LLM-based agents increasingly automate business and consumer tasks but are slow and expensive. Decision models, a new class that chooses among options without generating text, are far faster and less costly. Developers call them "System One models," referencing dual process theory. We ask whether such models can be steered by digital nudges online and whether, as the theory predicts, automatic nudges affect them more than reflective ones. We adapted an online shopping experiment, previously run with humans and LLM agents, to three decision models (Jev, Decision-1, d1). Across 600 runs per model, they chose a preselected default in 97.5-99.9% and a product with social influence information in 75-96% of choices, versus 47-49% in the control. All responded more strongly to the automatic nudge, the opposite of what has been reported for reasoning-capable LLM agents. We provide first evidence that non-generative decision models are susceptible to digital nudges in a System 1 pattern, implying agent-type-specific nudge effects.

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