This Week in Logic at CUNY

Computational Logic Seminar
January 29, Time 2:00 – 4:00 PM, Room 3209
Speaker: Sergei Artemov, CUNY Graduate Center
Title: Definitive solutions of strategic games

Abstract: In his dissertation of 1950, Nash based his concept of
solution to a game on the principles that “a rational prediction
should be unique, that the players should be able to deduce and make
use of it.” In this paper, we address the issue of when Nash
expectations of a definitive solution hold and whether the Nash
Equilibrium (NE) solution concept is a match for such definitive
solutions. We show that indeed, an existence of NE is a necessary
condition for a definitive solution, and each NE σ is a definitive
solution for some notion of rationality individually tuned for this σ.
However, for specific notions of rationality, e.g., Aumann’s
rationality, NE is not an exact match to definitive solutions, many
games with NE do not have definitive solutions at all. In particular,
strategic ordinal payoff games with two or more Nash equilibria, and
even some games with a unique NE do not have definitive solutions. We
also show that the iterated dominance approach is a better candidate
for Nash’s definitive solution concept than the Nash Equilibrium.

 

Set theory seminar
Friday, February 1, 2013, 10:00 am
GC 5383 (New location)
Joel David Hamkins, The City University of New York
Superstrong cardinals are never Laver indestructible, and neither are
extendible, almost huge and rank-into-rank cardinals

Although the large cardinal indestructibility phenomenon, initiated
with Laver’s seminal 1978 result that any supercompact cardinal
$\kappa$ can be made indestructible by $<\kappa$-directed closed
forcing and continued with the Gitik-Shelah treatment of strong
cardinals, is by now nearly pervasive in set theory, nevertheless I
shall show that no superstrong strong cardinal–and hence also no
$1$-extendible cardinal, no almost huge cardinal and no rank-into-rank
cardinal–can be made indestructible, even by comparatively mild
forcing: all such cardinals $kappa$ are destroyed by $Add(\kappa,1)$,
by $Add(\kappa,\kappa^+)$, by $Add(\kappa^+,1)$ and by many other
commonly considered forcing notions.

This is very recent joint work with Konstantinos Tsaprounis and Joan Bagaria.

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