Production priorities in dynamic relationships

We characterize optimal contracts in a dynamic principal–agent model of joint production in which project opportunities are heterogenous, utility from these projects is nontransferable, and the agent has the option to quit the relationship at any time. To demand the production of projects that benefit her but not the agent, the principal must commit to produce projects that benefit the agent in the future. Production at all stages of the relationship is ordered by projects' cost‐effectiveness, which is their efficiency in transferring utility between the principal and the agent: cost‐effective demands impose relatively low costs on the agent and cost‐effective compensation imposes relatively low costs on the principal. Over time, optimal contracts become more generous toward the agent by adding commitments to less cost‐effective compensation. In turn, because this new compensation cannot be profitably exchanged against less cost‐effective demands, the principal narrows the scope of her demands.

Randomized Social Choice Functions Under Metric Preferences

We determine the quality of randomized social choice algorithms in a setting in which the agents have metric preferences: every agent has a cost for each alternative, and these costs form a metric. We assume that these costs are unknown to the algorithms (and possibly even to the agents themselves), which means we cannot simply select the optimal alternative, i.e. the alternative that minimizes the total agent cost (or median agent cost). However, we do assume that the agents know their ordinal preferences that are induced by the metric space. We examine randomized social choice functions that require only this ordinal information and select an alternative that is good in expectation with respect to the costs from the metric. To quantify how good a randomized social choice function is, we bound the distortion, which is the worst-case ratio between the expected cost of the alternative selected and the cost of the optimal alternative. We provide new distortion bounds for a variety of randomized algorithms, for both general metrics and for important special cases. Our results show a sizable improvement in distortion over deterministic algorithms.

Application Research on Treatment of Micro-Polluted Raw Water in Winter Western Mountainous Cities Using Composite Coagulants of PAC-PDM

In this study, micro-polluted raw water in winter western mountainous cities was treated by PAC-PDM . The CCD model of response surface methodology was employed to investigate the removal rate of turbidity . Taken the model as constraint conditions and taken the minimum agent cost as the objective function, optimization model of composite coagulants is established. The results showed that when the turbidity was 1 NTU，the dosage of PAC (based on Al2O3) is about 26mg/L, and the proportion of optimization model of composite coagulant PAC-PDM is 5% and the dosage of PAC (based on Al2O3) is about 8mg/L. Therefore the dosage of PAC of the optimized composite coagulant could be decreased by about70%, and agent costs decreased by about 56% compared with those of PAC.