Building game-theoretic models of conversations

J U N M I Y O S H I

K A N T O - G A K U I N U N I V E R S I T Y

2 0 0 7

Евстигнеева Настя ОТиПЛ, II курс

Introduction

Conversation – the collective activity of intelligent subjects maximizing utility for themselves, cooperatively or competitively. Previous game-theoretic studies of conversations: Asher et al. (2001), Hashida (1996) and Parikh (2001, 2006) Inadequacies: • Hashida (1996): “communication is inherently collaborative” Cohen&Levesque: “a hearer automatically obeys a speaker’s request” • they miss the structure of a whole conversation, because deal with only a small part of it • each of these studies is only for one particular purpose • they do not make the best use of game theory

Action, Tree and Path in Conversation

Cons of describing a conversation as a sequence of the utterances: it doesn’t include non-linguistic behaviour it doesn’t show the connection between utterances and actions

A conversation is a sequence of speech acts (or illocutionary acts) and physical acts.

The speakers = the players Speech acts and related physical acts = actions

Turn-taking = a component of a game tree

The conversation develops along its subgame perfect equilibrium path: backwards induction.

A General Model (a family of games with perfect and complete information)

Some remarks: • The set of illocutionary forces F includes “executing”, which indicates doing a physical act. Ex: (executing, “Player 2 opens the window”) • (executing, Ø) = “doing nothing”, “dummy move” • (executing, s) -> (f, Ø) if s in S is a description of a physical act that has the illocutionary force. Ex: ((stating, “It rains”), (agreeing, Ø)) • S also involves false sentences: (stating, s)

Some Applications of Game Theory

Some well known theorems in game theory can be applied to C:

A More Realistic Model (a family of games with incomplete information)

A player cannot choose the subgame perfect equilibrium path, but there is the counterpart of it. A player can: estimate the utility value for each player at each horizontal node; choose an action.

The Strengths of the Models

Values of utility functions are left open. The models cover all parts of a conversation, from the opening section to the closing. The structure of a whole conversation is apparent. Game theory can be fully applied.

The Weaknesses of the Models

The models do not deal with utterance understanding. BUT: • a sequence of actions is observationally more approachable than an utterance-interpretation pair; • the pair should be located in a total conversation to be studied precisely; • an utterance understanding costs more or less. The models presuppose discrete time.