4, Games That Agents Play

Notes taken from ‘Games that agents play: A formal framework for dialogues between autonomous agents’ (2001), by Peter McBurney and Simon Parsons

“… Our ultimate objective in this work is to represent complex dialogues occurrences which may involve more than one atomic type, e.g. dialogues which may contain sub-dialogues embedded within them…”

The major contribution of this paper has been to:
- Present a logic-based formalism for modelling of dialogues between intelligent and autonomous software agents.
- Build on a theory of abstract dialogue games.
- Enable representation of complex dialogues as sequences of moves in a combination of dialogue games.
- Allow dialogues to be embedded inside one another.
- Enable different types of dialogues to be represented, because of its modular nature.
- Develop a formal and potentially-generative language for dialogues between autonomous agents which admits combinations of different types of dialogues.
- Extend previous work in formalising generic dialogue game protocols.
- Present a single, unifying framework for representing disparate types of dialogue, including those in the typology of [36].

1, Introduction
Autonomous agents interact to achieve individual or group objectives, on the basis of possibly different sets of assumptions, beliefs, preferences and objectives.

2, Dialogues and Dialogue Games
Types of dialogue (as in [36] – based upon the information the participants have at the commencement of a dialogue, their individual goals for the dialogue, and the goals they share):
- Information-Seeking Dialogues are those where one participant seeks the answer to some question(s) from another participant, who is believed by the first to know the answer(s).
- In Inquiry Dialogues the participants collaborate to answer some question or questions whose answers are not known to any one participant.
- Persuasion Dialogues involve one participant seeking to persuade another to accept a proposition he or she does not currently endorse.
- In Negotiation Dialogues, the participants bargain over the division of some scarce resources.
- Participants of Deliberation Dialogues collaborate to decide what action or course of action should be adopted in some situation.

Dialogue games are interactions between two or more players where each player “moves” by making utterances. The components/rules are:
- Commencement Rules, which define the circumstances under which the dialogue commences.
- Locutions, which indicate what utterances are permitted, e.g., assert propositions, question/contest prior assertions, justify assertions.
- Combination Rules, which define the dialogical contexts under which particular locutions are permitted or not, or obligatory or not.
- Commitment, which define the circumstances under which participants express commitment to a proposition.
- Termination Rules, which define the circumstances under which the dialogue ends.

… We suggest that agent dialogue protocols should be defined in purely syntactical terms, so that conformance with the protocol may always be verified by observing actual agent utterances (externalisation)…

… We distinguish between dialogical commitments, which incur burdens on the speaker only inside the dialogue, and semantic commitments, which incur burdens on the speaker in the world beyond the dialogue…

3, Formal Dialogue Frameworks
We present a three-level hierarchical formalism for agent dialogues:
- At the lowest level, the topics which are the subjects of dialogues;
- The dialogues themselves – instantiations of persuasions, inquiries, etc, and combinations of these – which we represent by means of formal dialogue games.
- At the highest level, control dialogues, where agents decide which dialogues to enter, if any.

… no particular dialogue may commence without the consent of all those agents participating.

… every dialogue game has a legal locution which proposes to the participants that they interrupt the current dialogue and return to the Control Layer.

… A dialogue may terminate when all participants agree to terminate it (or, for example, one participant, or only when a majority wish to do so). This may occur even though the dialogue may not yet have ended, for instance, when a persuasion dialogue does not result in all the participants accepting the proposition at issue…

Dialogues about dialogues: Because our application domain involves consenting agents, the selection of the dialogue-type may itself be the subject of debate between the agents concerned.

Treat G and H as dialogues, then the Dialogue Combinations are as follows: Iteration (n-fold repetition of G), Sequencing (G immediately followed by H), Parallelization (G and H undertaken simultaneously), Embedding (undertaking H within G), Testing (to assess the truth-status of some proposition which has become the subject of contention in a dialogue, and which makes reference to the world external to that dialogue, e.g., interrogation of a database or conduct of a scientific experiment).

… For conflicts between semantic commitments from different dialogue occurrences, the dialogue participants may have different opinions on the appropriate form of resolution. For example… commitments from earlier (later) dialogues should take precedence over those from later (earlier) ones…

If we had generative mechanisms for each of the atomic dialogue-types, then we would have them for all dialogue types, by simple inspection of the Dialogue Combination Rules…

4, Example
We illustrate the framework with a dialogue occurrence between a potential buyer and potential seller of used motor cars…

… whether or not a particular type of sub-dialogue is appropriate at a specific place in a larger dialogue should be a matter for the participants to the dialogues to decide at the time. The formalism we have presented here enables such decisions to be made mutually and contextually.