Engineering Simplicity: Simple Mechanism Interfaces Steer LLM Agents

Kehang Zhu; Anand Shah; David Parkes

cs.AISep 28, 2026

Engineering Simplicity: Simple Mechanism Interfaces Steer LLM Agents

Authors: Kehang Zhu, Anand Shah, David Parkes

Organizations: Harvard University

Abstract

Can interaction formats and textual scaffolds help large language model (LLM) agents make better decisions, and do better decisions come with better explanations? We study these questions in auctions and matching, multi-agent environments with explicit rules and known optimal strategies. These settings let us vary how a decision problem is presented while retaining a benchmark for evaluating behavior. Drawing on human-motivated theories of simplicity, we compare interfaces that elicit a complete bid or ranking with sequential interfaces that make safe choices easier to identify. We then hold the interaction format fixed and vary reasoning scaffolds and rule descriptions. Across four model families, the ascending auction interface substantially reduces bid deviations. The matching comparison also shows why sequential responses require different error accounting from complete rankings. Laying out payoff contingencies and explaining why truth-telling is safe also improve choices, whereas prompts to plan through matching rounds or form beliefs about opponents worsen play overall. In auctions, these behavioral gains are not accompanied by corresponding improvements in measured verbal indicators of strategic understanding in the agents' short stated plans. Other prompts change those indicators without improving bids. Our findings suggest that human-motivated theories of simplicity can inform the design of decision environments for artificial agents. They also show why scaffolds should be evaluated through realized choices as well as explanations: improvements in one need not appear in the other.

Figures & tables

Figure 1 : Auction and matching interface comparisons across four model families. Top: signed bid deviations (

b-v

) in sealed-bid (gray) and ascending-clock (colored) auctions; dashed lines indicate means. Bottom: recorded normalized Kendall

\tau

distances in direct DA and iterative DA. Direct DA elicits full rankings; iterative DA reveals only partial preferences. Its zero recorded distance does not establish error-free responses: observations with fewer than two ranked schools contribute zero, and the statistic does not score all yes/no answers. Separate decision-level errors for the sequential-query protocol are reported in the text and Appendix E .

Figure 2 : Contingent reasoning: Payoff Tree intervention. Top row: Second-price auction bid deviations (

\text{bid}-\text{value}

); baseline SPSB in gray, intervention in color. Bottom row: Deferred acceptance Kendall

\tau

errors; baseline direct DA in gray, intervention in color. The payoff tree scaffold consistently improves play across all models in both domains, roughly halving the distance from truthful.

Figure 3 : Mechanism description: outcome safety interventions. Top row: Payoff Safety in second-price auctions (“your bid determines IF you win, not WHAT you pay”). Bottom row: Rejection Safety in deferred acceptance (“rejections only redirect, never eliminate”). Baseline in gray, intervention in color. Both interventions improve play dramatically. Rejection safety reduces mean complete-ranking error in DA from

4.2\%

0.2\%

Figure 4 : Language and bid responses to six selected interventions (four model families, sealed second-price conditions). Effects are treatment minus baseline. Left: changes in targeted language, shown as point estimates; more target language need not mean better understanding. Right: changes in mean absolute bid error with percentile run-cluster-bootstrap 95% intervals; negative values indicate smaller errors. The menu removes the measured rule vocabulary, so its language contrast is omitted. The intervals use a different procedure from the wild-bootstrap tests in Table 1 ; all twenty comparisons are in Table 6 .

		Stated reasoning		Bids, mean $\|b-v\|$ ($)
Lever	Targeted language	$\Delta$ prevalence	$p$ / $q$	base $\to$ treated	$p$ / $q$	Cell
Primary contrasts (raw wild-cluster-bootstrap $p$ )
Payoff Safety	invariant echo	$0\%\to 0\%$	—	$3.20\to 1.95$	$p=.015$	bids only
Payoff Tree	rule rehearsal	$33.0\%\to 32.7\%$	$p=.90$	$3.20\to 1.29$	$p=.017$	bids only
Worst-case scaffold	worst-case rhetoric	$2.0\%\to 43.0\%$	$p=.0075$	$3.24\to 3.07$	$p=.81$	words only
Menu restatement	rule rehearsal	(by construction)	—	$3.20\to 3.55$	$p=.66$	neither

Table 1 : Joint response of stated reasoning and bids for the headline levers (pooled over the four families, sealed second-price cells; run-level wild-cluster bootstrap; the full twenty-row table with per-family sign vectors is Table 6 in Appendix C ). Baselines are the pooled contingent-reasoning and belief baseline cells (

3.20

); the worst-case scaffold is compared with its own grid’s baseline (

3.24

) and the belief rows with theirs (

3.16

). Under correction across all twenty interventions the two primary improvements carry

q=0.068

. No lever occupies the “both improve” cell.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Category	Prompt ID	Description
Deferred Acceptance — Direct Revelation
Base	da_direct_null $\star$	Minimal baseline; no mechanism explanation
Base	da_direct_traditional $\star$	Full 5-step DA algorithm description
Deferred Acceptance — OSP Sequential [ Ashlagi and Gonczarowski, 2018 ]
OSP	da_osp_yesno $\star$	Binary with consequence explanation (obviousness witness)
DA Axis 1: Contingent Reasoning

Appendix

Table 2 : Complete list of prompt templates.

\star

= full prompt shown;

\dagger

= intervention-specific text shown.

Figure 17 : Loss aversion interventions in SPSB auctions. Baseline SPSB in gray, intervention in color. Dashed lines indicate means. None of the framing interventions consistently improve play relative to the SPSB baseline (

\mu=-2.67

). The loss frame (

\mu=-3.44

) and endowment (

\mu=-3.40

) worsen underbidding, while the gain frame (

\mu=-2.51

) and WTA/WTP (

\mu=-2.17

) show modest, inconsistent effects.

Figure 18 : Loss aversion interventions in deferred acceptance. Baseline direct DA in gray, intervention in color. The results are noisy and largely negative: most framing interventions worsen play relative to the baseline (

\mu=4.2\%

), with WTA/WTP producing the worst outcomes (

\mu\approx 12.6\%

across models with data). Claude is particularly sensitive to these framings.

Figure 19 : Risk preference interventions in SPSB auctions. Risk aversion increases underbidding (

\mu=-4.71

), while risk-seeking dramatically shifts Claude to overbidding (

\mu=+8.40

). Risk neutrality (

\mu=-1.82

) modestly improves play relative to the SPSB baseline (

\mu=-2.67

Figure 20 : Risk preference interventions in deferred acceptance. Risk aversion dramatically worsens play (

\mu\approx 18.8\%

, compared to baseline

4.2\%

). Risk neutrality and risk-seeking also worsen play, though less severely.

Group	Feature	Fires when the plan…
Normative	dominance_language	invokes dominance (“dominant strategy,” “regardless of others”)
recognition	truthful_intent	states an intent to bid exactly one’s value
	payment_rule_correct	correctly rehearses that the winner pays the second-highest bid
	second_price_mention	name-drops “second-highest”/“second price” (weak rule mention)
	first_price_mention	calls the auction “first-price” (mechanism confusion)
Opponents &	opponent_modeling	speculates about other bidders’ values or bids

Appendix

Table 3 : The frozen trace feature dictionary: eighteen binary keyword features in five groups. Exact regular expressions and per-cell prevalence are in the replication package ( analysis/build_trace_features.py ; results/traces/trace_features.csv ).

Figure 21 : Primary decision script per plan, by model and mechanism (rule-based taxonomy; hatched cells are structurally unavailable labels). The plans of the four families in our main panel (“legacy”) state heterogeneous sealed-bid heuristics dominated by first-price shading and overpayment avoidance; the ascending clock collapses every family onto the price-threshold exit rule; the frontier families discussed in Appendix C switch to formal derivation or truthful assertion. LLM-judge replication of the taxonomy: $\kappa=0.55$ at the coarse grain shown; ten-label grain and confusion matrix in Appendix C .

Feature (% of plans)	Claude	Gemini	GPT-4o	Gemma
dominance_language	0.0	0.7	0.0	0.0
truthful_intent	8.0	2.7	2.0	0.0
payment_rule_correct	11.3	0.0	9.3	0.0
second_price_mention	50.7	10.0	39.3	46.0
first_price_mention	18.7	0.0	0.0	0.0
opponent_modeling	8.0	4.7	20.0	73.3

Appendix

Table 4 : Feature prevalence in the baseline SPSB cell, by model (percent of plans; Claude 3.5 Haiku, Gemini 2.0 Flash, GPT-4o, Gemma 27B). Gemini is a near-pure shader; Claude is the only model that mislabels the mechanism “first-price” and has both the most stated overbidding and the most stated truthful intent; Gemma produces the least value-anchored language but the most opponent modeling, conservative self-description, and overpayment concern; GPT-4o shades and has the highest rate of the zero-profit fallacy. Prevalence for every model

\times

lever cell: results/traces/feature_prevalence_model_family.csv .

Model	Rule	Plans	shading_intent	H1 or H2 primary	bid/value
GPT-4o (main grid)	first-price	3,711	66%	68%	0.82
	second-price	3,600	68%	66%	0.88
	third-price	3,696	60%	59%	0.88
Gemini 2.0 Flash (robustness grid)	first-price	180	45%	75%	0.88
	second-price	264	64%	80%	0.93
	third-price	330	86%	87%	0.90

Appendix

Table 5 : Cross-mechanism script invariance ( results/traces/script_invariance.csv ). For Gemma, the mechanism-insensitive script is overpayment concern ( overpay_concern

88\%

84\%

71\%

across the three rules), not shading. The rule-rehearsal features are mechanically zero outside the second-price format and are omitted.

Figure 22 : Execution fidelity versus plan selection (main panel, sealed second-price cells). (a) Realized bid against the dollar amount stated in the plan; per-model binned means,

r=0.97

–

0.99

, mean

|\text{stated}-\text{realized}|

0.28–

0.82. (b) Realized deviation conditional on the stated-intent class; the plans that never anchor on value carry the largest errors. Stated plans are executed faithfully; the failure is in which plan is chosen.

Lever	Targeted feature	% base $\to$ treated	$q$	base $\to$ treated	$q$	Echo	Sign	Cell
		Stated reasoning		Bids, mean $\|b-v\|$ ($)
Payoff Safety †	safety_recognition	$0.0\to 0.0$	—	$3.20\to 1.95$	0.068 ∗	clean	----	bids-only
Worst-case scaffold †	worst_case	$2.0\to 43.0$	0.020	$3.24\to 3.07$	0.93	partial	-+-+	language-only
Payoff Tree †	second_price_mention	$33.0\to 32.7$	0.91	$3.20\to 1.29$	0.068 ∗	clean	----	bids-only
Dominated	dominance_language	$0.0\to 20.5$	0.035	$3.24\to 2.88$	0.93	partial	-+-+	language-only
Enumerate	opponent_modeling	$29.1\to 39.3$	0.84	$3.24\to 3.28$	0.93	partial	-+-+	neither

Appendix

Table 6 : The full set of interventions, pooled over the four families (sealed second-price cells). Primary contrasts ( Payoff Safety , Payoff Tree , worst-case scaffold, menu restatement) are classified at their raw wild-cluster-bootstrap

p

-values (see text); all other rows at the full-set

q

shown. ∗ : significant by the run-level wild-cluster bootstrap but soft under the four-model-cluster permutation test. Echo : “clean” means the targeted vocabulary does not appear in the prompt; “partial” means part of the language response is the prompt’s own vocabulary read back; “by constr.” means the menu wording removes the targeted vocabulary by construction, so its language column is not a comprehension measure; “manip.” means the language is the manipulation (the two clock-framed descriptions), so it is not a comprehension measure either. † : primary contrast. Sign : the direction of the

|b-v|

change in Claude, Gemini, Gemma, GPT-4o (

-

improves,

+

worsens; dissociation_per_family.csv , auction-level clusters, descriptive since there is one run per model

\times

cell). Cell : joint-response class. Every quantity is stable on the deduplicated pool.

Model	Corpus	Plans	Formal (%)	Truthful (%)	$\|b-v\|$ , formal	$\|b-v\|$ , other	Wrong mech.
Claude Sonnet 5	frontier	1,650	42.6	28.0	1.55	0.00	145
Gemini 2.5 Flash	frontier	1,608	11.8	25.8	0.20	0.61	9
GPT-5	frontier	603	54.6	26.9	0.00	0.00	0
GPT-5 mini	frontier	1,374	35.7	51.9	0.00	0.00	0
Claude 3.5 Haiku	main panel	3,513	0.7	8.3	1.59	2.27	11
Gemini 2.0 Flash	main panel	3,486	1.2	1.6	3.68	1.51	1

Appendix

Table 7 : Decision scripts at the frontier versus the main panel, sealed second-price plans ( results/traces/formal_derivation_prevalence.csv ). “Formal” is the share of plans whose primary script is a formal dominance derivation (H7); “Truthful” the share with an informal truthful/dominance statement (T); “

|b-v|

, formal/other” the mean absolute deviation conditional on a formal derivation or on its absence. “Wrong mech.” counts plans that formally derive another mechanism’s equilibrium (for Claude Sonnet 5, the first-price Nash bid). Conditional

|b-v|

is in dollars; “—” means no plan of that kind.

Model	Informative decisions	Errors	Error rate	False NO / YES
Claude	194	16	$8.2\%$	13 / 2
Gemini	179	0	$0.0\%$	0 / 0
GPT-4o	188	0	$0.0\%$	0 / 0
Gemma	210	3	$1.4\%$	3 / 0

Appendix

Table 8: Decision errors in the sequential-query DA logs. Informative decisions include yes/no answers and final choices among at least two schools. The last column counts false rejections and false acceptances; Claude’s remaining error is a final-choice error. These are descriptive rates: decisions from the same market are dependent, and zero observed errors does not establish a zero population error rate.

Figure 23 : Forward planning: lookahead interventions in deferred acceptance. Top row: One-step lookahead; bottom row: two-step lookahead. Each cell overlays the direct DA baseline (gray) with the intervention (colored). Lookahead scaffolds worsen play overall, with the damage concentrated in GPT-4o and Gemma; Claude and Gemini are largely unaffected.

Figure 24 : Belief formation interventions across both mechanisms. Top two rows: Second-price auction bid deviations under first-order and second-order belief scaffolds. Bottom two rows: Deferred acceptance Kendall

\tau

errors under the same scaffolds. Baseline distributions in gray, interventions in color. Belief scaffolds almost uniformly worsen play, with second-order beliefs causing the most damage. Gemini is the notable exception, showing near-immunity to belief scaffolding.

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