In this article, we consider a knowledge accumulation problem within an organization that cannot prevent the worker from quitting and using the knowledge outside the organization. We show that knowledge accumulation is delayed: The fraction of working time allocated to knowledge creation is highest at the early career stage, falls gradually, then rises again, before falling finally toward zero. We determine the effect of a change in the severity of the enforcement problem (or the specificity of knowledge). We also discuss the form of the optimal life'cycle wage profiles, the role of the initial knowledge level, and the role of discounting.

In this paper, we consider minimization problems with constraints. We show that, if the set of constraints is a Finslerian manifold of non-positive flag curvature, and the objective function is differentiable and satisfies the Kurdyka-Lojasiewicz property, then the proximal point method can be naturally extended to solve this class of problems. We prove that the sequence generated by our method is well defined and converges to a critical point. We show how tools of Finslerian geometry, specifically non-symmetrical metrics, can be used to solve non-convex constrained problems in Euclidean spaces. As an application, we give one result regarding decision-making speed and costs related to change.

This paper develops some mathematical models arising in psychology and some other areas of behavioral sciences that are formalized via general preferences with variable ordering structures. Our considerations are based on the recent variational rationality approach, which unifies numerous theories in different branches of behavioral sciences using, in particular, worthwhile change and stay dynamics and variational traps. In the mathematical framework of this approach, we derive a new variational principle, which can be viewed as an extension of the Ekeland variational principle to the case of set-valued mappings on quasimetric spaces with cone-valued ordering variable structures. Such a general setting is proved to be appropriate for broad applications to the functioning of goal systems in psychology, which are developed in the paper. In this way, we give a certain answer to the following striking question: in the world, where all things change (preferences, motivations, resistances, etc.), where goal systems drive a lot of entwined course pursuits between means and ends, what can stay fixed for a while? The obtained mathematical results and new insights open the door to developing powerful models of adaptive behavior, which strongly depart from pure static general equilibrium models of the Walrasian type, which are typical in economics.

We consider minimization problems with constraints. We show that if the set of constraints is a Riemannian manifold of non positive curvature and the objective function is lower semicontinuous and satisfies the Kurdyka-Lojasiewicz property, then the alternating proximal algorithm in Euclidean space is naturally extended to solve that class of problems. We prove that the sequence generated by our algorithm is well defined and converges to an inertial Nash equilibrium under mild assumptions about the objective function. As an application, we give a welcome result on the difficult problem of "learning how to play Nash" (convergence, convergence in finite time, speed of convergence, constraints in action spaces in the context of "alternating potential games" with inertia).