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J. P. Caulkins, G. Feichtinger, D. Grass, G. Tragler:
"Bifurcating DNS thresholds in a model of organizational bridge building";
Journal of Optimization Theory and Applications, 133 (2007), 19 - 35.

A simple optimal control model is introduced, where "bridge building"
positions are rewarded. Optimal solutions can be classified with regard to the two
parameters (i) the cost of adjusting one´s position in a social network and (ii) the
discount rate. A complete analytical description is derived for the bifurcation lines
in parameter space, which separate regions with different optimal behavior. These
behaviors are always approaching the organizational boundary, always falling away
from the boundary, and deciding based on one´s initial state. The latter case gives rise
to the emergence of so-called Dechert-Nishimura-Skiba (DNS) points describing
optimal solution strategies. Furthermore the bifurcation from a single DNS point into
two DNS points is analyzed in parameter space. All these strategies have a sensible
interpretation within the context of the model.

Optimal control · Thresholds · Multiple equilibria · Political behavior