@conference{Breitholtz.Cooper_LACL_2018,
author = "Ellen Breitholtz and Robin Cooper",
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",
address = "Stockholm",
booktitle = "Symposium on Logic and Algorithms in Computational Linguistic",
month = "aug",
note = "Invited Talk",
title = "{H}ow to play games with types",
year = "2018",
}