ON THE OPTIMAL COORDINATION OF UNINFORMED AGENTS BY AN INFORMED PRINCIPAL

We consider organizations with a single principal and many agents who interact in an environment with the following features -- (a) Nature im-perfectly informs the principal via a state-contingent signal, but not the agents, about the state of the world, (b) the principal selectively shares this information with the agents, thereby endogenously endow-ing them with private information that is coarser than his own, (c) the principal assigns action spaces to the agents, and (d) an agent’s control over the choice from his assigned action space is inalienable. Designing an organization involves specifying (c) and specifying an information dissemination system for implementing (b). Searching for an optimal design involves (1) deriving optimal performance from each design, and (2) comparing designs on the basis of their best performances. Our ex-istence results show the feasibility of performing Step (1) in a large class of cases.Existence theorems, optimal design, team, organization, principal-agent model

Non-holonomy, critical manifolds and stability in constrained Hamiltonian systems

We approach the analysis of dynamical and geometrical properties of nonholonomic mechanical systems from the discussion of a more general class of auxiliary constrained Hamiltonian systems. The latter is constructed in a manner that it comprises the mechanical system as a dynamical subsystem, which is confined to an invariant manifold. In certain aspects, the embedding system can be more easily analyzed than the mechanical system. We discuss the geometry and topology of the critical set of either system in the generic case, and prove results closely related to the strong Morse-Bott, and Conley-Zehnder inequalities. Furthermore, we consider qualitative issues about the stability of motion in the vicinity of the critical set. Relations to sub-Riemannian geometry are pointed out, and possible implications of our results for engineering problems are sketched.Comment: Latex, 58 page

On a fixed point theorem Krasnoselskii-Shafer type

In this paper a variant of a fixed point theorem to Krasnoselskii-Schaefer type is proved and it is further applied to certain nonlinear integral equation of mixed type for proving the existence of the solution