19 research outputs found
A Rank-Based Reward between a Principal and a Field of Agents: Application to Energy Savings
We consider a problem where a Principal aims to design a reward function to a
field of heterogeneous agents. In our setting, the agents compete with each
other through their rank within the population in order to obtain the best
reward. We first explicit the equilibrium for the mean-field game played by the
agents, and then characterize the optimal reward in the homogeneous setting.
For the general case of a heterogeneous population, we develop a numerical
approach, which is then applied to the specific case study of the market of
Energy Saving Certificates
Ergodic control of a heterogeneous population and application to electricity pricing
We consider a control problem for a heterogeneous population composed of
customers able to switch at any time between different contracts, depending not
only on the tariff conditions but also on the characteristics of each
individual. A provider aims to maximize an average gain per time unit,
supposing that the population is of infinite size. This leads to an ergodic
control problem for a "mean-field" MDP in which the state space is a product of
simplices, and the population evolves according to a controlled linear
dynamics. By exploiting contraction properties of the dynamics in Hilbert's
projective metric, we show that the ergodic eigenproblem admits a solution.
This allows us to obtain optimal strategies, and to quantify the gap between
steady-state strategies and optimal ones. We illustrate this approach on
examples from electricity pricing, and show in particular that the optimal
policies may be cyclic-alternating between discount and profit taking stages
Quadratic Regularization of Unit-Demand Envy-Free Pricing Problems and Application to Electricity Markets
We consider a profit-maximizing model for pricing contracts as an extension
of the unit-demand envy-free pricing problem: customers aim to choose a
contract maximizing their utility based on a reservation bill and multiple
price coefficients (attributes). A classical approach supposes that the
customers have deterministic utilities; then, the response of each customer is
highly sensitive to price since it concentrates on the best offer. A second
approach is to consider logit model to add a probabilistic behavior in the
customers' choices. To circumvent the intrinsic instability of the former and
the resolution difficulties of the latter, we introduce a quadratically
regularized model of customer's response, which leads to a quadratic program
under complementarity constraints (QPCC). This allows to robustify the
deterministic model, while keeping a strong geometrical structure. In
particular, we show that the customer's response is governed by a polyhedral
complex, in which every polyhedral cell determines a set of contracts which is
effectively chosen. Moreover, the deterministic model is recovered as a limit
case of the regularized one. We exploit these geometrical properties to develop
an efficient pivoting heuristic, which we compare with implicit or non-linear
methods from bilevel programming. These results are illustrated by an
application to the optimal pricing of electricity contracts on the French
market.Comment: 37 pages, 9 figures; adding a section on the pricing of electricity
contract
Monitored eCLIP: high accuracy mapping of RNA-protein interactions
International audienceCLIP-seq methods provide transcriptome-wide snapshots of RNA-protein interactions in live cells. Reverse transcriptases stopping at cross-linked nucleotides sign for RNA-protein binding sites. Reading through cross-linked positions results in false binding site assignments. In the 'monitored enhanced CLIP' (meCLIP) method, a barcoded biotiny-lated linker is ligated at the 5 end of cross-linked RNA fragments to purify RNA prior to the reverse transcription. cDNAs keeping the barcode sequence correspond to reverse transcription read-throughs. Read through occurs in unpredictable proportions, representing up to one fourth of total reads. Filtering out those reads strongly improves reliability and precision in protein binding site assignment
A Rank-Based Reward between a Principal and a Field of Agents: Application to Energy Savings
We consider a problem where a Principal aims to design a reward function to a field of heterogeneous agents. In our setting, the agents compete with each other through their rank within the population in order to obtain the best reward. We first explicit the equilibrium for the mean-field game played by the agents, and then characterize the optimal reward in the homogeneous setting. For the general case of a heterogeneous population, we develop a numerical approach, which is then applied to the specific case study of the market of Energy Saving Certificates
A Rank-Based Reward between a Principal and a Field of Agents: Application to Energy Savings
We consider a problem where a Principal aims to design a reward function to a field of heterogeneous agents. In our setting, the agents compete with each other through their rank within the population in order to obtain the best reward. We first explicit the equilibrium for the mean-field game played by the agents, and then characterize the optimal reward in the homogeneous setting. For the general case of a heterogeneous population, we develop a numerical approach, which is then applied to the specific case study of the market of Energy Saving Certificates
Ergodic control of a heterogeneous population and application to electricity pricing
We consider a control problem for a heterogeneous population composed of customers able to switch at any time between different contracts, depending not only on the tariff conditions but also on the characteristics of each individual. A provider aims to maximize an average gain per time unit, supposing that the population is of infinite size. This leads to an ergodic control problem for a "mean-field" MDP in which the state space is a product of simplices, and the population evolves according to a controlled linear dynamics. By exploiting contraction properties of the dynamics in Hilbert's projective metric, we show that the ergodic eigenproblem admits a solution. This allows us to obtain optimal strategies, and to quantify the gap between steady-state strategies and optimal ones. We illustrate this approach on examples from electricity pricing, and show in particular that the optimal policies may be cyclic-alternating between discount and profit taking stages