How to play games with types

Abstract:

Inspired by Heather Burnett’s and E. Allyn Smith’s course at ESSLLI 2017 I have been thinking about how the kind of game theory they present could be connected to work on TTR, a type theory with records, and Ginzburg’s KOS. Here are some points I will consider, as of yet programatically, but I hope we can discuss the viability of this as a research programme at the workshop. 1. Recasting GT in TTR. They both talk about types (of action) and when GT talks about possible worlds it’s 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 the paper I am circulating (more detail in the partial book draft) and also in 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 (basically you have a string type for a string of events on the gameboard and you traverse it 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. I think 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 the paper I am circulating. 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) you could have a superordinate theory of action which would tell you what you might do depending on which strategy you are using. Literature: Cooper, R. (2014). How to do things with types. In Joint Proceedings of the Second Workshop on Natural Language and Computer Science (NLCS 2014) & 1st International Workshop on Natural Language Services for Reasoners (NLSR 2014) July (pp. 17-18).

Research areas:

• Dialogue
• DRiPS

Year:

2017

Type of Publication:

In Proceedings

Book title:

Workshop on Context and Reasoning in Dialogue and Other Media

Address:

Paris

Month:

December