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Christian Hellwig, and Nicolas Werquin

2026, forthcoming

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Alexandre de Cornière, and Greg Taylor

2026, forthcoming

Cyberattacks are a pervasive threat in the digital economy, with the potential to harm firms and their customers. Larger firms constitute more valuable targets to hackers, thereby creating negative network effects. These can be mitigated by investments in security, which play both a deterrent and a...

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Céline Giner, Céline Nauges, and Katherine Hassett

2026, forthcoming

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Matti Liski, and François Salanié

2026, forthcoming

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Jérôme Bolte, Tam Le, Eric Moulines, and Edouard Pauwels

2026, forthcoming

Motivated by the extensive application of approximate gradients in machine learning and optimization, we investigate inexact subgradient methods subject to persistent additive errors. Within a nonconvex semialgebraic framework, assuming boundedness or coercivity, we establish that the method yields...

Article

Léo Portales, Elsa Cazelles, and Edouard Pauwels

2026, forthcoming

Lloyd’s algorithm is an iterative method that solves the quantization problem, that is, the approximation of a target probability measure by a discrete one, and is particularly used in digital applications. This algorithm can be interpreted as a gradient method on a certain quantization functional...

Article

Rossi Abi Rafeh, Pierre Dubois, Rachel Griffith, and Martin O'Connell

2026, forthcoming

We develop a dynamic equilibrium model of firm competition to analyze the effects of counterfactual policies, such as taxes and advertising restrictions, on pricing, advertising, consumption, and welfare. Using micro-level data, we estimate how consumer exposure to television commercials influences...

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Christophe Cahn, Patrick Fève, and Julien Matheron

2026, forthcoming

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Violeta I. Haas, Konstantin Bogatyrev, Tarik Abou-Chadi, Heike Klüver, and Lukas F. Stoetzer

2026, forthcoming

Do strategies of state-sponsored homophobia translate into electoral gains? While a growing body of literature documents the increasing politicization of LGBTQ- and gender-related issues by illiberal elites, little is known about the electoral effects of these strategies. We address this important...

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Michael Albertus, and Victor Gay

2026, forthcoming

Early modern European powers were beset by episodic unrest as they sought to consolidate their authority and build empires. We examine how growing state communication networks and the penetration of society impacted unrest by combining original and detailed parish-level data from pre-Revolutionary...

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