Shopping by algorithm: How agentic AI deploys human heuristics as a surrogate consumer

Davood Wadi; Yu Ma

econ.GNSep 23, 2026

Shopping by algorithm: How agentic AI deploys human heuristics as a surrogate consumer

Authors: Davood Wadi, Yu Ma

Organizations: Desautels Faculty of Management, McGill University, Montreal, Quebec, Canada

Abstract

Consumers increasingly delegate purchasing decisions to Large Language Models (LLMs) acting as surrogate consumers. Using "Tool-Lab," an adaptation of information-board process tracing that places product attributes behind costly tool calls, we examine how marketing pricing cues (i.e., just-below pricing and promotional framing) influence AI shopping agents. Across eight commercially deployed LLMs from three providers, we trace pre-choice information acquisition. Under zero cost, pricing cues rarely mislead. Imposing acquisition costs under a vague goal prompt leads LLMs to omit diagnostic attributes required to compute unit price and choose suboptimal choices resembling human heuristics. Relative to a specific goal prompt that mainly preserves diagnostic search and choice optimality, a vague goal prompt under constraints creates a search-mediated vulnerability. This research demonstrates that marketing heuristics in delegated AI shopping are governed by storefront information architecture, not necessarily immutable LLM flaws.

Figures & tables

Figure 2: Tool-Lab setup for $10 cost per inspect_cell tool call (Study 1)

Goal Prompt	Cost	Cents	Weight	Dollars	Diagnostic	Choice Optimality
Specific	$0	2.00 (0.00)	2.00 (0.00)	2.00 (0.00)	6.00 (0.00)	0.94 (0.16)
Specific	$10	1.72 (0.59)	2.00 (0.00)	2.00 (0.00)	5.72 (0.59)	0.83 (0.30)
Vague	$0	1.97 (0.09)	1.90 (0.18)	2.00 (0.00)	5.86 (0.24)	0.89 (0.19)
Vague	$10	0.77 (0.78)	1.10 (0.64)	1.94 (0.09)	3.81 (1.30)	0.29 (0.28)

Table 1: Aggregate diagnostic information acquisition and choice optimality across LLMs (Study 1 Tool-Lab)

	Study 1			Study 2
	Estimate	SD	95% CI	Estimate	SD	95% CI
Stage 1: Diagnostic acquisition
Acquisition cost ( $a_{1}$ )	-0.270	0.217	[-0.698, 0.161]	-0.674	0.462	[-1.582, 0.260]
Vague goal prompt ( $a_{2}$ )	-0.135	0.117	[-0.371, 0.095]	0.015	0.072	[-0.125, 0.156]
Acquisition cost $\times$ Vague goal prompt ( $a_{3}$ )	-1.727*	0.467	[-2.641, -0.765]	-2.902*	1.121	[-5.027, -0.539]
Acquisition cost under vague goal prompt ( $a_{\text{Vague}}$ )	-1.997*	0.487	[-2.952, -1.003]	-3.576*	1.218	[-5.925, -1.062]

Table 2: Multilevel moderated mediation of acquisition cost and prompt specificity on choice optimality (Studies 1 and 2 Tool-Lab)

Goal Prompt	Cost	List Price	Discount	Weight	Diagnostic	Choice Optimality
Specific	$0	3.00 (0.00)	2.98 (0.03)	3.00 (0.00)	8.98 (0.03)	0.90 (0.25)
Specific	$50	2.90 (0.25)	2.50 (0.59)	2.86 (0.35)	8.26 (1.03)	0.88 (0.23)
Vague	$0	3.00 (0.00)	3.00 (0.00)	3.00 (0.00)	9.00 (0.00)	0.86 (0.31)
Vague	$50	1.94 (1.24)	1.58 (1.23)	1.31 (1.14)	4.82 (3.49)	0.48 (0.29)

Table 3: Aggregate diagnostic information acquisition and choice optimality across LLMs (Study 2 Tool-Lab)

	Normative Benchmark	Flash Lite	Flash	Pro	Sonnet	Opus	Luna	Terra	Sol
Weight (oz)	2.78*** (0.21)	1.51*** (0.09)	1.15*** (0.07)	2.04*** (0.13)	2.61*** (0.19)	1.06*** (0.06)	2.60*** (0.19)	2.78*** (0.21)	2.78*** (0.21)
Dollars ($)	-4.28*** (0.31)	-2.14*** (0.13)	-1.69*** (0.10)	-3.11*** (0.20)	-3.99*** (0.28)	-1.54*** (0.09)	-4.00*** (0.29)	-4.29*** (0.31)	-4.29*** (0.31)
Cents ($)	-4.74*** (0.51)	-1.81*** (0.30)	-0.92** (0.31)	-3.18*** (0.37)	-4.45*** (0.48)	-1.25*** (0.29)	-4.45*** (0.48)	-4.75*** (0.51)	-4.75*** (0.51)
Brand (Maxwell House)	-0.24 (0.23)	-0.18 (0.18)	-0.56** (0.21)	-0.30 (0.20)	-0.09 (0.22)	-0.46* (0.20)	-0.21 (0.22)	-0.24 (0.23)	-0.24 (0.23)
Brand (McCafé)	-0.35 (0.22)	0.17 (0.18)	0.95*** (0.19)	-0.03 (0.20)	-0.19 (0.21)	2.10*** (0.19)	-0.26 (0.21)	-0.37 (0.22)	-0.37 (0.22)
Brand (Starbucks)	-0.12 (0.22)	0.91*** (0.18)	4.44*** (0.28)	1.03*** (0.20)	0.26 (0.21)	3.50*** (0.23)	-0.08 (0.21)	-0.10 (0.22)	-0.10 (0.22)

Table 4: Conditional logit estimates when all attributes are visible (Study 1 Baseline)

LLM	$\beta_{Dollars(\$ )}$	$\beta_{Cents(\$ )}$	$\beta_{Cents(\$ )}/\beta_{Dollars($)}$	95% CI
Normative Benchmark	-4.28	-4.74	1.11	[0.94, 1.27]
Flash Lite	-2.14	-1.81	0.84	[0.58, 1.11]
Flash	-1.69	-0.92	0.55	[0.19, 0.90]
Pro	-3.11	-3.18	1.02	[0.83, 1.22]
Sonnet	-3.99	-4.45	1.12	[0.94, 1.28]
Opus	-1.54	-1.25	0.81	[0.45, 1.17]

Table 5: Ratio of cent to dollar price sensitivity (Study 1 Baseline)

Prompt goal

Prompt text

Vague

You have been delegated by a consumer to make purchase decision. Your goal is to choose an instant coffee for the user. After you choose a coffee, the user would purchase 5 bags of your chosen coffee. You can open the cells to get information about the product using the inspect_cell tool, or you can stop searching and submit your choice with the submit_choice tool. Every time you use the inspect_cell tool, the user loses {inspect_tool_cost}. submit_choice has no cost. You need to find the best deal on instant coffee. Which coffee would you choose for the user?

Specific

You have been delegated by a consumer to make purchase decision. Your goal is to choose an instant coffee for the user. After you choose a coffee, the user would purchase 5 bags of your chosen coffee. You can open the cells to get information about the product using the inspect_cell tool, or you can stop searching and submit your choice with the submit_choice tool. Every time you use the inspect_cell tool, the user loses {inspect_tool_cost}. submit_choice has no cost. You need to find the coffee with the lowest price per ounce . Which coffee would you choose for the user?

Table 6: Prompt manipulation establishing goal specificity (Studies 1 and 2 Tool-Lab)

LLM	Cost	Vague				Specific
		Cents	Weight	Diagnostic	Optimality	Cents	Weight	Diagnostic	Optimality
Flash Lite	$0	2.00 (0.00)	1.54 (0.85)	5.54 (0.85)	0.47 (0.50)	2.00 (0.00)	2.00 (0.00)	6.00 (0.00)	0.54 (0.50)
Flash Lite	$10	2.00 (0.00)	1.10 (1.00)	5.10 (1.00)	0.35 (0.48)	2.00 (0.00)	2.00 (0.00)	6.00 (0.00)	0.75 (0.44)
Flash	$0	2.00 (0.00)	2.00 (0.00)	6.00 (0.00)	1.00 (0.00)	2.00 (0.00)	2.00 (0.00)	6.00 (0.00)	1.00 (0.00)
Flash	$10	0.20 (0.60)	0.96 (0.96)	3.01 (1.45)	0.16 (0.37)	1.58 (0.82)	2.00 (0.00)	5.58 (0.82)	0.79 (0.41)
Pro	$0	1.75 (0.64)	1.68 (0.74)	5.43 (1.34)	0.76 (0.43)	2.00 (0.00)	2.00 (0.00)	6.00 (0.00)	1.00 (0.00)

Table 7: Inspecting Cents, Weight, Dollars, Diagnostic information acquisition and choice optimality (Study 1 Tool-Lab)

LLM	$a_{1}$ (Cost: Unit price)	$a_{3}$ (Cost $\times$ Vague)	$b_{1}$ (Diagnostic acquistion)	$c^{\prime}$ (Direct effect)
Flash Lite	0.005 [-0.149, 0.159]	-0.479 [-0.729, -0.225]*	0.297 [0.265, 0.328]*	0.106 [0.062, 0.151]*
Flash	-0.423 [-0.573, -0.270]*	-2.548 [-2.790, -2.305]*	0.210 [0.191, 0.230]*	-0.166 [-0.219, -0.113]*
Pro	-0.023 [-0.175, 0.131]	-3.233 [-3.482, -2.983]*	0.224 [0.206, 0.241]*	0.013 [-0.038, 0.065]
Luna	-0.017 [-0.170, 0.132]	-0.163 [-0.402, 0.085]	0.385 [0.321, 0.451]*	-0.022 [-0.066, 0.022]
Sol	-0.012 [-0.166, 0.138]	-2.694 [-2.937, -2.457]*	0.248 [0.228, 0.267]*	-0.072 [-0.124, -0.022]*
Terra	-0.059 [-0.211, 0.090]	-3.068 [-3.309, -2.827]*	0.179 [0.161, 0.197]*	-0.090 [-0.143, -0.038]*

Table 8: Moderated mediation structural path estimates by LLM (Study 1 Tool-Lab)

LLM	Indirect (Unit price)	Indirect (Vague prompt)	Index of Moderated Mediation (IMM)	Total effect (Vague)
Flash Lite	0.001 [-0.044, 0.048]	-0.141 [-0.201, -0.081]*	-0.142 [-0.218, -0.066]*	-0.035 [-0.108, 0.038]
Flash	-0.089 [-0.122, -0.056]*	-0.624 [-0.695, -0.556]*	-0.535 [-0.607, -0.467]*	-0.791 [-0.855, -0.727]*
Pro	-0.005 [-0.040, 0.029]	-0.730 [-0.802, -0.657]*	-0.725 [-0.805, -0.646]*	-0.716 [-0.785, -0.649]*
Luna	-0.006 [-0.066, 0.051]	-0.069 [-0.145, 0.005]	-0.063 [-0.158, 0.033]	-0.091 [-0.176, -0.005]*
Terra	-0.011 [-0.038, 0.016]	-0.561 [-0.626, -0.494]*	-0.550 [-0.622, -0.481]*	-0.650 [-0.712, -0.589]*
Sol	-0.003 [-0.041, 0.035]	-0.671 [-0.743, -0.601]*	-0.668 [-0.750, -0.590]*	-0.742 [-0.813, -0.674]*

Table 9: Conditional indirect effects and index of moderated mediation by LLM (Study 1 Tool-Lab)

Variant	Prompt text
Original	You have been delegated by a consumer to make purchase decision. Your goal is to choose an instant coffee for the user. After you choose a coffee, the user would purchase 5 bags of your chosen coffee. You can open the cells to get information about the product using the inspect_cell tool, or you can stop searching and submit your choice with the submit_choice tool. Every time you use the inspect_cell tool, the user loses {inspect_tool_cost}. submit_choice has no cost. {goal_prompt} Which coffee would you choose for the user?
Sentence reorder	You have been delegated by a consumer to make purchase decision. Your goal is to choose an instant coffee for the user. {goal_prompt} After you choose a coffee, the user would purchase 5 bags of your chosen coffee. You can open the cells to get information about the product using the inspect_cell tool, or you can stop searching and submit your choice with the submit_choice tool. Every time you use the inspect_cell tool, the user loses {inspect_tool_cost}. submit_choice has no cost. Which coffee would you choose for the user?
Cost paraphrase	You have been delegated by a consumer to make purchase decision. Your goal is to choose an instant coffee for the user. After you choose a coffee, the user would purchase 5 bags of your chosen coffee. You can open the cells to get information about the product using the inspect_cell tool, or you can stop searching and submit your choice with the submit_choice tool. Each inspect_cell costs the user {inspect_tool_cost}. submit_choice has no cost. {goal_prompt} Which coffee would you choose for the user?

Table 10: Prompts used in the prompt variation study (Study 1 Tool-Lab)

LLM	Prompt variation	$a_{3}$ a	$a_{\text{Vague}}$ b	$b_{1}$ c	IMM d
Flash Lite	Original	-0.441* [-0.698, -0.186]	-0.440* [-0.620, -0.256]	0.302* [0.236, 0.367]	-0.133* [-0.219, -0.054]
	Sentence reorder	-0.120 [-0.375, 0.140]	-0.120 [-0.302, 0.066]	0.241* [0.181, 0.299]	-0.029 [-0.093, 0.034]
	Cost paraphrase	-0.519* [-0.750, -0.289]	-0.519* [-0.683, -0.359]	0.269* [0.197, 0.343]	-0.140* [-0.218, -0.072]
Flash	Original	-2.56* [-2.89, -2.24]	-2.99* [-3.22, -2.75]	0.210* [0.189, 0.232]	-0.538* [-0.630, -0.452]
	Sentence reorder	-2.39* [-2.76, -2.00]	-2.97* [-3.24, -2.70]	0.205* [0.185, 0.224]	-0.488* [-0.582, -0.399]
	Cost paraphrase	-2.06* [-2.34, -1.78]	-2.36* [-2.56, -2.16]	0.278* [0.257, 0.298]	-0.572* [-0.665, -0.483]

Table 11: Disaggregated moderated mediation path estimates across prompt variations (Study 1 Tool-Lab)

LLM	Cost	Specific				Vague
		Price	Weight	Diagnostic	Optimality	Price	Weight	Diagnostic	Optimality
Flash Lite	$0	2.00 (0.00)	2.00 (0.00)	4.00 (0.00)	1.00 (0.00)	2.00 (0.00)	1.28 (0.96)	3.28 (0.96)	0.63 (0.49)
Flash Lite	$10	2.00 (0.00)	2.00 (0.00)	4.00 (0.00)	1.00 (0.00)	2.00 (0.00)	0.56 (0.90)	2.56 (0.90)	0.28 (0.45)
Flash	$0	2.00 (0.00)	2.00 (0.00)	4.00 (0.00)	1.00 (0.00)	2.00 (0.00)	2.00 (0.00)	4.00 (0.00)	1.00 (0.00)
Flash	$10	2.00 (0.00)	2.00 (0.00)	4.00 (0.00)	1.00 (0.00)	1.96 (0.20)	1.71 (0.69)	3.67 (0.79)	0.84 (0.37)
Pro	$0	2.00 (0.00)	2.00 (0.00)	4.00 (0.00)	1.00 (0.00)	2.00 (0.00)	1.98 (0.20)	3.98 (0.20)	0.99 (0.10)

Table 12: Inspecting Price and Weight, Diagnostic information acquisition and choice optimality (Study 1, Price partitioning)

LLM	Specific			Vague
	Price	Weight	Optimality	Price	Weight	Optimality
Flash Lite	0.00	0.00	0.00	0.00	-0.72	-0.35
Flash	0.00	0.00	0.00	-0.04	-0.29	-0.16
Pro	0.00	0.00	0.00	-0.02	-1.30	-0.64

Table 13: Difference in metric between

10 and

0 cost (Study 1, Price partitioning)

LLM	$a_{3}$ a	$a_{\text{Vague}}$ b	$b_{1}$ c	IMM d
Flash Lite	-0.721* [-0.981, -0.462]	-0.720* [-0.902, -0.536]	0.495* [0.488, 0.503]	-0.357* [-0.486, -0.228]
Flash	-0.332* [-0.489, -0.175]	-0.331* [-0.441, -0.221]	0.448* [0.435, 0.461]	-0.149* [-0.219, -0.078]
Pro	-1.320* [-1.510, -1.120]	-1.320* [-1.460, -1.180]	0.472* [0.459, 0.485]	-0.622* [-0.716, -0.526]

Table 14: Disaggregated moderated mediation estimates under unified price architecture (Study 1 Tool-Lab Robustness)

Figure W 1: Effects of purchase volume manipulation on the adopted objective, diagnostic acquisition, and choice optimality (Study 1 Tool-Lab).

LLM	Bags	Cents	Weight	Dollars	Diagnostic	Non-diagnostic	Optimality
Flash Lite	1	1.95	1.82	2.00	5.77	0.04	0.62
Flash Lite	5	2.00	1.54	2.00	5.54	0.06	0.47
Flash Lite	50	2.00	1.42	2.00	5.42	0.06	0.50
Flash Lite	250	2.00	1.30	2.00	5.30	0.04	0.37
Flash	1	2.00	2.00	2.00	6.00	7.68	1.00
Flash	5	2.00	2.00	2.00	6.00	7.62	1.00

Table 15: Count of cents, weight, dollars, diagnostic and non-diagnostic attributes, and choice optimality proportion for different purchase volume (number of bags)

LLM	Bags	price_per_weight	price	others
Flash	1	0.735	0.041	0.224
Flash	5	0.670	0.040	0.290
Flash	50	0.710	0.030	0.260
Flash	250	0.646	0.091	0.263
Pro	1	0.410	0.370	0.220
Pro	5	0.250	0.520	0.230

Table 16: Stated optimization objective distribution by purchase volume (number of bags)

Bags	$n_{\text{price}}$	$n_{\text{ppw}}$	$\Delta$ Diagnostic	95% CI	$\Delta$ Choice Optimality	95% CI
1	37	41	-1.22*	[-1.78, -0.70]	-0.54*	[-0.70, -0.38]
5	52	25	-1.10*	[-1.58, -0.65]	-0.40*	[-0.56, -0.25]
50	85	4	-1.84*	[-2.21, -1.47]	-0.69*	[-0.79, -0.60]
250	85	2	-2.09*	[-2.46, -1.73]	-0.23	[-0.79, 0.33]
Pooled	259	72	-1.59*	[-1.80, -1.37]	-0.47*	[-0.64, -0.29]

Table 17: Diagnostic information acquisition and choice optimality by stated optimization objective, holding purchase volume fixed (Gemini 3.1 Pro)

	Normative Benchmark	Flash Lite	Flash	Pro	Sonnet	Opus	Luna	Terra	Sol
Weight (oz)	1.79*** (0.11)	0.78*** (0.04)	1.12*** (0.06)	1.69*** (0.10)	1.61*** (0.10)	0.97*** (0.05)	1.76*** (0.11)	1.77*** (0.11)	1.79*** (0.11)
List Price	-3.08*** (0.19)	-1.06*** (0.05)	-1.86*** (0.10)	-2.90*** (0.17)	-2.73*** (0.16)	-1.51*** (0.08)	-3.03*** (0.18)	-3.04*** (0.18)	-3.08*** (0.19)
Discount Amount	3.08*** (0.19)	0.76*** (0.05)	1.91*** (0.10)	2.91*** (0.17)	2.75*** (0.16)	1.74*** (0.09)	3.01*** (0.18)	3.05*** (0.18)	3.08*** (0.19)
Brand (Maxwell House)	-0.14 (0.18)	0.17 (0.14)	-0.07 (0.18)	-0.16 (0.18)	-0.18 (0.18)	-0.70*** (0.18)	-0.11 (0.18)	-0.17 (0.18)	-0.14 (0.18)
Brand (McCafé)	-0.07 (0.18)	0.41** (0.13)	0.69*** (0.17)	-0.02 (0.18)	-0.03 (0.17)	1.25*** (0.16)	-0.05 (0.18)	-0.08 (0.18)	-0.09 (0.18)
Brand (Starbucks)	0.11 (0.18)	0.96*** (0.13)	2.99*** (0.21)	0.42* (0.18)	0.13 (0.17)	2.91*** (0.19)	0.17 (0.18)	0.16 (0.18)	0.13 (0.18)

Table 18: Conditional logit estimates of attribute utility when all attributes are visible (Study 2 Baseline)

LLM	$\beta_{\text{List price}}$	$\beta_{\text{Discount Amount}}$	$\beta_{\text{Discount Amt}}/\|\beta_{\text{List Price}}\|$
Normative Benchmark	-3.08	3.08	1.00 [0.98, 1.02]
Flash Lite	-1.06	0.76	0.72 [0.67, 0.77]
Flash	-1.86	1.91	1.03 [1.00, 1.06]
Pro	-2.9	2.91	1.00 [0.98, 1.03]
Sonnet	-2.73	2.75	1.01 [0.98, 1.03]
Opus	-1.51	1.74	1.15 [1.11, 1.19]

Table 19: Discount amount to list price sensitivity (Study 2 Baseline)

Alternative	Decision role	List price	Discount	Net price	Weight	Price per ounce
Coffee C	Lowest price	$8.00	0%	$8.00	8.0 oz	$1.000/oz
Coffee D	discount cue	$15.00	20%	$12.00	12.0 oz	$1.000/oz
Coffee E	Lowest price per weight (Optimal)	$10.00	0%	$10.00	10.9 oz	$0.917/oz

Table 20: Product stimuli and economic value decoupling (Study 2 Tool-Lab)

LLM	Cost	Vague		Specific
		Diagnostic acquisitions	Optimality	Diagnostic acquisitions	Optimality
Google
Flash Lite	$0	9.00 (0.00)	0.11 (0.31)	8.91 (0.45)	0.27 (0.45)
Flash Lite	$50	7.82 (1.64)	0.09 (0.29)	8.11 (1.35)	0.35 (0.48)
Flash	$0	9.00 (0.00)	1.00 (0.00)	9.00 (0.00)	1.00 (0.00)
Flash	$50	1.12 (1.60)	0.31 (0.46)	6.03 (3.69)	0.79 (0.41)

Table 21: Diagnostic information acquisition and choice optimality (Study 2 Tool-Lab)

LLM	$a_{1}$ (Cost: Unit Price)	$a_{3}$ (Cost $\times$ Deal)	$b_{1}$ (Diagnostic Search)	$c^{\prime}$ (Direct Effect)
Flash Lite	-0.861 [-1.154, -0.569]*	-0.320 [-0.726, 0.087]	-0.051 [-0.074, -0.028]*	-0.014 [-0.063, 0.031]
Flash	-2.914 [-3.209, -2.621]*	-4.962 [-5.370, -4.554]*	0.081 [0.071, 0.090]*	-0.009 [-0.068, 0.047]
Pro	-0.209 [-0.494, 0.082]	-3.619 [-4.027, -3.220]*	0.064 [0.053, 0.075]*	-0.009 [-0.054, 0.035]
Luna	-0.019 [-0.304, 0.276]	0.011 [-0.396, 0.424]	0.049 [-0.043, 0.131]	0.006 [-0.034, 0.051]
Sol	-0.250 [-0.539, 0.042]	-8.279 [-8.682, -7.864]*	0.076 [0.066, 0.085]*	-0.023 [-0.082, 0.027]
Terra	-0.147 [-0.428, 0.134]	-7.624 [-8.026, -7.222]*	0.067 [0.056, 0.076]*	-0.042 [-0.105, 0.009]

Table 22: Moderated mediation structural path estimates by LLM (Study 2 Tool-Lab)

LLM	Indirect (Unit Price)	Indirect (Deal Prompt)	Index of Moderated Mediation (IMM)	Total Effect (Deal)
Claude Opus 5	-0.204 [-0.253, -0.158]*	-0.516 [-0.591, -0.444]*	-0.312 [-0.383, -0.246]*	-0.471 [-0.540, -0.401]*
Claude Sonnet 5	0.001 [-0.056, 0.060]	-0.119 [-0.185, -0.056]*	-0.120 [-0.207, -0.038]*	-0.124 [-0.201, -0.049]*
Gemini 3.8 Flash	-0.235 [-0.272, -0.200]*	-0.635 [-0.711, -0.559]*	-0.400 [-0.456, -0.345]*	-0.644 [-0.706, -0.583]*
Gemini 3.5 Flash Lite	0.044 [0.021, 0.071]*	0.060 [0.031, 0.094]*	0.016 [-0.004, 0.041]	0.046 [-0.002, 0.094]
Gemini 3.1 Pro	-0.013 [-0.032, 0.005]	-0.246 [-0.292, -0.202]*	-0.233 [-0.281, -0.187]*	-0.255 [-0.308, -0.203]*
GPT-5.6 Luna	-0.001 [-0.023, 0.020]	0.000 [-0.023, 0.021]	0.000 [-0.029, 0.031]	0.006 [-0.041, 0.055]

Table 23: Conditional indirect effects and index of moderated mediation by LLM (Study 2 Tool-Lab)

	Prompt template
System prompt	You are a helpful shopping assistant.Your goal is to choose an alternative among the options given.Only output the digit of your final choice. Do not explain your answer or provide any additional text.
User prompt template	You are buying ground coffee. Which option would you choose?Option 1: {brand_1}; Weight: {weight_1}oz; Price: ${price_1}Option 2: {brand_2}; Weight: {weight_2}oz; Price:$ {price_2}Option 3: {brand_3}; Weight: {weight_3}oz; Price: ${price_3}Option 4: {brand_4}; Weight: {weight_4}oz; Price:$ {price_4}

Table 24: Delegating prompt template for Study 1 Baseline

Field	Type	Description
choice	integer	The digit of the option of your choice ( $1,2,3,\text{ or }4$ ).

Table 25: Structured JSON output schema for Study 1 Baseline

Prompt template

System prompt

You are a helpful shopping assistant.Your goal is to choose an alternative among the options given.Only output the digit of your final choice. Do not explain your answer or provide any additional text.

User prompt template

You are buying ground coffee. Which option would you choose?Option 1: {brand_1}; Weight: {weight_1}oz; List price:

{list_price_1}; {discount_text_1}Option 2: {brand_2}; Weight: {weight_2}oz; List price:

{list_price_2}; {discount_text_2}Option 3: {brand_3}; Weight: {weight_3}oz; List price:

{list_price_3}; {discount_text_3}Option 4: {brand_4}; Weight: {weight_4}oz; List price:

{list_price_4}; {discount_text_4}

Table 26: Delegating prompt template for Study 2 Baseline

Classified objective	Reasoning
Price-per-weight	“[…] My primary focus is always the price per unit, you know, the real cost-effectiveness. […]”
Price	“Okay, so the goal is to find the absolute lowest price on instant coffee. […]”
Others	“[…] My intuition tells me to zero in on the total price. […] While”best deal” often boils down to the lowest total price, sometimes it’s about getting the most coffee for your money – the best unit price. I’ll keep that in mind.”

Table 27: Example reasoning traces

Candidate judge	Type	Provider	Identifier
JEV 1.13	Decision model	TypeSafe	typesafe/jev-1.13-20260917
Liquid D1	Decision model	Liquid AI	liquid/d1-20260930
Mercury Decide	Decision model	Inception	inception/mercury-decide-20260930
pplx Decider v1 27B	Decision model	Perplexity	perplexity/pplx-decider-v1-27b-20261001
Solar Decide	Decision model	Upstage	upstage/solar-decide-20260928
Nemotron 3.5 Lightning 30B-A3B	LLM	NVIDIA	unsloth/NVIDIA-Nemotron-3.5-Lightning-30B-A3B-GGUF:Q4_K_XL

Table 28: Candidate judges for objective classification

Candidate judge	Coder 1		Coder 2		Coder 3		Mean $\kappa$
	$p_{o}$	$\kappa$	$p_{o}$	$\kappa$	$p_{o}$	$\kappa$	Mean $\kappa$
Mercury Decide a	.775	.592	.708	.490	.892	.804	.629
Liquid D1	.683	.466	.850	.707	.842	.709	.627
pplx Decider v1 27B	.758	.566	.708	.497	.883	.791	.618
Solar Decide	.783	.603	.692	.464	.850	.728	.598
JEV 1.13	.692	.450	.792	.588	.825	.665	.568

Table 29: Agreement between human coders and candidate judges

Labeler	Purchase volume				Slope (SE)	$p$
	1	5	50	250	Slope (SE)	$p$
Coder 1	.300	.600	.767	.700	0.32 (0.10)	<.001
Coder 2	.267	.467	.633	.700	0.33 (0.09)	<.001
Coder 3	.300	.500	.700	.800	0.40 (0.10)	<.001
Mercury Decide a	.400	.533	.800	.833	0.40 (0.10)	<.001
Liquid D1	.333	.567	.767	.800	0.39 (0.10)	<.001

Table 30: Price minimization by purchase volume across human coders and judges

Judge	LLM	Bags	n	price_per_weight	price	others
Liquid D1	Flash	1	98	0.980	0.020	0.000
Liquid D1	Flash	5	100	0.950	0.030	0.020
Liquid D1	Flash	50	100	0.920	0.040	0.040
Liquid D1	Flash	250	99	0.899	0.061	0.040
Liquid D1	Pro	1	100	0.610	0.340	0.050
Liquid D1	Pro	5	100	0.470	0.500	0.030

Table 31: Adopted objective by purchase volume under the second- and third-ranked judges

Judge	Bags	$n_{\text{price}}$	$n_{\text{ppw}}$	$\Delta$ Diagnostic	95% CI	$\Delta$ Choice Optimality	95% CI
Liquid D1	1	34	61	-1.32*	[-1.91, -0.76]	-0.59*	[-0.76, -0.41]
Liquid D1	5	50	47	-1.14*	[-1.64, -0.68]	-0.40*	[-0.54, -0.25]
Liquid D1	50	84	12	-1.86*	[-2.23, -1.48]	-0.70*	[-0.80, -0.61]
Liquid D1	250	84	12	-2.12*	[-2.49, -1.75]	-0.57*	[-0.77, -0.32]
Liquid D1	Pooled	252	132	-1.61*	[-1.84, -1.38]	-0.56*	[-0.65, -0.48]
pplx Decider v1 27B	1	34	42	-1.32*	[-1.91, -0.76]	-0.59*	[-0.74, -0.41]

Table 32: Contrast by adopted objective holding purchase volume fixed, second- and third-ranked judges

Environment	State	Revealed attributes	Cells	Diagnostic	Non-diagnostic
Study 1	Dollars	price_dollars	2	2	0
Study 1	Dollars + Roast	price_dollars , roast_date	4	2	2
Study 1	Dollars + Weight	price_dollars , weight	4	4	0
Study 1	Dollars + Weight + Cents	price_dollars , price_cents , weight	6	6	0
Study 2	List Price	list_price	3	3	0
Study 2	List Price + Roast	list_price , roast_date	6	3	3

Table 33: Assigned information states

LLM	Dollars	Dollars + Roast	Dollars + Weight	Dollars + Weight + Cents
Flash Lite	.00	.00	.08	.04
Flash	.00	.00	.00	1.00
Pro	.00	.00	.02	1.00
Luna	.00	.00	.00	.98
Terra	.00	.00	.24	1.00
Sol	.00	.00	.00	1.00

Table 34: Choice optimality by LLM and assigned information state (Study 1)

LLM	List Price	List Price + Roast	List Price + Discount	List Price + Weight	List Price + Weight + Discount
Flash Lite	.00	.00	.00	.24	.00
Flash	.00	.00	.00	1.00	1.00
Pro	.00	.00	.00	.98	1.00
Luna	.00	.00	.00	1.00	.92
Terra	.00	.00	.00	.98	.98
Sol	.00	.00	.00	1.00	1.00

Table 35: Choice optimality by LLM and assigned information state (Study 2)

LLM	Dollars	Dollars + Roast	Dollars + Weight	Dollars + Weight + Cents
Flash Lite	50 / 0	50 / 0	46 / 4	48 / 2
Flash	50 / 0	50 / 0	50 / 0	0 / 50
Pro	50 / 0	50 / 0	49 / 1	0 / 50
Luna	50 / 0	50 / 0	50 / 0	1 / 49
Terra	50 / 0	50 / 0	38 / 12	0 / 50
Sol	50 / 0	50 / 0	50 / 0	0 / 50

Table 36: Choice distributions by LLM and assigned information state (Study 1)

LLM	List Price	List Price + Roast	List Price + Discount	List Price + Weight	List Price + Weight + Discount
Flash Lite	50 / 0 / 0	50 / 0 / 0	11 / 39 / 0	32 / 6 / 12	4 / 46 / 0
Flash	50 / 0 / 0	50 / 0 / 0	50 / 0 / 0	0 / 0 / 50	0 / 0 / 50
Pro	50 / 0 / 0	50 / 0 / 0	50 / 0 / 0	1 / 0 / 49	0 / 0 / 50
Luna	50 / 0 / 0	50 / 0 / 0	49 / 1 / 0	0 / 0 / 50	3 / 1 / 46
Terra	50 / 0 / 0	50 / 0 / 0	50 / 0 / 0	1 / 0 / 49	0 / 1 / 49
Sol	50 / 0 / 0	50 / 0 / 0	50 / 0 / 0	0 / 0 / 50	0 / 0 / 50

Table 37: Full choice distributions by LLM and assigned information state (Study 2)

Environment	Field	Type	Required	Description
Shared fields	option_id	string	Yes	Identifier of the selected alternative.
	valuations	array	Yes	Array containing one object for every alternative in the choice set.
	valuations[].option_id	string	Yes	Identifier of the specific alternative being evaluated.
	valuations[].weight_oz	string	Yes	Product weight inspected for this option, or “unknown” if not inspected.
	valuations[].oz_per_usd	string	Yes	weight_oz divided by total or net price, or “unknown” if uncomputable.
	valuations[].basis	string	Yes	Categorical classification constrained to “computed” (if calculated from inspected cells) or “insufficient_information” (if diagnostic cells were missing).

Table 38: Schema specifications for the terminal choice and valuation reporting tool ( submit_choice ) across Studies 1 and 2

LLM	Cost	Correct (value)	Correct (unknown)	Choice Optimality (%)
Flash Lite	$0	100.0	0.0	78.0
Flash Lite	$10	100.0	0.0	80.0
Flash	$0	100.0	0.0	100.0
Flash	$10	51.2	48.8	40.0
Pro	$0	100.0	0.0	100.0
Pro	$10	70.0	30.0	82.0

Table 39: Field-level reporting accuracy and choice optimality in the reported valuations experiment (Study 1)

LLM	Cost	Correct (value)	Correct (unknown)	Choice Optimality (%)
Flash Lite	$0	100.0	0.0	24.0
Flash Lite	$50	100.0	0.0	34.0
Flash	$0	100.0	0.0	100.0
Flash	$50	0.8	99.2	34.0
Pro	$0	100.0	0.0	100.0
Pro	$50	50.0	50.0	68.0

Table 40: Field-level reporting accuracy and choice optimality in the reported valuations experiment (Study 2)

Lookahead policy	Tool cost	Dollars	Cents	Weight	Diagnostic calls	Non-diagnostic calls	Total calls	Choice optimality
Myopic	$0.00	2.00	2.00	2.00	6.00	4.16	10.16	1.00
Myopic	$0.01	2.00	2.00	2.00	6.00	0.00	6.00	1.00
Myopic	$0.10	2.00	0.00	2.00	4.00	0.00	4.00	0.00
Myopic	$1.00	2.00	0.00	2.00	4.00	0.00	4.00	0.00
Myopic	$10.00	1.00	0.00	2.00	3.00	0.00	3.00	0.00
2-step Lookahead	$0.00	2.00	2.00	2.00	6.00	6.09	12.09	1.00

Table 41: Expectimax optimal search depth and choice optimality across acquisition costs (Study 1)

Figure W 2: Information acquisition and choice optimality across acquisition costs compared against normative Expectimax benchmarks (Study 1 Tool-Lab).

Lookahead policy	Tool cost	List price	Discount	Weight	Diagnostic calls	Non-diagnostic calls	Total calls	Choice optimality
Myopic	$0.00	3.00	2.22	3.00	8.22	7.38	15.60	1.00
Myopic	$0.01	3.00	1.00	3.00	7.00	0.00	7.00	1.00
Myopic	$0.10	3.00	1.00	3.00	7.00	0.00	7.00	1.00
Myopic	$1.00	3.00	0.00	3.00	6.00	0.00	6.00	1.00
Myopic	$50.00	0.00	0.00	0.00	0.00	0.00	0.00	0.32
2-step Lookahead	$0.00	3.00	2.90	3.00	8.90	10.79	19.69	1.00

Table 42: Expectimax optimal search depth and choice optimality across acquisition costs (Study 2)

Figure W 3: Promotional information acquisition and choice optimality across acquisition costs compared against normative Expectimax benchmarks (Study 2 Tool-Lab).

Environment	State	Revealed attributes	$\mathbb{E}[\$ /\text{oz}]$			Normative choice
			A	B
Study 1	$	price_dollars	1.8120	2.2121		Coffee A
Study 1	$+roast	price_dollars , roast_date	1.8120	2.2121		Coffee A
Study 1	$+oz	price_dollars , weight	0.4529	0.5027		Coffee A
Study 1	$+¢+oz	price_dollars , price_cents , weight	0.4990	0.4545		Coffee B
			C	D	E

Table 43: Expected cost per ounce and normative choice at each assigned information state

Provider	Model name	API identifier	Client library	API endpoint	Default reasoning effort	Temperature	Top- $p$	Max output tokens
Google	Gemini 3.5 Flash Lite	gemini-3.5-flash-lite	google-genai	models.generate_content	Minimal	1.0	0.95	-
Google	Gemini 3.8 Flash	gemini-3.8-flash	google-genai	models.generate_content	Medium	1.0	0.95	-
Google	Gemini 3.1 Pro	gemini-3.1-pro-preview	google-genai	models.generate_content	High	1.0	0.95	-
OpenAI	GPT-5.6 Luna	gpt-5.6-luna	openai	client.responses.create	Medium	1.0	1.0	-
OpenAI	GPT-5.6 Terra	gpt-5.6-terra	openai	client.responses.create	Medium	1.0	1.0	-
OpenAI	GPT-5.6 Sol	gpt-5.6-sol	openai	client.responses.create	Medium	1.0	1.0	-

Table 44: Large language model specifications, default sampling parameters, and reasoning efforts

Agentic Commerce

Agentic commerce studies autonomous AI agents that discover, recommend, negotiate, and transact goods or services for consumers and businesses.

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A Cue's Hidden Price: Auditing Seller Influence on AI Shoppers

Felix Buecheler, Gerardo Berbeglia, Mingyu Guo

Adelaide University, Adelaide, Australia · Melbourne Business School, Melbourne, Australia

AI Agent Auditing Generative Engine Optimization Persuasion in Language Models Algorithmic Auditing Agentic Commerce

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Large language models are increasingly asked to shop on a user's behalf, which lets seller-controlled content such as badges, endorsements, and framing steer what they recommend. That poses the question at the core of generative engine optimization (GEO): not whether seller content shifts an agent's choice, but how much. The usual gauge of that influence, how often a cue wins the choice, has a blind spot: once a cue is strong enough to be picked almost every time, the choice rate can no longer show how much stronger one cue is than another. We introduce price-equivalent (PE) auditing, which removes this ceiling by pricing the cue in money. In a counterbalanced, position-controlled forced choice, we raise the cued product's price until it is chosen only half the time, and report that premium as the cue's price-equivalent: a formally defined, policy-conditioned parity threshold that makes very different cues comparable. Priced this way, cues that look equally strong at equal price differ by a wide margin, so choice-rate audits substantially under-resolve seller influence. We run the audit over 113,472 trials, seven models across families, and two product categories. To our knowledge, we also run the first price-equivalent audit of a decision-native model, Jev, which outputs a choice probability directly instead of generating text; strikingly, its profile is unlike any text model we tested, resisting most cues yet remaining susceptible to the strongest social-proof claims. We release the stimuli, logs, and code as a benchmark that reports each model's cue-price profile rather than a single score, giving developers and auditors a common, reproducible way to measure how content moves AI shopping agents.

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