Contracts and Inequity Aversion

Inequity aversion is a special form of other regarding preferences and captures many features of reciprocal behavior, an apparently robust pattern in human nature. Using this concept we analyze the Moral Hazard problem and derive several results which differ from conventional contract theory. Our three key insights are: First, inequity aversion plays a crucial role in the design of optimal contracts. Second, there is a strong tendency towards linear sharing rules, giving a simple and plausible rationale for the prevalence of these schemes in the real world. Third, the Sufficient Statistics result no longer holds as optimal contracts may be ''too'' complete. Along with these key insights we derive a couple of further results.contract theory, linear contracts, incentives, sufficient statistics result, inequity aversion

Bayesian Conditional Density Filtering

We propose a Conditional Density Filtering (C-DF) algorithm for efficient online Bayesian inference. C-DF adapts MCMC sampling to the online setting, sampling from approximations to conditional posterior distributions obtained by propagating surrogate conditional sufficient statistics (a function of data and parameter estimates) as new data arrive. These quantities eliminate the need to store or process the entire dataset simultaneously and offer a number of desirable features. Often, these include a reduction in memory requirements and runtime and improved mixing, along with state-of-the-art parameter inference and prediction. These improvements are demonstrated through several illustrative examples including an application to high dimensional compressed regression. Finally, we show that C-DF samples converge to the target posterior distribution asymptotically as sampling proceeds and more data arrives.Comment: 41 pages, 7 figures, 12 table

Dynamical typicality for initial states with a preset measurement statistics of several commuting observables

We consider all pure or mixed states of a quantum many-body system which exhibit the same, arbitrary but fixed measurement outcome statistics for several commuting observables. Taking those states as initial conditions, which are then propagated by the pertinent Schr\"odinger or von Neumann equation up to some later time point, and invoking a few additional, fairly weak and realistic assumptions, we show that most of them still entail very similar expectation values for any given observable. This so-called dynamical typicality property thus corroborates the widespread observation that a few macroscopic features are sufficient to ensure the reproducibility of experimental measurements despite many unknown and uncontrollable microscopic details of the system. We also discuss and exemplify the usefulness of our general analytical result as a powerful numerical tool