When two people engage in a conversation, knowingly or unknowingly, they are playing a game. Players of such games have diverse objectives, or winning conditions: an applicant trying to convince her potential employer of her eligibility over that of a competitor, a prosecutor trying to convict a defendant, a politician trying to convince an electorate in a political debate, and so on. We argue that infinitary games offer a natural model for many structural characteristics of such conversations. We call such (...) games message exchange games, and we compare them to existing game theoretic frameworks used in linguistics—for example, signaling games—and show that message exchange games are needed to handle non-cooperative conversation. In this paper, we concentrate on conversational games where players’ interests are opposed. We provide a taxonomy of conversations based on their winning conditions, and we investigate some essential features of winning conditions like consistency and what we call rhetorical cooperativity. We show that these features make our games decomposition sensitive, a property we define formally in the paper. We show that this property has far-reaching implications for the existence of winning strategies and their complexity. There is a class of winning conditions for which message exchange games are equivalent to Banach- Mazur games, which have been extensively studied and enjoy nice topological results. But decomposition sensitive goals are much more the norm and much more interesting linguistically and philosophically. (shrink)

This paper refines the game theoretic analysis of conversations in Asher et al. by adding epistemic concepts to make explicit the intuitive idea that conversationalists typically conceive of conversational strategies in a situation of imperfect information. This ‘epistemic’ turn has important ramifications for linguistic analysis, and we illustrate our approach with a detailed treatment of linguistic examples.

We study repeated normal form games where the number of players is large. We argue that it is interesting to look at such games as being divided into subgames, each of which we call a neighbourhood. The structure of such a game is given by a graph G whose nodes are players and edges denote visibility. The neighbourhoods are maximal cliques in G. The game proceeds in rounds where in each round the players of every clique X of G play (...) a strategic form game among each other. A player at a node v strategises based on what she can observe, i.e., the strategies and the outcomes in the previous round of the players at vertices adjacent to v. Based on this, the player may switch strategies in the same neighbourhood, or migrate to another neighbourhood.We are interested in addressing questions regarding the eventual stability of such games. We incrementally impose constraints on the ‘types’ of the players. First, we look at players who are unconstrained in their strategising abilities, in that, players who may use unbounded memory. We then consider the case of memoryless players. We show that in both these cases the eventual stability of the game can be characterised in terms of potentials. We then introduce a simple modal logic in which the types of the players can be specified. We show that when the players play according to these specified types, it can be effectively decided whether the game stabilises. Finally, we look at the important heuristic of imitation. Simple imitative strategies can be specified in the logic introduced by us. We show that in a population of optimisers and imitators, we can decide how ‘worse-off’ the imitators are by playing imitative strategies rather than optimal ones. (shrink)

In this paper, we show how game theoretic work on conversation combined with a theory of discourse structure provides a framework for studying interpretive bias and how bias affects the production and interpretation of linguistic content. We model the influence of author bias on the discourse content and structure of the author’s linguistic production and interpreter bias on the interpretation of ambiguous or underspecified elements of that content and structure. Interpretive bias is an essential feature of learning and understanding but (...) also something that can be exploited to pervert or subvert the truth. We develop three types of games to understand and to analyze a range of interpretive biases, the factors that contribute to them, and their strategic effects. (shrink)

Our paper, ‘Message Exchange Games in Strategic Contexts’ lost the funding information and acknowledgments. We had put in it on its way to publication. We include them in this erratum here.