Extensive Games with
Possibly Unaware Players
Abstract:
Standard game theory assumes that the structure of the game is
common knowledge among players. We relax this assumption by
considering extensive games where agents may be unaware of the
complete structure of the game. In particular, they may not be
aware of moves that they and other agents can make. We show how
such
games can be represented; the key idea is to describe the game
from the point of view of every agent at every node of the game
tree. We provide a generalization of Nash equilibrium and show
that every game with awareness has a generalized Nash
equilibrium. Finally, we extend these results to games with
awareness of unawareness,
where a player $i$ may be aware that a player j can make moves
that i is not aware of and to subjective games, where players
may have no common knowledge regarding the actual game.
This is joint work
with Leandro Rego.
Papers:
paper1,
paper2.
Biography:
Joseph
Y. Halpern received a B.Sc. in mathematics from the University
of Toronto in 1975 and a Ph.D. in mathematics from Harvard in
1981. In between, he spent two years as the head of the
Mathematics Department at Bawku Secondary School, in Ghana.
After a year as a visiting scientist at MIT, he joined the IBM
Almaden Research Center in 1982, where he remained until 1996.
He served as manager of the Mathematics and Related Computer
Science Department at IBM from 19881990 and was a consulting
professor at Stanford from 19841996. In 1996, he moved to
Cornell University, where he is a professor in Computer Science.
His major research interests are in reasoning about knowledge
and uncertainty, qualitative reasoning, causality, belief
revision, (faulttolerant) distributed computation, game theory,
decision theory, and security. Together with his former student,
Yoram Moses, he pioneered the approach of applying reasoning
about knowledge to analyzing distributed protocols and
multiagent systems. He has coauthored 5 patents, two books
("Reasoning About Knowledge" and "Reasoning about Uncertainty"),
and well over 100 journal publications and 100 conference
publications. He was designated Highly Cited Researcher by the
Institute for Scientific Information.
Halpern was program chair and organizer of the first conference
on Theoretical Aspects of Reasoning about Knowledge, and program
chair of the 5th ACM Symposium on Principles of Distributed
Computing, the 23rd ACM Symposium on Theory of Computing, and
the 16th IEEE Symposium on Logic in Computer Science. He
received the Publishers' Prize for Best Paper at at the
International Joint Conference on Artificial Intelligence in
1985 (joint with Ronald Fagin) and in 1989, the 1997 Godel Prize
(joint with Yoram Moses), and two IBM Outstanding Innovation
Awards. He is a Fellow of AAAI (American Association of
Artificial Intelligence), AAAS (American Association for the
Advancement of Science), and ACM (Association for Computing
Machinery), and in 200102 was the recipient of a Guggenheim and
a Fulbright Fellowship. He was editorinchief of Journal of the
ACM, and currently serves on the editorial board of Journal of
Logic and Computation, Games and Economic Behavior, and
Artificial Intelligence.
