A simple optimal control model is introduced, where "bridge building" positions are rewarded. The optimal solutions can be classified in regards of the two extern parameters, (1) costs for the control staying at such an exposed position and (2) the discount rate. A complete analytical description of the bifurcation lines in parameter space is derived, which separates regions with different optimal behavior. These are resisting the influence from inner and outer forces, always fall off from the boundaries or decide based on one’s initial state. This 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 has been analyzed in parameter space. All these strategies have a funded interpretation within the limits of the model.
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