How to play games with types

Abstract:

This talk will discuss how the kind of game theory (GT) presented in the course by Heather Burnett and E. Allyn Smith at ESSLLI 2017 (https://www.irit.fr/esslli2017/courses/6) and Burnett’s paper “Signalling Games, Sociolinguistic Variation and the Construction of Style” (http://www.heatherburnett.net/uploads/9/6/6/0/96608942/burnett_smgs.pdf) could be connected to work on TTR, a type theory with records, and Ginzburg’s KOS, a formal approach to conversational semantics. Here are some points I will consider: 1. Recasting GT in TTR. They both talk about types (of action) and when GT talks about possible worlds it is really what TTR would call types of situations. (The same holds of the use of the term “possible worlds” in probability theory). I will sketch an example of how it might look. 2. But what might doing (1) add to a linguistic theory? KOS/TTR might provide a framework for dealing with issues like choosing which games to play, misunderstandings between two agents about what game is being played or accommodating a game on the basis of another agent’s behaviour. There is a notion of game in my paper “How to do things with types” (https://www.cisuc.uc. pt/ckfinder/userfiles/files/TR%202014-02.pdf). There is more detail in my book draft (https://sites.google.com/site/typetheorywithrecords/drafts) and also in Ellen Breitholtz’s work on enthymemes and topoi in her thesis and book in preparation. Ginzburg’s work on genre and conversation types is related. The games in this literature are very simple from the perspective of GT. They are defined in terms of a string type for a string of events on the gameboard which is traversed by an agent trying to realize the types. We have nothing to say about how you would make choices in a non-deterministic game, but GT would add that. It could be extremely productive to embed game theory in a theory of dialogue — one even begins to imagine metagames, games you play about concerning which game to play. We can perhaps supply a way of connecting GT to dialogue and grammar in a formal setting. 3. We could view this as making a connection between games and a general theory of action along the lines of ”How to do things with types”. The assumption seems to be that you compute utility and then perform the action that has highest utility for you. But you could think of other strategies: e.g. cooperative (make the move that has the highest utility irrespective of player), altruistic (maximize the utility of the other player). If you think of games as assigning utilities to event types at a given state of play, perhaps exploiting techniques from our work on probabilistic TTR (http://csli-lilt.stanford.edu/ojs/index.php/LiLT/articleview/52) you could have a superordinate theory of action which would tell you what you might do depending on which strategy you are using

Research areas:

• Dialogue
• DRiPS

Year:

2018

Type of Publication:

In Proceedings

Book title:

Symposium on Logic and Algorithms in Computational Linguistic

Address:

Stockholm

Month:

August

Note:

Invited Talk