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Message Exchange Games in Strategic Contexts

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Nicholas Asher at Toulouse Institute of Computer Science Research
Nicholas Asher
Soumya Paul
Soumya Paul
Soumya Paul
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Antoine Venant
Antoine Venant
Antoine Venant
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Abstract

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 (decomposition invariant 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.
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J Philos Logic (2017) 46:355–404
DOI 10.1007/s10992-016-9402-1
Message Exchange Games in Strategic Contexts
Nicholas Asher1·Soumya Paul2·Antoine Venant2
Received: 26 August 2014 / Accepted: 26 May 2016 / Published online: 20 June 2016
© Springer Science+Business Media Dordrecht 2016
Abstract 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 try-
ing 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 strate-
gies and their complexity. There is a class of winning conditions (decomposition
invariant winning conditions) for which message exchange games are equivalent to
Banach- Mazur games, which have been extensively studied and enjoy nice topolog-
ical results. But decomposition sensitive goals are much more the norm and much
more interesting linguistically and philosophically.
Keywords Philosophy of language ·Dialogue ·Game theory ·Strategic reasoning
Nicholas Asher
nicholas.asher@irit.fr
1CNRS, IRIT, Toulouse, France
2Universit´
e de Toulouse 3, IRIT, Toulouse, France
Content courtesy of Springer Nature, terms of use apply. Rights reserved.
... Now awareness of the need to give up the uniformity assumption goes back at least to major figures such as Wittgenstein, who introduced the notion of a language game (Wittgenstein, 1953) and Bakhtin, who independently argued for relativizing linguistic activity to speech genres (Bakhtin, 1986). Neither Wittgenstein nor Bakhtin provided an explication of their notions, though subsequently various explications and technical terms have been introduced by a variety of scholars in Sociolinguistics (Hymes, 1972), in Pragmatics (Levinson, 1979;Allwood, 2000), in AI (Schank & Abelson, 1977), in dialogical semantics (Larsson, 2002;Ginzburg, 2012), and in game-theoretic pragmatics (Asher et al., 2017;Burnett, 2017). No one technical term has become established; we will mostly use the term conversational type, though this term, like the others, has its drawbacks. ...
... However, this work has not applied game theory to take a global perspective on conversations. One notable exception is work by Asher et al. (2017). The starting point of Asher et al. (2017) is the framework of Banach-Mazur games (Revalski, 2003). ...
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