A Systematic Approach to Mechanism Design with Stochastic Dynamic Stability
Abstract
We consider a resource allocation problem with strategic agents that have private stochastic satisfaction functions and local constraints. To achieve a global optimal solution, we propose an incentive mechanism that induces a game among the agents. For the payment function of the mechanism, we construct a family of quadratic functions using the linear matrix inequality (LMI) approach that implements the social welfare maximizing outcome on the unique Nash equilibrium (NE) of the induced game while ensuring budget balance and individual rationality. Moreover, we propose a decentralized variable sample-size proximal best-response (VS-PBR) algorithm with Krasnoselskij iteration where only aggregate information is available to the agents. The algorithm is dynamically stable, as it is proven to converge in the mean-square sense to the NE of the game. The efficiency of the mechanism is then investigated on the Sioux Falls City transportation network, where electric vehicle (EV) users jointly select their destination and route.
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BibTeX
@misc{garjani2026systematic,
title = {{A Systematic Approach to Mechanism Design with Stochastic Dynamic Stability}},
author = {Shaya Garjani and Mohammad Shokri and Hamed Kebriaei},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29130},
eprint = {2608.29130},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29130},
}
RIS
TY - UNPB
TI - A Systematic Approach to Mechanism Design with Stochastic Dynamic Stability
AU - Shaya Garjani
AU - Mohammad Shokri
AU - Hamed Kebriaei
PY - 2026
DA - 2026/08/29
PB - arXiv
DO - 10.48550/arxiv.2608.29130
UR - https://arxiv.org/abs/2608.29130
AB - We consider a resource allocation problem with strategic agents that have private stochastic satisfaction functions and local constraints. To achieve a global optimal solution, we propose an incentive mechanism that induces a game among the agents. For the payment function of the mechanism, we construct a family of quadratic functions using the linear matrix inequality (LMI) approach that implements the social welfare maximizing outcome on the unique Nash equilibrium (NE) of the induced game while ensuring budget balance and individual rationality. Moreover, we propose a decentralized variable sample-size proximal best-response (VS-PBR) algorithm with Krasnoselskij iteration where only aggregate information is available to the agents. The algorithm is dynamically stable, as it is proven to converge in the mean-square sense to the NE of the game. The efficiency of the mechanism is then investigated on the Sioux Falls City transportation network, where electric vehicle (EV) users jointly select their destination and route.
ER -