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arXiv · 2303.05489

Robust Social Welfare Maximization via Information Design in Linear-Quadratic-Gaussian Games

Furkan Sezer·Ceyhun Eksin
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Abstract

Information design in an incomplete information game includes a designer with the goal of influencing players' actions through signals generated from a designed probability distribution so that its objective function is optimized. We consider a setting in which the designer has partial knowledge on agents' utilities. We address the uncertainty about players' preferences by formulating a robust information design problem against worst case payoffs. If the players have quadratic payoffs that depend on the players' actions and an unknown payoff-relevant state, and signals on the state that follow a Gaussian distribution conditional on the state realization, then the information design problem under quadratic design objectives is a semidefinite program (SDP). Specifically, we consider ellipsoid perturbations over payoff coefficients in linear-quadratic-Gaussian (LQG) games. We show that this leads to a tractable robust SDP formulation. Numerical studies are carried out to identify the relation between the perturbation levels and the optimal information structures.

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Furkan Sezer, Ceyhun Eksin. 2023-03-09. Robust Social Welfare Maximization via Information Design in Linear-Quadratic-Gaussian Games. https://doi.org/10.1109/lcsys.2023.3291659

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