Sentimental equilibria with optimal control
The ubiquitous phenomenon of marital dissolution in the West poses a major theoretical problem that is not well understood. The fact that most couples declare that they are committed to an enduring and happy relationship allows us to model their sentimental relationship as a simple optimal control problem. A state variable monitors the wellness of the relationship whose natural decay in time must be counteracted with effort - the control variable - according to a widely accepted principle in marital psychology. Equilibria are basic desirable solutions of this control problem. In this note key properties of equilibria - in particular, existence, dynamical instability and sensitivity analysis - are obtained for a class of decaying sentimental dynamics. An underlying mechanism combining the existence of an effort stress with the instability of the model may be identified as a main cause of distress for the couple relationship. (C) 2012 Elsevier Ltd. All rights reserved.
optimal control marriage divorce couple disruption equilibrium