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Trajectories more stable than the paper claims

Posted by kens on 29 May 2010 at 03:36 GMT

Interesting paper. I think the mathematical model could be applied to any activity that requires increasing levels of effort to support higher levels of success: from piano playing to exercise.

However, I think the paper looks at the wrong set of non-optimal trajectories; in particular there are many more equilibrium points, with the result that relationships are more stable than the paper concludes.

I discuss this in more detail at

No competing interests declared.

RE: Trajectories more stable than the paper claims

JMRey replied to kens on 29 May 2010 at 19:14 GMT

While the comments by kens are interesting, a crucial point is missing in the accompanying argument and proposed solutions: there is no trace of a consistent behavioral rule. A key assumption in the paper is that couples are formed with the intention of being as happy as possible. This entails –via the maximum principle- a rule for optimizing behavior in the short term, which implies following some of the trajectories in figure 3. On one hand the trajectories piecewise maximize some continuous sum of wealth. More importantly, they represent the tracks of a behavioral rule –naturally expressed in form of differential equation. Following trajectories of figure 3 thus seems the only possibility for the couples considered in the paper. This particularly applies when the relationship is out of the stable manifold, something that the couple cannot easily perceive.

It is clear that setting c=c* from the beginning is a possible –lazy- solution, but this is a myopic policy that forgets the role of the effort variable and entails no concern for couple’s wealth tomorrow. The equilibrium achieved that way is a poor solution in terms of total wealth and also may easily lead to an unsatisfactory feeling state. It is not a solution –either globally or locally- for the couple’s problem. The same applies to other solutions obtained by setting c=constant (non null).

Notice also that figure 4 just suggests a possible story for the breakup of a couple. One could probably tell other different –non optimal- breakup stories with the participation of the main actors in the paper, namely the presence of the effort gap plus the unstable nature of the combined feeling-effort dynamics.

The trajectories proposed by kens tell stories that do not correspond to couples trying to solve the problem (P) considered in the paper. In particular, the proposed set of solutions at the vertical nullcline are not equilibria of the feeling-effort system –which is the relevant dynamics for the couple that is trying to be happy.

No competing interests declared.