dr. Peter van Emde Boas
hours:
Tuesday 09.30 -- 11.--
Zaal
I 201 (Diamantslijperij)
Friday
09.30
-- 11.-- Zaal P 016
Our apologies for these cruel hours.
Effective
Friday Sep 08 the classes will change to 9.30 - 11.-- (without break).
We will have a short sanitary stop in the middle however....
THE EXCERCISES PAGE IS NOW COMPLETE.
Scheme of classes (with tentative subjects):
Week Tuesday
Friday
37 Sep 05
Games
and Computer Science
Sep 08 Extensive Game models
38 Sep
12
Other Game models, Backward Induction
Sep 15
Games as Acceptors, the Tiling Game
39 Sep
19 When is Backward
Induction
in PSPACE Sep 22 Understanding PSPACE
40
Sep 26 No Class - worshop in Poland
Sep 29 Savitch Game, Start Alternating Model
41 Oct 03 No Class - be
invited at
gllc14 in
Amsterdam
Oct
06 Alternation model and semantics
42 Oct 10
Two person tiling game & Geography
Oct 13 Complexity, Speed-up and
Compression
43
Oct 17 No Class (Ph.D. at
KdV institute)
Oct 20 No
Class (Ph.D. at IvI )
44
Oct 24 No Class (exam week)
Oct 27 No Class (exam week)
45 Oct 31 No
class (ILLC visitation)
Nov 03 No
Class (Ph.D. at IvI )
46 Nov
07 More Examples,
Probabilistic moves
Nov
10 Probabilistic moves cont.
47 Nov
14
Parcheesi; Utility
theory
Nov
17 Utility Theory cont.
48 Nov
21 Election
Special - D.G. Saari: Chaotic Elections
Nov
24 Utility Theory - Allais example and
axiomatics
49 Nov
28 No
Class (Ph.D. at IvI )
Dec 01 Dominated strategies
50 Dec 05 Nash Bargaining Theory
Dec 08 Von Neuman Max-Min Theorem
51
Dec 12 More on Euilibria
Dec
15 The Pebble Game
52 Dec 19 No Class
(exam
week)
Dec 22
No Class (exam week)
This course is offered in
the
master programs GGrid Computing, Artificial Intelligence
and Master of Logic , in all cases as an elective course. The course is
open as a choice subject for
students of other programs.
The course is a successor
course
and merger of two courses from the old program: Theoretische Modellen and Intelligent Databases ,
both offered for the last time in the year 2002 - 2003.
During the year 2006 -
2007
a number of other game related courses will be offered in the Master of
Logic
Program:
Semester 1:
B Loewe: Advanced Topics
in
Set Theory: Infinite Games
J.F.A.K. van Benthem: Caput Logic,
Language
and Information
Semester 2:
U. Endriss: Computational
Social
Choice
K.R. Apt: Cooperative
game
theory
J. Zuidema: Evolutionary
Game
Theory & Language
Course Contents:
Game theory originates from
Economical
Sciences; it
treates theories about
strategic
interaction and
related rationality concepts.
The
subject is currently attracting researchers from
Computer Science and
Technology,
particularly involving
themes about controling
behavior
of unrelyable agents on the
Internet.
Fact is that concepts from
game
theory have been used in
Computer Science already much
longer.
Several of the models
used in theoretical Computer
Science
for analysing problems with regards to
effectivity and efficiency can
be
quite reasonably be described and analysed
in terms of games.
This link will be
illustrated
in this course on the basis of a number
of models which originally
date
from the 70-ies and 80-ies.
The main target is to
illustrate
that games represent a computational
model in the same way
nondeterministic
computations do.
The course moreover
includes an
introduction to some fundamental models and concepts
in Classical game theory: game models, probabilistic games, utility
functions,
and equilibria.
Examples of models connecting games and computation theory are:
The theory of Traub and
Wozniakowski
on the solution of numerical
problems.
Deciding Graph properties
from
Adjacency Matrices ("Twenty Questions");
theory of Evasiveness.
The pebling game, used as a
model
both for register allocation
and in the context of machine
model
theory.
The Tiling game and its use in Reduction Theory
The Alternating Machine
model
and its connection to
logic description languages
and
games.
Interactive protocols for
convincing
opponents about the presence of
information, without leaking
more
information than
necessary: (Interactive
proofs,
Arthur Merlin games, Zero Knowledge
proofs, ...)
The design of mechanisms
for tweaking
agents on the internet to behave
in a truthful manner.
Except for the latter
problem
the game theory involved deals combinatorial
games rather than the more
stochasitic
real valued games studied in
Econmical Sciences. The game
theory
involved therefore is rather
elementary.
Sheets available: (from the previous course; Updates, if available, will be linked here)
Part
1: Topics: Introduction, Games and
Tilings:
Updated version Available in Powerpoint00 format and pdf format
Part
2: Topics: Endgame Analysis, PSPACE
and Parallellism:
Updated version Available in Powerpoint00 format
and pdf format
Part
3: Topics: PSPACE, Alternation,
Games:
Updated version Available in Powerpoint00 format
and pdf format
Part
4:
Topics: Introductionary Examples
Updated version Available in Powerpoint00 format and pdf format
Part
5:
Topics: Games with chance moves
Updated version Available in Powerpoint00 format and pdf format
Part
6:
Topics: Utility Theory
with an extension into the axiomatic theory of Utility
based on material by Wakker and Meyerson listed below.
Updated version Available in Powerpoint00
format and pdf format
Extra:
Topics: Chaotic Elections (after Donald G. Saari):
Available in Powerpoint00
format
and pdf
format
Part
7:
Topics: Domination of strategies
Updated
version
Available
in Powerpoint00
format and pdf format
Part
8:
Topics: Cooperative games:
Most recent version
Available
in Powerpoint00
format and pdf format
Part
9:
Topics: Mixed Strategies and von Neuman Min-Max Theorem
Most recent version Available in Powerpoint00 format and
pdf format
Part 10:
Topics:
More on equilibria and correlated equilibria
Most recent version Available in Powerpoint00 format and
pdf format
Part 11:
Topics:
Mechanism Design after Nissan & Ronen
Old version Available in Powerpoint00 format and
pdf form
Part 12:
Topics: the Pebble Game:
Last version Available in Powerpoint00 Format
and pdf format
Part
13: Topics: Diagonalization and
Compression:
Updated and Extended version Available in Powerpoint00 format and
pdf format
Sheets available: (from the previous course Theoretical Models)
Part
1: Topics: Introduction, Games and
Tilings:
Available in Powerpoint00 format and
pdf format
Part
2: Topics: Endgame Analysis, PSPACE
and Parallellism:
Available in Powerpoint00 format and
pdf format
Part
3: Topics: PSPACE, Alternation,
Games:
Available in Powerpoint00 format and
pdf format
Part
4: Topics: the Pebble Game:
Available in Powerpoint00 Format and pdf format
Part
5: Topics: Diagonalization and
Compression: (version 2000)
Available in Powerpoint00 format and
pdf format
Part
6: Topics: Interactive Proof
Systems:
Available in Powerpoint00 format and pdf format
Part 7:
Controling
Selfish Agents on the Internet:
Available in Powerpoint00 format and pdf format
Sheets available: (from the last course
Intelligent
Databases)
Chapter
0:
Topics: Introduction.
Available in Powerpoint98 format and pdf format
Chapter
1:
Topics: Basic Concepts
Available in Powerpoint98 format and
pdf format:
Chapter
2:
Topics: Games with chance moves
Available in Powerpoint98 format and pdf format
Chapter
3:
Topics: Utility Theory
with an extension into the axiomatic theory of Utility
based on material by Wakker and Meyerson listed below.
Available in Powerpoint98 format and pdf format
Chapter
4:
Topics: Domination of strategies
Available in Powerpoint98 format and pdf format
Chapter
5:
Topics: Cooperative games:
Available in Powerpoint98 format and pdf format
Chapter
6:
Topics: Mixed Strategies
Available in Powerpoint98 format and pdf format
Chapter
7:
Topics: On Equilibria: cheap talk and correlated equilibria
Available in Powerpoint98 format and
pdf format
Contents
of previous courses 2002 and 2003 are almost identical, but beware for
obsolete
URL references !
Aditional Material related
to
games available as slides.
Extra: Topics: The Game of Chaos:
Presentation
at the 34 Dutch Mathematics Conference April 1999
Nov 19-20 1999. Available in Powerpoint98
Format and pdf
format
See also: P. van Emde Boas
& E.H. van Emde Boas, The Game of Chaos, as included in the
bibliography below.
Extra:
Topics: Games in the Classroom:
Available in Powerpoint98 format and pdf format
Extra:
Topics: The connection between Games and Computer Science,
Talks prepared for a trip to China, April 2000:
Available in Powerpoint98 format and pdf format
Extra:
Topics: The Games of Computer Science,
Talk at TU Delft, Feb 23 2001:
Available in Powerpoint98 format and pdf format
Extra:
Topics: Playing Savage:
Available in Powerpoint98 format and pdf
format
Manuscript available in Postscript
Extra: Topics:
Imperfect
Information Games, looking for the right model.
Talk at Algemeen Wiskunde Colloquium, Feb 27 2002:
Available in Powerpoint2000 format
Extra: Topics:
Imperfect
Information Games, what makes them hard to decide.
Talk at Amsterdam Aachen Exchange Feb 15, 2002:
Available in Powerpoint2000 format
Extra: Topics: IF
Logic;
slides of the presentation of Merlijn Sevenster on Nov 29 2004
Available in pdf format
Extra:
Topics: Games in Computation and Complexity Theory,
Tutorials at the workshop Games and Logic Kazimierz Dolny (PL), Sep
25-26 2006
Available in Powerpoint2000 format and pdf format
Literature: (will be extended during the course).
Game Theory.
Ken Binmore, Fun and
Games,
Houghton Mifflin Company, 1992;
this is a textbook which is
used
for this course
Elwyn R. Berlekamp, John H.
Conway
& Richard K. Guy,
Winning Ways (Vol 1
and
Vol. 2), Academic Press, 1982.
John H. Conway, On Numbers and Games, Academic Press 1976.
the above two references develop the mathematics of combinatorial games in great depth.
V.W. Gijlswijk, G.A.P.
Kindervater,
G.J. van Tubergen & J.J.O.O Wiegerinck,
Computer Analysis of E. de
Bono's
L-Game, Rep. Math, Inst. UvA 76-18
(an early computerized
backward
analysis of a non-trivial game; also an early
student project in our
department...)
M.J. Osborne & A. Rubinstein, A Course in Game Theory, MIT Press 1994.
Alexander Mehlman, The
Game's
Afoot!, Game Theory in Mythand Paradox,
Amer. Math. Soc. Student Math.
Library
5, 2000
Introduction, with many
examples
drawn from the literature and
mythology; however, in final
sections
rather difficult.
Steven J. Brams, Superior
Beings,
Springer Verlag 1983;
Game theory applied to
Theology.
Boudewijn de Bruin, Explaining Games,
On the
Logic of Game Theoretic Explanations,
Ph.D. Thesis ILLC UvA 20041207,
ILLC
Dissertation Series DS-2004-03
An in depth study of the connections between Backward Induction,
Elimination
of dominated strategies,
and Common Knowledge of Rationality.
K.R.
Apt,
"Order Independence and
Rationalizability''
,
Proc. of the 10th Conference on
Theoretical Aspects of Rationality and Knowledge
(TARK X),
pp. 22-38, 2005.
K.R. Apt,
"The Many Faces of
Rationalizability''.
Manuscript, August
2006.
Computation Theory.
John E. Hopcroft &
Jeffrey
D. Ullman, Intorduction to Automata Theory,
Languages and Computation,
Addison Wesley, 1979.
David Harel, Algorithmics;
the Spirit of Computing, (second Edition),
Addison Wesley 1992.
Thomas A. Sudkamp, Languages
and Machines; An Introduction to the
Theory of Computer Science,
(second Edition), Addison Wesley 1997.
a formerly used textbook for
the
course Automata and Complexity Theory
Harry R. Lewis &
Christos
H. Papadimitriou,
Elements of the Theory of
Computation,
Prentice Hall 1981.
Christos H. Papadimitriou, Computational
Complexity,
Addison Wesley 1995.
Chapter 19 covers many
of
the computation theory subjects dealt with in this course!
Cees Slot & Peter van
Emde
Boas, The Problem of Space Invariance for
Sequential Machines,
Inf.
and Comp. 77 (1988) 93--122.
Peter van Emde Boas, Space
Measures for Storage Modification Machines,
Inf. Proc. Letters 30
(1989)
103--110.
Peter van Emde Boas, Machine
Models and Simulations, in
J. van Leeuwen, Handbook of
Theoretical
Computer Science vol A,
Algorithms and
Complexity, Elsevier, 1990, pp 3--66;
preprint: ITLC-CT-89-02.
The last three papers concern the Invariance Thesis.
The pebling game, used as a
model
both for register allocation
and in the context of machine
model
theory.
J.E. Hopcroft, W. Paul
& L.
Valiant, On Time versus Space,
J. Assoc. Comput. Mach., 24
(1977)
332--337.
A. Lingas, A PSPACE
Complete
Problem related to a Pebble Game,
G. Ausiello & C Böhm
eds.,
Proc. ICALP'78,
Springer LNCS 62, 1978, pp.
300--321.
P. van Emde Boas & Jan
Van
Leeuwen, Move Rules and
Trade-Offs in the Pebble
Game,
in K. Weihrauch ed.,
Proc. 4th GI Theoretical
Computer
Science Conference,
Springer LNCS 67 1979, pp.
101--112.
John R. Gilbert, Thomas
Lengauer
& Robert E. Tarjan,
The Pebbling Problem is
Complete
in Polynomial Space,
SIAM J. Comput. 9 (1980)
513--524.
Hiroaki Tohyama & Akeo
Adachi,
Complexity of path
discovery
game problems,
Theor. Comp. Sci.. 237, 2000,
381--406.
another PSPACE-hard solitaire
game.
Tiling Game and its use in Reduction Theory
Bogdan S. Chlebus, Domino-Tiling
Games, J. Comput. Syst. Sci. 32
(1986), 374--392.
Martin. P.W. Savelsberg
& Peter van Emde Boas, BOUNDED TILING,
an alternative to
SATISFIABILITY?,
in G.Wechsung ed., proc. 2nd
Frege Memorial Conference,
Schwerin,
Sep 1984, Akademie Verlag,
Mathematische Forschung vol.
20,
1984, pp. 401--407.
preprint: rep. CWI-OS-R8405.
Peter van Emde Boas, The
Convenience
of Tilings, in: Andrea Sorbi, ed.,
Complexity, Logic and
Recursion
Theory, lecture notes in pure and
applied mathetaics vol 187,
1997,
pp. 331--363. (for ps. version of preprint
).
The sheets of this lecture are
available
at sheets in postscript . However
beware: on behalf of its origin as a (by now obsolete MacWrite
document)
the Postscript pages are
sorted
in reverse order.
Peter van Emde Boas, Is elf plus
één
twaalf?; over rekenen en puzzelen.
Explanation of the construction of the tiling puzzle
demonstration
model for precollege students (in Dutch). Text
available
in Postscript
.
The corresponding figures are available in
Postscript
also: pict1pict2pict3pict4
.
David Harel, Recurring
Dominos:
making the Highly Undecidable
Highly Understandable,
Ann.
Discrete Math. 24 (1985) 51--72.
David Harel, Dynamic
Logic,
in D. Gabbay & F. Guenthner (eds.)
Handbook of
PhilosophicalLogic,
Vol II, D. Reidel 1984, pp. 497--604.
Background information on
Dynamic
Logic for the reduction to
PDL-Satisfiability from the
two
person tiling game as invented by
Chlebus.
The Alternating Machine
model
and its connection to
logic description languages
and
games.
A.K. Chandra, D. Kozen
& L.J.
Stockmeyer, Alternation,
J.Assoc. Comput. Mach. 28
(1981)
114--133.
Christos H. Papadimitriou, Computational
Complexity,
Addison Wesley 1995. See chapter 19 in particular.
L.J. Stockmeyer & A.R.
Meyer,
Word problems requiring exponential time,
Proc STOC 5 (1973), pp 1--9.
An important early paper and
the
source of the QBF problem.
T.J. Schäfer, Complexity
of some two-person perfect-information games,
J.Comput. Syst. Science, 16
(1978)
185--225.
The first PSPACE complete
game:
Geography.
D. Lichtenstein & M.
Sipser,
GO is polynomial-space hard,
J. Assoc. Comput. Mach, 27
(1980)
393--401.
S. Even & R.E. Tarjan, A
combinatorial game which is complete for polynomial
space, J. Assoc.
Comput.
Mach, 23 (1976) 710--719.
S. Reisch, HEX ist PSPACE-volständig, Acta Informatica 15 (1981) 167--191.
A.S. Fraenkel, M.R. Garey,
D.S.
Johnson, T. Schäfer & Y. Yesha,
The complexity of checkers
on
an N X N board - preliminary report,
Proc IEEE FOCS 19 (1978) pp.
55--64.
A.S. Fraenkel & D.
Lichtenstein,
Computing a perfect strategy for n x n chess
requires time exponential
in
n, J. Combin. Theory series A 31 (1981) 119--213.
G.W. Flake & E.B. Baum,
Rush
Hour is PSPACE-complete, or "Why you should generously tip
parking lot attendants",
Theoretical Computer Science, 270 (2002) 895--911.
A very simple combinatorial
solitaire
game which is PSPACE-complete. For a yet simpler version
see this note
by John Tromp.
Erik D. Demaine,
Playing
Games with Algorithms: Algorithmic Combinatorial Game Theory ,
MFCS 2001, Springel LNCS 2136,
pp.
18-32 .
Much more information is
available
from his impressive website .
The above five papers involve games played by real people.
P. van Emde Boas, The
Second
Machine Class 2, an Encyclopedic View on the
Parallel Computation Thesis.
in: H. Rasiowa ed., Mathematical Problems in
Computation Theory, Banach
Center
Publications, vol 20, PWN Warsaw 1988,
pp. 235--256.
An older version of sections 3
and
4 in my Handbook Chapter.
Slides about this subject are
available
in Postscript
(but again in reverse
order...).
Robert A. Stegwee, Leen Torenvliet & Peter
van Emde
Boas,
The Power of your Editor, Rep. IBM RJ 4711
(50179)
5/21/85;
also: Report FVI-UvA-85-03.
Sheets have been placed on the
Web;
once more in reverse order Postscript
Interactive Proof systems and other models of interaction and/or randomized computation
Carsten Lund, Lance Fortnow
& Howard Karloff, Algebraic Methods for Interactive Proof
Systems,
J. ACM. 39 (1992) 859-868.
Adi Shamir, IP = PSPACE, J.ACM. 93 (1992) 869-877.
A. Shen, IP= PSPACE: Simplified Proof, J.ACM. 93 (1992) 878-880.
L. Babai, E-mail
and
the unexpected power of interaction, Proc. IEEE Symp. Structure in
Complexity Theory 5,
Barcelona,
July 08-11 1990, pp. 30--44.
Shafi Goldwasser, Silvio
Micali
& Charles Rackoff, The Knowledge Complexity of
Interactive Proof Systems,
SIAM, J. Comput. 18 (1989), 186-208.
Christos H. Papadimitriou, Games against Nature, Proc. IEEE FOCS 1983, pp. 446-450
L. Babai &S. Moran, Arthur-Merlin
Games: a Randomized Proof System and a Hierarchy
of Complexity Classes,
J.
Comput. Syst. Sci. 36 (1988) 254-276.
The design of mechanisms
for tweaking
agents on the internet to behave
in a truthful manner.
Noam Nissan & Amir
Ronen,
Algorithmic Mechanism Design,
proc. ACM STOC 31 (1999).
Noam Nisan, Algorithms
for
Selfish Agents,
in C. Meinel & S. Tison,
eds.,
Proc. STACS'99,
Springer LNCS 1563, 1999, pp.
1--15.
Amir Ronen, Algorithms
for
Rational Agents,
proc. SOFSEM 2000, Springer
LNCS
1963, 56--70.
Evasiveness problem ("twenty questions")
M.R. Best, P. van Emde Boas
and
H.W. Lenstra, jr.,
A Sharpened version of the
Aandera-Rosenberg
Conjecture,
rep. MC-ZW-30-74, October 1974.
Ronald L. Rivest & Jean
Vuillemin,
On recognizing Graph
properties
from Adjacency Matrices,
Theor. Comp. Sci. 3 (1976)
371-384.
J.Kahn, M. Saks, D. Sturtevant, A topological
Approach
to Evasiveness,
Combinatorica 4 (1984) 297-306.
N. Illies, A counterexample to the
Generalized Aanderaa-Rosenberg
Conjecture,
Inf. Proc. Letters, 7 (1978) 154-155.
Unrelated but still about Games and/or Computer Science.
Peter van Emde Boas, Games
in the Classroom,
position paper at OOPSLA'99
Workshop
#2, Quest for Effective Classroom Examples.
Postscript version Available .
H. Jaap van den Herik, Jos
W.H.M.
Uiterwijk & Jack van Rijswijck,
Games solved: Now and in
the
future,
Artificial Intelligence 134
(2002),
277-311.
A survey on the state of the
art
in real life game analysis by computers;
the entire issue of Artificial
Intelligence
is dedicated to this problem area in AI.
Donald G. Saari,
Chaotic
Elections! A mathematical Looks at Voting,
AMS 2001.
A thorough analysis on how
voting
systems fail to implement democracy.
Mandatory reading material for
voters.
Course Evaluation:
Except for specific student
contributions
(with previous arrangements
with the teacher) the students
will
be graded on their solutions of
homework exercises which will be made
public
on the website gradually
during the course. Answers
should
be returned within the deadline as listed with
the exercise, only on paper.
Even
when the answers are prepared electronically
the solution must be submitted
on
paper.