Stabilization of Collective Motion in Synchronized, Balanced and Splay Phase Arrangements on a Desired Circle

This paper proposes a design methodology to stabilize collective circular motion of a group of N-identical agents moving at unit speed around individual circles of different radii and different centers. The collective circular motion studied in this paper is characterized by the clockwise rotation of all agents around a common circle of desired radius as well as center, which is fixed. Our interest is to achieve those collective circular motions in which the phases of the agents are arranged either in synchronized, in balanced or in splay formation. In synchronized formation, the agents and their centroid move in a common direction while in balanced formation, the movement of the agents ensures a fixed location of the centroid. The splay state is a special case of balanced formation, in which the phases are separated by multiples of 2 pi/N. We derive the feedback controls and prove the asymptotic stability of the desired collective circular motion by using Lyapunov theory and the LaSalle's Invariance principle.

Money buys happiness in constant payments

Resumen: Nobody doubts that money buys at least some happiness. The question is how and why. This study answers that question. Some university students were asked to imagine they would win a one million dollars prize payable in five yearly payments, and to choose what plan –an increasing, constant, or decreasing payments plan– would make them happier. They were also asked why, and what would they spend the money on. The findings suggest that money buys happiness in constant payments because of better expense management on basic goods. And they provide converging evidence that money promotes happiness when spent on others.

Payments for Water Ecosystem Services in Latin America: Evidence from Reported Experience

27 p.

Opt-out options in new product co-development partnerships

We study three contractual arrangements—co-development, licensing, and co-development with opt-out options—for the joint development of new products between a small and financially constrained innovator firm and a large technology company, as in the case of a biotech innovator and a major pharma company. We formulate our arguments in the context of a two-stage model, characterized by technical risk and stochastically changing cost and revenue projections. The model captures the main disadvantages of traditional co-development and licensing arrangements: in co-development the small firm runs a risk of running out of capital as future costs rise, while licensing for milestone and royalty (M&R) payments, which eliminates the latter risk, introduces inefficiency, as profitable projects might be abandoned. Counter to intuition we show that the biotech's payoff in a licensing contract is not monotonically increasing in the M&R terms. We also show that an option clause in a co-development contract that gives the small firm the right but not the obligation to opt out of co-development and into a pre-agreed licensing arrangement avoids the problems associated with fully committed co-development or licensing: the probability that the small firm will run out of capital is greatly reduced or completely eliminated and profitable projects are never abandoned.