Anton Benz

An Introduction to Game Theory for Linguists

In a very general sense we can say that we play a game together with other people whenever we have to decide between several actions such that the decision depends on the choice of actions by others and on our preferences over the ultimate results. Obvious examples are card games, chess, or soccer. If I am to play a card to a trick, then it depends on the cards played by my playing partners whether or not I win the trick. Whether my move in chess leads to a win usually depends on the subsequent moves of my opponent. Whether I should pass the ball to this or that team member depends not in the least on my expectations about whether or not he will pass it on to a player in an even more favourable position. Whether or not my utterance is successful depends on how it is taken up by its addressee and the overall purpose of the current conversation. This provides the basis for applications of game theory in pragmatics.

Utility and Relevance of Answers

How to answer a question? If the inquirer asks it in order to make a decision about something, then a wide range of reactions can be appropriate. If asked ‘Who of the applicants is qualified for the job?’, reactions may range from ‘Only Muller and Schmidt’, ‘At least Muller’, over ‘Muller has working experience in this field, ‘Schmidt needs extra training’’, to ‘The younger ones show more enthusiasm’, or even ‘The job needs an expert in PCF Theory’. This paper divides into two parts. The goal of the first part is to derive a measure of utility for answers from a game theoretic model of communication. We apply this measure to account for a number of judgements about the appropriateness of partial and mention-some answers. Under the assumption that interlocutors are Bayesian utility optimisers we see questioning and answering as a two-person game with complete coordination of preferences. Our approach builds up on work by A. Merin and R. v. Rooij on decision theoretically formulated measures of relevance.1 In the second part we study the relation between their approaches and our game theoretic model of answering. We are aiming for principled characterisations, and are especially interested in clarifying when and why we have to model this type of communication as a two-person game.

Language, games, and evolution: trends in current research on language and game theory

Recent years witnessed an increased interest in formal pragmatics and especially the establishment of game theory as a new research methodology for the study of language use. Game and Decision Theory (GDT) are natural candidates if we look for a theoretical foundation of linguistic pragmatics. Over the last decade, a firm research community has emerged with a strong interdisciplinary character, where economists, philosophers, and social scientists meet with linguists. Within this field of research, three major currents can be distinguished: one is closely related to the Gricean paradigm and aims at a precise foundation of pragmatic reasoning, the second originates in the economic literature and is concerned with the role of game theory in the context of language use, and the third aims at language evolution seen either from a biological or from a cultural perspective. Edited in collaboration with FoLLI, the Association of Logic, Language and Information, this volume is based on a selection of papers of two international conferences, one organised at ESSLLI in 2007 on language, games, and evolution, and the other organised at the ZAS in Berlin on games and decisions in pragmatics in 2008. This volume is rounded off by additional invited papers and now contains eight articles of leading researchers in the field which together provide a state-of-the-art survey of current research on language evolution and game theoretic approaches to pragmatics.

Pragmatic question answering: A game-theoretic approach

Abstract We present results of quantitative evaluations of a content selection scheme for answer generation in sales dialogue which is based on an interactive game-theoretic model of the dialogue scenario. The model involves representing a probability distribution over possible customer requirements, i.e., needs that must be met before a customer will agree to buy an object. Through game-theoretic analysis we derive a content selection procedure which constitutes an optimal strategy in the dialogue game. This procedure is capable of producing pragmatically appropriate indirect answers to yes/no questions, and is implemented in an online question answering system. Evaluation results show that these answers are pragmatically natural and contribute to dialogue efficiency. The model allows for systems that learn probabilities of customer requirements, both online and from previous data.

Language, games, and evolution: an introduction

Recent years have witnessed an increased interest in formal pragmatics and especially the establishment of game theory as a new research methodology for the study of language use. Within this field of research, three major currents can be distinguished: one is closely related to the Gricean paradigm and aims at a precise foundation of pragmatic reasoning, the second originates in the economic literature and is concerned with the role of game theory in the context of language use, and the third aims at language evolution seen either from a biological or from a cultural perspective.

Pragmatic Query Answering: Results from a Quantitative Evaluation

This paper reports on an implementation of methods for generating indirect responses in question-answering dialogue based on domain-level strategic reasoning. User’s questions are interpreted as reflexes of underlying user requirements which are potentially satisfied by information beyond what is directly asked about. We find that the algorithms that reason about user requirements yield significantly shorter dialogues than a simpler baseline, and that users are able to interact with these systems in a pragmatically natural way.