Saurabh Vaishampayan

Leo Landolt, Anna Maddux, Andreas Schlaginhaufen et al.

We study resource allocation problems in which a central planner allocates resources among strategic agents with private cost functions in order to minimize a social cost, defined as an aggregate of the agents' costs. This setting poses two main challenges: (i) the agents' cost functions may be unknown to them or difficult to specify explicitly, and (ii) agents may misreport their costs strategically. To address these challenges, we propose an algorithm that combines preference-based learning with Vickrey-Clarke-Groves (VCG) payments to incentivize truthful reporting. Our algorithm selects informative preference queries via D-optimal design, estimates cost parameters through maximum likelihood, and computes VCG allocations and payments based on these estimates. In a one-shot setting, we prove that the mechanism is approximately truthful, individually rational, and efficient up to an error of $\tilde{\mathcal O}(K^{-1/2})$ for $K$ preference queries per agent. In an online setting, these guarantees hold asymptotically with sublinear regret at a rate of $\tilde{\mathcal O}(T^{2/3})$ after $T$ rounds. Finally, we validate our approach through a numerical case study on demand response in local electricity markets.

Saurabh Vaishampayan, Maryam Kamgarpour

Local energy markets empower prosumers to form coalitions for energy trading. However, the optimal partitioning of the distribution grid into such coalitions remains unclear, especially in constrained grids with stochastic production and consumption. This analysis must take into account the interests of both the grid operator and the constituent prosumers. In this work, we present a cooperative game theoretic framework to study distribution grid partitioning into local energy market coalitions under uncertain prosumption and grid constraints. We formulate the optimal stable partitioning problem to balance the interests of the grid operator with that of prosumers. Under deterministic load and generation, we show that the largest market coalition is the optimal stable partition. For the case of stochastic loads and generation, we provide an algorithm to evaluate the optimal stable partition. Numerical experiments are performed on benchmark and real world distribution grids. Our results help in understanding how uncertainty affects local energy market partitioning decisions in constrained distribution grids.