Bifurcating DNS Thresholds in a Model of Organizational Bridge Building

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.