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This paper is concerned with two-person mean-field linear-quadratic non-zero sum stochastic differential games in an infinite horizon. Both open-loop and closed-loop Nash equilibria are introduced. The existence of an open-loop Nash equilibrium is characterized by the solvability of a system of mean-field forward-backward stochastic differential equations in an infinite horizon and the convexity of the cost functionals, and the closed-loop representation of an open-loop Nash equilibrium is given through the solution to a system of two coupled non-symmetric algebraic Riccati equations. The existence of a closed-loop Nash equilibrium is characterized by the solvability of a system of two coupled symmetric algebraic Riccati equations. Two-person mean-field linear-quadratic zero-sum stochastic differential games in an infinite horizon are also considered. Both the existence of open-loop and closed-loop saddle points are characterized by the solvability of a system of two coupled generalized algebraic Riccati equations with static stabilizing solutions. Mean-field linear-quadratic stochastic optimal control problems in an infinite horizon are discussed as well, for which it is proved that the open-loop solvability and closed-loop solvability are equivalent.

Industrial emissions play a major role in the global methane budget. The Permian basin is thought to be responsible for almost half of the methane emissions from all U.S. oil- and gas-producing regions, but little is known about individual contributors, a prerequisite for mitigation. We use a new class of satellite measurements acquired during several days in 2019 and 2020 to perform the first regional-scale and high-resolution survey of methane sources in the Permian. We find an unexpectedly large number of extreme point sources (37 plumes with emission rates >500 kg hour −1 ), which account for a range between 31 and 53% of the estimated emissions in the sampled area. Our analysis reveals that new facilities are major emitters in the area, often due to inefficient flaring operations (20% of detections). These results put current practices into question and are relevant to guide emission reduction efforts.