise all B has a
fixation probability greater (smaller) than the neutral threshold 1=N, the inverse population size. We
examine the case where at an A-frequency of 1=3, the fitness of an A player is exactly equal to the fitness
of a B player. We find that in this case the relative magnitude of the cross payoffs matters: If the payoff
of A against B is larger (smaller) than the payoff of B against A, then a single A mutant has a fixation
probability larger (smaller) than 1=N. If the cross payoffs coincide, we are in the special case of a
partnership game, where the deviation cost from an inefficient equilibrium is exactly balanced by the
potential gain of switching to the payoff dominant equilibrium. We show that in this case the fixation
probability of A is lower than 1=N. Finally, we illustrate our findings by a language game with
differentiated costs of signals.
[2008] Christina Pawlowitsch: Why evolution does not always lead to an optimal signaling system. Games and Economic Behavior 63: 203-26.
Abstract:
This paper gives a complete characterization of neutrally stable strategies for sender–receiver games in
the style of Lewis, or Nowak and Krakauer [Lewis, D., 1969. Convention: A Philosophical Study. Harvard
Univ. Press, Cambridge, MA; Nowak, M., Krakauer, D., 1999. The evolution of language. Proc. Nat. Acad.
Sci. USA 96, 8028–8033]. Due to the dynamic implications of neutral stability, the replicator dynamics
of this model does not necessarily lead to the rise of an optimal signaling system, where every state of the
world is bijectively linked to one signal and vice versa, but it can be trapped in suboptimum situations where
two (or more) signals are used for the same event, or two (or more) events are associated with one and the
same signal.
[2007] Christina Pawlowitsch: Finite populations choose an optimal language. Journal of Theoretical Biology 249: 606-16.
Abstract:
This paper studies the evolution of a proto-language in a finite population under the frequency-dependent Moran process. A protolanguage can be seen as a collection of concept-to-sign mappings. An efficient proto-language is a bijective mapping from objects of
communication to used signs and vice versa. Based on the comparison of fixation probabilities, a method for deriving conditions of
evolutionary stability in a finite population [Nowak et al., 2004. Emergence of cooperation and evolutionary stability in finite
populations. Nature 428, 246–650], it is shown that efficient proto-languages are the only strategies that are protected by selection, which
means that no mutant strategy can have a fixation probability that is greater than the inverse population size. In passing, the paper
provides interesting results about the comparison of fixation probabilities as well as Maynard Smith’s notion of evolutionary stability for
finite populations [Maynard Smith, 1988. Can a mixed strategy be stable in a finite population? J. Theor. Biol. 130, 247–251] that are
generally true for games with a symmetric payoff function.
r 2007 Elsevier Ltd. All rights reserved.
|