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

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

Direct Proofs of Order Independence

We establish a generic result concerning order independence of a dominance relation on finite games. It allows us to draw conclusions about order independence of various dominance relations in a direct and simple way.Comment: 9 page

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

A Proof Theoretic View of Constraint Programming

We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and illustrate their use by analyzing the constraint propagation process for the {\tt SEND + MORE = MONEY} puzzle. We also show how this approach allows one to build new constraint solvers.Comment: 25 page