45,756 research outputs found
Credible Group Stability in Many-to-Many Matching Problems
It is known that in two-sided many-to-many matching problems, pairwise stable matchings may not be immune to group deviations, unlike in many- to-one matching problems (Blair 1988). In this paper, we show that pairwise stability is equivalent to credible group stability when one side has responsive preferences and the other side has categorywise- responsive preferences. A credibly group-stable matching is immune to any âexecutableâ group deviations with an appropriate definition of executability. Under the same preference restriction, we also show the equivalence between the set of pairwise-stable matchings and the set of matchings generated by coalition-proof Nash equilibria of an appropriately defined strategic-form game.
Strongly reinforced P\'olya urns with graph-based competition
We introduce a class of reinforcement models where, at each time step ,
one first chooses a random subset of colours (independent of the past)
from colours of balls, and then chooses a colour from this subset with
probability proportional to the number of balls of colour in the urn raised
to the power . We consider stability of equilibria for such models
and establish the existence of phase transitions in a number of examples,
including when the colours are the edges of a graph, a context which is a toy
model for the formation and reinforcement of neural connections.Comment: 32 pages, 5 figure
Hamiltonian Relative Equilibria with Continuous Isotropy
In symmetric Hamiltonian systems, relative equilibria usually arise in
continuous families. The geometry of these families in the setting of free
actions of the symmetry group is well-understood. Here we consider the question
for non-free actions. Some results are already known in this direction, and we
use the so called bundle equations to provide a systematic treatment of this
question which both consolidates the known results, extending the scope of the
results to deal with non-compact symmetry groups, as well as producing new
results. Specifically we address questions about the stability, persistence and
bifurcations of these relative equilibria
Stability of relative equilibria with singular momentum values in simple mechanical systems
A method for testing -stability of relative equilibria in Hamiltonian
systems of the form "kinetic + potential energy" is presented. This method
extends the Reduced Energy-Momentum Method of Simo et al. to the case of
non-free group actions and singular momentum values. A normal form for the
symplectic matrix at a relative equilibrium is also obtained.Comment: Partially rewritten. Some mistakes fixed. Exposition improve
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