The notion of an A-nowhere dense set for various subsets A of the reals may prove to be of interest in its own right, but this paper will be concerned exclusively with the special case A = Q. Notice that rational perfect sets introduced by Miller in [1] form a subset of the Q-nowhere dense sets since the closure of a set is rational perfect if it is perfect and disjoint from the rationals. On t...

A refinement of the set of Nash equilibria that satisfies two assumptions is shown to select a subset that is stable in the sense defined by Kohlberg and Mertens. One assumption requires that a selected set is invariant to adjoining redundant strategies and the other is a strong version of backward induction. Backward induction is interpreted as the requirement that each player’s strategy is se...

Game theory (GT) is an essential formal tool for interacting entities; however computing equilibria in GT is a hard problem. When the same game can be played repeatedly over time, the problem becomes even more complicated. The existence of multiple game states makes the problem of computing equilibria in such games extremely difficult. In this paper, we approach this problem by first proposing ...

We investigate the existence of perfect homogeneous sets for analytic colorings. An analytic coloring of X is an analytic subset of [X] , where N > 1 is a natural number. We define an absolute rank function on trees representing analytic colorings, which gives an upper bound for possible cardinalities of homogeneous sets and which decides whether there exists a perfect homogeneous set. We const...

In a directed graph, a kernel is a subset of vertices that is both stable and absorbing. Not all digraphs have a kernel, but a theorem due to Boros and Gurvich guarantees the existence of a kernel in every clique-acyclic orientation of a perfect graph. However, an open question is the complexity status of the computation of a kernel in such a digraph. Our main contribution is to prove new polyn...

We give a new, elementary, purely analytical development of Descartes’ theorem that a smooth connected surface is a perfect focusing lens if and only if it is a connected subset of the ovoid obtained by revolving a cartesian oval around its axis of symmetry.

We study a bilateral multi-issue bargaining procedure with complete information and endogenous unrestricted agenda, in which offers can be made in any subset of outstanding issues. We find necessary and sufficient conditions for this procedure to have a unique subgame perfect equilibrium agreement.  2002 Elsevier Science B.V. All rights reserved.

The R7RS (small) language standard can be implemented while preserving near-perfect backward compatibility with the R6RS standard and substantial compatibility with the R5RS and IEEE/ANSI standards for the Scheme programming language. When this is done, as in Larceny, R6RS Scheme becomes a proper subset of R7RS Scheme.

In this paper, we first present an alternative way of generating oversampled linear phase perfect reconstruction filter banks (OSLPPRFB). We show that this method provides the minimal factorization of a subset of existing OSLPPRFB. The combination of the new structure and the conventional one leads to efficient implementations of a general class of OSLPPRFB. Possible application of the new sche...