6,262 research outputs found
The Role of Monotonicity in the Epistemic Analysis of Strategic Games
It is well-known that in finite strategic games true common belief (or common
knowledge) of rationality implies that the players will choose only strategies
that survive the iterated elimination of strictly dominated strategies. We
establish a general theorem that deals with monotonic rationality notions and
arbitrary strategic games and allows to strengthen the above result to
arbitrary games, other rationality notions, and transfinite iterations of the
elimination process. We also clarify what conclusions one can draw for the
customary dominance notions that are not monotonic. The main tool is Tarski's
Fixpoint Theorem.Comment: 20 page
Edsger Wybe Dijkstra (1930 -- 2002): A Portrait of a Genius
We discuss the scientific contributions of Edsger Wybe Dijkstra, his opinions
and his legacy.Comment: 10 pages. To appear in Formal Aspects of Computin
The Role of Commutativity in Constraint Propagation Algorithms
Constraint propagation algorithms form an important part of most of the
constraint programming systems. We provide here a simple, yet very general
framework that allows us to explain several constraint propagation algorithms
in a systematic way. In this framework we proceed in two steps. First, we
introduce a generic iteration algorithm on partial orderings and prove its
correctness in an abstract setting. Then we instantiate this algorithm with
specific partial orderings and functions to obtain specific constraint
propagation algorithms.
In particular, using the notions commutativity and semi-commutativity, we
show that the {\tt AC-3}, {\tt PC-2}, {\tt DAC} and {\tt DPC} algorithms for
achieving (directional) arc consistency and (directional) path consistency are
instances of a single generic algorithm. The work reported here extends and
simplifies that of Apt \citeyear{Apt99b}.Comment: 35 pages. To appear in ACM TOPLA
Epistemic Analysis of Strategic Games with Arbitrary Strategy Sets
We provide here an epistemic analysis of arbitrary strategic games based on
the possibility correspondences. Such an analysis calls for the use of
transfinite iterations of the corresponding operators. Our approach is based on
Tarski's Fixpoint Theorem and applies both to the notions of rationalizability
and the iterated elimination of strictly dominated strategies.Comment: 8 pages Proc. of the 11th Conference on Theoretical Aspects of
Rationality and Knowledge (TARK XI), 2007. To appea
Semantics of Input-Consuming Logic Programs
Input-consuming programs are logic programs with an additional restriction on the selectability (actually, on the resolvability) of atoms. this class of programs arguably allows to model logic programs employing a dynamic selection rule and constructs such as delay declarations: as shown also in [5], a large number of them are actually input-consuming. \ud
in this paper we show that - under some syntactic restrictions - the tex2html_wrap_inline117-semantics of a program is correct and fully abstract also for input-consuming programs. this allows us to conclude that for a large class of programs employing delay declarations there exists a model-theoretic semantics which is equivalent to the operational one
Order Independence and Rationalizability
Two natural strategy elimination procedures have been studied for strategic
games. The first one involves the notion of (strict, weak, etc) dominance and
the second the notion of rationalizability. In the case of dominance the
criterion of order independence allowed us to clarify which notions and under
what circumstances are robust. In the case of rationalizability this criterion
has not been considered. In this paper we investigate the problem of order
independence for rationalizability by focusing on three naturally entailed
reduction relations on games. These reduction relations are distinguished by
the adopted reference point for the notion of a better response. Additionally,
they are parametrized by the adopted system of beliefs. We show that for one
reduction relation the outcome of its (possibly transfinite) iterations does
not depend on the order of elimination of the strategies. This result does not
hold for the other two reduction relations. However, under a natural assumption
the iterations of all three reduction relations yield the same outcome. The
obtained order independence results apply to the frameworks considered in
Bernheim 84 and Pearce 84. For finite games the iterations of all three
reduction relations coincide and the order independence holds for three natural
systems of beliefs considered in the literature.Comment: Appeared in: Proc. of the 10th conference on Theoretical Aspects of
Rationality and Knowledge (TARK X), pp. 22-38 (2005
Relative Strength of Strategy Elimination Procedures
We compare here the relative strength of four widely used procedures on
finite strategic games: iterated elimination of weakly/strictly dominated
strategies by a pure/mixed strategy. A complication is that none of these
procedures is based on a monotonic operator. To deal with this problem we use
'global' versions of these operators.Comment: 8 page
One More Revolution to Make: Free Scientific Publishing
Computer scientists are in the position to create new, free high-quality
journals. So what would it take?Comment: Taken from
http://www.acm.org/pubs/citations/journals/cacm/2001-44-5/p25-apt/ Posted
with permission of the AC
The Many Faces of Rationalizability
The rationalizability concept was introduced in \cite{Ber84} and
\cite{Pea84} to assess what can be inferred by rational players in a
non-cooperative game in the presence of common knowledge. However, this notion
can be defined in a number of ways that differ in seemingly unimportant minor
details. We shed light on these differences, explain their impact, and clarify
for which games these definitions coincide. Then we apply the same analysis to
explain the differences and similarities between various ways the iterated
elimination of strictly dominated strategies was defined in the literature.
This allows us to clarify the results of \cite{DS02} and \cite{CLL05} and
improve upon them. We also consider the extension of these results to strict
dominance by a mixed strategy. Our approach is based on a general study of the
operators on complete lattices. We allow transfinite iterations of the
considered operators and clarify the need for them. The advantage of such a
general approach is that a number of results, including order independence for
some of the notions of rationalizability and strict dominance, come for free.Comment: 39 pages, appeared in The B.E. Journal of Theoretical Economics: Vol.
7 : Iss. 1 (Topics), Article 18. Available at:
http://www.bepress.com/bejte/vol7/iss1/art1
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