J. P. Caulkins, G. Feichtinger, D. Grass, G. Tragler:
"A model of moderation: finding Skiba points on a slippery slope";
Central European Journal of Operations Research,
A simple model is considered that rewards "moderation" - finding
the right balance between sliding down either of two "slippery slopes".
Optimal solutions are computed as a function of two key parameters:
(1) the cost of resisting the underlying uncontrolled dynamics and (2)
the discount rate. Analytical expressions are derived for bifurcation lines
separating regions where it is optimal to fight to stay balanced, to give in
to the attraction of the "left" or the "right", or to decide based on one's
initial state. The latter case includes situations both with and without
so-called Dechert-Nishimura-Skiba (DNS) points defining optimal solution
strategies. The model is unusual for having two DNS points in a one-state
model, having a single DNS point that bifurcates into two DNS points,
and for the ability to explicitly graph regions within which DNS points
occur in the 2-D parameter space. The latter helps give intuition and
insight concerning conditions under which these interesting points occur.
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