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Preprints

1. 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 : Xⁿ → {0,1} be a measurable map. Define the influence of the k-th variable on f, denoted by I_f(k), as follows: For u = (u₁,u₂,...,u_n-1) ∈ X^n-1 consider the set l_k(u) = {(u₁,u₂,...,u_k-1,t,u_k,...,u_n-1) : t ∈ X}. I_f(k) = Pr(u ∈ X^n-1: f is not constant on l_k(u)).

2. 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:

   1. 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.
   2. 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 well-defined 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.

3. S. Shelah: Every null additive set of real in meagre additive.

4. S. Shelah: Cardinalities of countably bases topologies.

5. M. Goldstern, S. Shelah: Many cardinal invariants for the continuum.

6. T. Luczak, S. Shelah: Convergence in homogeneous random graphs.