Agentic AI is shifting online shopping from search toward delegated purchasing, where autonomous buying agents monitor markets and decide when to buy on a consumer's behalf. We study the design of such strategic buying agents, which must decide when to purchase within a finite shopping window, translating price observations, the remaining time horizon, and beliefs about future price changes into a purchase policy. We formulate this problem across three information regimes: stationary, Bayesian, and robust, and treat the resulting optimal policies as a policy menu for implementation. In the stationary regime, price adjustments follow a Poisson arrival process with a known post-adjustment price distribution; the optimal policy is a dynamic purchase-threshold rule, with the threshold governed by an ordinary differential equation. In the Bayesian regime, the adjustment intensity is known, but the price-adjustment distribution is uncertain; the optimal rule remains threshold-based, now depending on posterior beliefs, and we bound the value of knowing the true distribution. In the robust regime, the agent has only price bounds and seeks worst-case protection; randomized threshold policies achieve optimal competitive-ratio and minimax-regret guarantees. We evaluate the proposed policies on Amazon price histories from Keepa (367 items, 48,933 timestamped observations) and examine their integration into language-model buying agents. The stationary and Bayesian policies perform competitively on mean normalized consumer surplus despite their stylized assumptions, while the robust policy performs best at the distribution's 10th percentile. Results suggest language models are better suited to selecting among regimes and calibration samples than to making buy-or-wait decisions directly.
Agentic commerce is moving from concept to deployed infrastructure: payment networks, retailers, and AI platforms are setting the stage for agents to transact on behalf of merchants and consumers. Yet whether the LLMs behind these agents can price competently in real markets, where customer preferences are hidden, competitors adapt in real time, and demand can shift without warning, has not been systematically tested. We introduce Bazaar, a dynamic sealed-bid benchmark for multi-attribute auction under these conditions. Despite its dynamics, the benchmark is grounded in closed-form customer utilities, enabling exact evaluation. Across 11 frontier LLMs from four providers, the leading agents on customer acquisition (e.g. Gemini 3.1 Pro) are often not the leading agents on profit (e.g. Opus 4.6). The ranking shifts again under demand shocks: agents that learned fastest pre-shock are typically the slowest to revise their beliefs afterwards, while Gemini 3.1 Pro recovers fastest despite not leading on profit. However, even the strongest agent captures less than a third of hindsight-optimal profit, suggesting current LLMs are progressing in agentic commerce but leave substantial headroom.
Search rankings are valuable because human attention is scarce and sequential. Higher-placed alternatives are easier to find, so they are examined and bought more often. Consumers are now delegating search to AI agents that can ingest an entire results page at once. Randomizing the order of one hundred hotel listings across 5,000 AI agent sessions, we compare four large language models against human field data. AI agents search more deeply than humans and never decline to buy. Position still predicts which listings are inspected, but weakly and non-monotonically: the middle of a results page has the lowest probability of inspection, not the bottom. Position reaches the choice stage for some models and not others, a heterogeneity that tracks neither provider nor capability. All models nonetheless converge on the same undominated listing. For agentic search, the attributes displayed on a results page matter more than placement within it.
Traditionally, decision support studies how humans use machine learning models to make better decisions. In modern agentic systems, this division of roles is increasingly reversed: AI agents act on behalf of users, while humans and tools becomes support mechanisms around them. This role reversal brings reliability concerns to the forefront, since agentic errors can be consequential and agent behavior must remain aligned with human goals and constraints. Departing from the classical view of decision support, we revisit its two basic principles, the cost--value tradeoff of seeking support and the role of uncertainty quantification, in a setting where AI agents are the central actors. We propose a framework for strategic decision support for AI agents through an optimization problem that minimizes support usage subject to controlling a counterfactual missed-support error: the probability that the agent acts alone on instances where support would have materially improved its output. At the population level, we show that the optimal policy is a threshold rule on the value of support. Building on this structure, we develop an online algorithm that adaptively thresholds such a score and uses randomized exploration to control missed-support error without distributional assumptions. We further introduce a calibration-on-the-fly method that reduces unnecessary support calls online. We instantiate this framework across diverse scenarios, including information gathering, human--AI collaboration, and tool use, showing how each can be modeled through the same strategic decision-support lens. Experiments across these settings show that our method reliably controls the target error while substantially reducing support usage in practice.