Consider the stochastic nonlinear oscillator equationwith β < 0 and σ = 0. If 4β + σ 2 > 0 then for small enough ε > 0 the system (x, ẋ) is positive recurrent in R 2 \ {(0, 0}. Now let λ(ε) denote the top Lyapunov exponent for the linearization of this equation along trajectories. The main result asserts thatas ε → 0 with λ > 0. This result depends crucially on the fact that the system above is a small perturbation of a Hamiltonian system. The method of proof can be applied to a more general class of small perturbations of two-dimensional Hamiltonian systems. The techniques used include (i) an extension of results of Pinsky and Wihstutz for perturbations of nilpotent linear systems, and (ii) a stochastic averaging argument involving motions on three different time scales.

No abstract

We are studying in this article an interplay between workers in organizations under the assumption that workers exhibit behavioral biases: envy, jealousy, or admiration toward the other coworkers' compensation. We assume workers care about their relative position, and we study the impact of this assumption on their efforts and on their optimal incentive contracts. We explicitly solve for the optimal incentive contract of moral hazard a la Holmstrom and Milgrom (Econometrica 55:303-328, 1987). We model team production by agents in which each agent's effort generates an observable signal and depends on efforts of other agents. One of the important findings is that an agent's optimal effort is negatively impacted by the behavioral biases in other agents' judgments. We also show envious behavior is destructive for organizations. Consistent with Tirole (Econometrica 69(1):1-35, 2001), our findings suggest that in the presence of agency problems induced by envy or jealousy, the optimal compensation exhibits high pay-for-performance sensitivity.

No abstract

No abstract