Preprints
List of Publications supported by the Landau Center for research in
Mathematical Analysis and Related Areas
1 October 1991  30 September 1992
 J. Bourgain, J. Kahn, Y. Katznelson, N. Linial:
The influence of variables in product spaces.
 Abstract:
Let X be a probability space and let f : X^{n}
→ {0,1}
be a measurable map. Define the influence of the kth variable on
f, denoted by I_{f}(k), as follows: For
u = (u_{1},u_{2},...,u_{n1}) ∈
X^{n1} consider the set l_{k}(u) =
{(u_{1},u_{2},...,u_{k1},t,u_{k},...,u_{n1}) : t ∈ X}. I_{f}(k) = Pr(u ∈ X^{n1}: f
is not constant on l_{k}(u)).
 B. Moldovanu, Ph. Jehiel: Delay and other effects of externalities
on negotiation.
 Abstract:
We show that the presence of negative externalities between potential buyers
of an indivisible object may have surprising effects on the strategic
equillibria of a negotiation game. Our main results are:
 The potentially infinite game where payoffs are time discounted does
not have, generically, subgame perfect Nash equillibria (SPNE) in pure
stationary strategies for values of the discount factor sufficiently close to
one. The complexity of the simplest SPNE in pure strategies tends to infinity
as the discount factor tends to one.
 In long finitely repeated generic games there are only two types of
SPNE. The first type involves huge delays. A transaction can take place only
in several stages before the deadline. In the second type of SPNE, in spite of
the random element in the game, a welldefined buyer exists that obtains the
object with probability close to one. This buyer is the only one to get
reasonable offers in almost all periods.
These results are strikingly different from the results obtained in the same
model without externalities.
 S. Shelah: Every null additive set of real in meagre additive.
 S. Shelah: Cardinalities of countably bases topologies.
 M. Goldstern, S. Shelah: Many cardinal invariants for the
continuum.
 T. Luczak, S. Shelah: Convergence in homogeneous random graphs.
