# Papers on Games and Language

• Explaining quantity implicatures . (with Tikitu de Jager, Journal of Logic, Language, and Information 2012) pdf file
We give derivations of two formal models of Gricean Quantity implicature and strong exhaustivity in bidirectional optimality theory and in a signalling games framework. We show that, under a unifying model based on signalling games, these interpretative strategies are game-theoretic equilibria when the speaker is known to be respectively minimally and maximally expert in the matter at hand. That is, in this framework the optimal strategy for communication depends on the degree of knowledge the speaker is known to have concerning the question she is answering. In addition, and most importantly, we give a game-theoretic characterisation of the interpretation rule \Grice{} (formalising Quantity implicature), showing that under natural conditions this interpretation rule occurs in the unique equilibrium play of the signalling game.

• Vagueness, Signaling and Bounded Rationality . (with Michael Franke and Gerhard Jaeger, in proceedings of LENLS2010) pdf file
Vagueness is a pervasive feature of natural language, but indeed one that is troubling for leading theories in semantics and language evolution. We focus here on the latter, addressing the challenge of how to account for the emergence of vague meanings in signaling game models of language evolution.

• Strategic Vagueness, and appropriate contexts . with Kris de Jaegher (in Meaning and Game Theory', edited by A. Benz, C. Ebert, G. Jaeger, and R. van Rooij, 2011) pdf file
This paper brings together several approaches to vagueness, and ends by suggesting a new approach. The common thread in these approaches is the crucial role played by context. We argue that the most plausible application to vagueness in natural language of these models is one where the listener only imperfectly observes the context in which the speaker makes her utterances. Yet, it is clear that not all vagueness can be accounted for by conflicts of interest. This is why the rest of the paper looks at the case of common interest. First, vagueness is thus seen as an application of Horn's pragmatic rule that (un)marked states get an (un)marked expression. Then we argue that the Sorities paradox arises from the use of vague predicates in an inappropriate context. Finally, we follow prospect theory and assume that context directly enter agents' utility functions in the form of reference points, with respect to which agents think in gains and losses. The rationale for vagueness here is that vague predicates allow players to express their valuations, without necessarily uttering the context, so that the advantage of vague predicates is that they can be expressed across contexts.

• Relevance in Cooperation and Conflict . with Michael Franke and Tikitu de Jager (in Journal of Logic and Computation, 2012) pdf file
If speaker and hearer preferences do not coincide, we can distinguish speaker relevance from hearer relevance. Taking speaker relevance seriously lets us extend the scope of linguistic pragmatics beyond cases of pure cooperation. Making use of game theoretical tool, in this paper we discuss (i) the speaker's motive to communicate in such situations at all, and (ii) what can be inferred from what is said in such situations.

• Revealed preference and Satisficing Behavior. (Synthese, 2011) pdf file
A much discussed topic in the theory of choice is how a preference order among options can be derived from the assumption that the notion of choice' is primitive. Assuming a choice function that selects elements from each finite set of options, Arrow (1959) already showed how we can generate a weak ordering by putting constraints on the behavior of such a function such that it behaves as a utility maximizer. Arrow proposed that rational agents can be modeled by such choice functions. Arrow's standard model of rationality has been criticized in economics and gave rise to approaches of {\it bounded rationality}. Two standard assumptions of rationality will be given up in this paper. First, the idea that agents are utility {\it optimizers} (Simon). Second, the idea that the relation of indifference' gives rise to an equivalence relation. To account for the latter, Luce (1956) introduced semi-orders. Extending some ideas of Van Benthem (1982), we will show how to derive semi-orders (and so-called interval orders) based on the idea that agents are utility {\it satisficers} rather than utility optimizers.

• Games and Quantity implicatures. (Journal of Economic Methodology, 2008, vol 15, issue 3, 261) pdf file
In this paper we seek to account for scalar implicatures and Horn's division of pragmatic labor in game-theoretical terms by making use mainly of refinements of the standard solution concept of signaling games. Scalar implicatures are accounted for in terms of Farrell's (1993) notion of a Neologism-Proof' equilibrium together with Grice's maxim of Quality. Horn's division of pragmatic labor is accounted for in terms of Cho \& Kreps' (1987) notion of equilibrium domination' and their Intuitive Criterion'.

• Optimal assertions, and what they implicate. (Topoi, 2007, 26: 63-78, with Anton Benz) pdf file
To determine what the speaker in a cooperative dialog meant with his assertion, on top of what he explicitly said, it is crucial that we assume that the assertion he gave was optimal. In determining optimal assertions we assume that dialogues are embedded in decision problems (van Rooij, 2003) and use backwards induction for calculating them (Benz, 2006). In this paper we show that in terms of our framework we can account for several types of implicatures in a uniform way, suggesting that there is no need for an independent linguistic theory of generalized implicatures. In the final section we show how we can embed our theory in the framework of signaling games, and how it relates with other game theoretic analyses of implicatures.

• Evolutionary motivations for semantic universals. (in Variation, Selection, Development -- Probing the evolutionary model of language change, Eckardt, Jaeger and Veenstra, 2008)pdf file
Most work in evolutionary linguistics' seeks to motivate the emergence of linguistic universals. Although the search for universals never played a major role in semantics, a number of such universals have been proposed concerning connectives, property and preposition denoting expressions, and quantifiers. In this paper we suggest some evolutionary motivations for these proposed universals using game theory.

• Book: Game Theory and Pragmatics (jointly edited with Anton Benz and Gerhard Jaeger) Rooted in Gricean tradition, this book concentrates on game- and decision-theoretic (GDT) approaches to the foundations of pragmatics. An Introduction to GDT, with an overview of GDT pragmatics research to date and its relation to semantics and to Gricean pragmatics is followed by contributions offering a high-level survey of current GDT pragmatics and the field of its applications, demonstrating that this approach provides a sound basis for synchronic and diachronic explanations of language use.\\ For more information, see http://www.palgrave.com/products/Catalogue.aspx?is=1403945721.

• Language Structure: Psychological and Social Constraints (With Gerhard Jaeger, Synthese, 2007, 159: 99-130), pdf file
In this article we discuss the notion of a linguistic universal, and possible sources of such invariant properties of natural languages. In the first part, we explore the conceptual issues that arise. In the second part of the paper, we focus on the explanatory potential of horizontal evolution. We particularly focus on two case studies, concerning Zipf's Law and universal properties of color terms respectively. We show how computer simulations can be employed to study the large scale, emergent, consequences of psycholinguistically and psychologically motivated assumptions about the working of horizontal language transmission.

• Different faces of risky speech (With Merlijn Sevenster, in Pragmatics and Game Theory' edited by Anton Benz, Gerhard Jeager and Robert van Rooij, 2005 pdf file
Sally (2003) has pointed out that in many game theoretical situations the Pareto optimal equilibrium is not the outcome we actually observe in case the preferences of the agents are not fully alinged. In those cases, avoidance of risk plays an important role as well. Following Sally's observations, we discuss the importance of risk for the use of expressions with an intended non-literal interpretation, or with an underspecified meaning.

• Cooperative versus argumentative communication (A part of this appeared in Philosophia Scientia, {\bf *} (2), 2004, 195-209) pdf file
Game theoretical analyses of communication (e.g. Lewis, Crawford \& Sobel) demand cooperation between conversational partners for reliable information exchange to take place. Similarly, in pragmatics, the theory of language use, it is standard to assume that communication is a cooperative affair. Recently, this standard view has come under attack by Durcot and Merin, and it has been proposed that an argumentative view on natural language use is more appropriate. In this paper I discuss to what extent this attack is justified and whether the alternative view can provide a more adequate analysis of pragmatic meaning', i.e., implicatures. I will investigate the game-theoretical underpinning of the argumentative view, and contrast Merin's analysis of scalar implicatures with one using the principle of exhaustive interpretation.

• Evolution of conventional meaning and conversational principles, In Synthese (Knowledge, Rationality and Action), 2004, 139: 331-366. Here is an almost final version: pdf file
In this paper language use and organisation are analyzed by making use of Lewisean signalling games. Standard game theoretical approaches are contrasted with evolutionary ones to analyze conventional meaning and conversational interpretation strategies. It is argued that analyzing successful communication in terms of standard game theory requires agents to be very rational and fully informed. The main goal of the paper is to show that in terms of evolutionary game theory we can motivate the emergence and self-sustaining force of (i) conventional meaning and (ii) some conversational interpretation strategies in terms of weaker and, perhaps, more plausible assumptions.

• Being polite is a handicap: Towards a game theoretical analysis of polite linguistic behavior (In proceedings of TARK 9, 2003, edited by M. Tennenholtz, pdf file );
In this paper I argue for a broad game theoretical perspective on language use. Polite linguistic behavior, in particular, should be taken as rational interaction of conversational partners that each come with their own beliefs and preferences. I argue that the {\it function} of making a request in a polite way is to turn a situation in which preferences are not well aligned to one where they are by assuming that to utter polite expressions is {\it costly}. This idea will be formalized by making use of Lewisean {\it signaling games} and the biological {\it handicap principle}.

• Quality and Quantity of Information Exchange (Journal of Logic, Language and Information, 2003, 12: 423-451). Here is an almost final version: pdf file )
The paper deals with credible and relevant information flow in dialogs: How useful is it for a receiver to get some information, how useful is it for a sender to give this information, and how much credible information can we expect to flow between sender and receiver? What is the relation between semantics and pragmatics? These Gricean questions will be addressed from a decision and game-theoretical point of view.

• Signalling games select Horn strategies; (Linguistics and Philosophy, 2004, 27: 493-527, written mainly in 2001 and finished in 2002, An earlier version appeared in the Proceedings of Sinn und Bedeutung 2001). Here is an almost final version: pdf file
In this paper I will discuss why (un) marked expressions typically get an (un)marked interpretation: Horn's division of pragmatic labor. It is argued that it is a {\it conventional} fact that we use language this way. This convention will be explained in terms of the equilibria of {\it signalling games} introduced by Lewis (1969), but now in an {\it evolutionary} setting. I will also relate this signalling game analysis with Parikh's (1991, 2000, 2001) game-theoretical analysis of successful communication, which in turn is compared with Blutner's (2000) bi-directional optimality theory.

• Bi-directional optimality theory; an application of Game Theory (Journal of Semantics 2000, 17: 217-242. with Paul Dekker) Note: my paper `Signalling games select Horn strategies' connects (evolutionary) game theory with Bi-directional OT in a much more satisfing way

• E-mail: R.A.M.VanRooijATuva.nl