Knowledge and Games: Theory and Implementation
Andreas Witzel
Abstract:
Does she know what he knows? And if so, what is she going to do?
This dissertation takes a computer science perspective on questions of
knowledge and interaction and presents approaches for endowing
artificial agents with corresponding reasoning capabilities.
To this end, we restrict general frameworks of epistemic logic and
game theory in order to obtain practical implementations grounded in
theory.
The basic idea of the main part of the dissertation (Chapters 1 to 3)
is to view computer processes, or otherwise distributed programs, as
players in a game-theoretic setting with incomplete information. As
such, they should be able to communicate in order to obtain
information, and to perform game-theoretic algorithms.
In Chapter 1, we establish the technical foundations to support
implementation of synchronous communication, and thus the attainment
of common knowledge, among computer processes representing players.
To this end, we examine dialects of the process calculus CSP, which is
available in the form of programming languages. We argue that for our
purposes the process system needs to exhibit a certain symmetry, and
show that to satisfy this requirement we need a certain guard
construct in the language. Since this construct is not commonly
provided, our result practically identifies a unique programming
language suitable for our purposes.
In Chapter 2, we define what we call interaction structures, a
concrete class of communication networks. We specify what kind of
communication scenario we focus on, and study properties of the
knowledge that results from such communication. These properties can
be used to simplify reasoning about knowledge in our setting.
In Chapter 3, we study games in the presence of an interaction
structure, which allows players to communicate their preferences,
assuming that each player initially only knows his own preferences.
We study the outcomes of iterated elimination of strictly dominated
strategies that can be obtained in any given state of communication.
The insights from the previous chapters are used in order to provide
an epistemic basis for our results and to show a distributed algorithm
that implements the procudures locally in each player process.
After this main part of the dissertation, we continue with more
loosely related satellite chapters.
Chapter 4 is close to the main part in spirit, with the difference
that it focuses on a centralized rather than a distributed approach,
and that it considers computer games rather than games in the strict
sense of game theory. We argue that reasoning about knowledge,
including about each other's knowledge, plays a crucial role in
real-life strategic and social interaction. We survey existing
literature and games which simulate such interaction, and show that
this issue is currently neglected. We give concrete scenarios from
existing computer games which could profit from incorporating such
reasoning techniques, and substantiate one of them by describing a
simple implementation intended for experimental evaluation.
In Chapter 5, we propose an abstract approach to coalition formation
that focuses on simple merge and split rules transforming partitions
of a group of players. We identify conditions under which every
iteration of these rules yields a unique partition. The main
conceptual tool is a specific notion of a stable partition. The
results are parametrized by a preference relation between partitions
of a group of players and naturally apply to coalitional TU-games,
hedonic games and exchange economy games.
In Chapter 6, we extend the existing framework of mixed multi-unit
combinatorial auctions to include time constraints, present an
expressive bidding language, and show how to solve the winner
determination problem for such auctions using an integer programming
implementation. Mixed multi-unit combinatorial auctions are auctions
where bidders can offer combinations of transformations of goods
rather than just simple goods. For example, a transformation might
take dough and water and yield bread. This model has great potential
for applications in the context of supply chain formation, which is
further enhanced by the integration of time constraints.
Finally, in Chapter 7 we give an outlook on possible future directions
for implementing epistemic logic.
This research was partially conducted at the Centrum voor Wiskunde &
Informatica (CWI) in Amsterdam.
Keywords: