Suchergebnisse

Some background on ordinary differential equations -- Pragmatic introduction to stochastic differential equations -- Itô calculus and stochastic differential equations -- Probability distributions and statistics of SDEs -- Statistics of linear stochastic differential equations -- Useful theorems and formulas for SDEs -- Numerical simulation of SDEs -- Approximation of non-linear SDEs -- Filtering and smoothing theory -- Parameter estimation in SDE models -- Stochastic differential equations in machine learning.

We study a 2-players stochastic differential game of lobbying. Players have opposite interests; at any date, each player invests in lobbying activities to alter the legislation, the continuous state variable of the game, in her own benefit. The payoffs are quadratic and uncertainty is driven by a Wiener process. We prove that while a symmetric Markov Perfect Equilibrium (MPE) always exists, (two) asymmetric MPE only emerge when uncertainty is large enough. In the latter case, the legislative state converges to a stationary invariant distribution. We fully characterize existence and stochastic stability of the legislative state for both types of MPE. We finally study the implications for rent dissipation asymptotically. We show in particular that while the average rent dissipation is lower with asymmetric equilibria relative to the symmetric, the former yield larger losses at the most likely asymptotic states for large enough but moderate uncertainty.