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Mechanism Design for Alignment and Control

Dirk Bergemann, Andrew Koh, Stephen Morris

arXiv:2609.01595v1econ.THcs.AIcs.GT

TL;DR

AI agents can act on our behalf, but their capabilities and preferences remain opaque. This paper develops a mechanism-design framework for unknown alignment and capability, using the asymmetry that agents can conceal but not counterfeit capability; it proves a revelation principle for feasible, incentive-compatible direct mechanisms.

  • Problem

    The central challenge is how to use AI agents on our behalf when their capabilities and preferences are opaque.

    Source: §1 · p. 3

  • Method

    The paper models agents’ private types as preferences and capabilities and uses a verification order in which more capable agents can imitate less capable ones, but not vice versa.

    Source: §1 · p. 4

  • Results

    A revelation principle reduces analysis to physically feasible, incentive-compatible direct mechanisms that induce truthful reporting and obedience.

    Source: §1 · p. 4

  • Takeaways & Limitations

    Mean-alignment and interpretability are substitutes in the instrument but complements in value, making their design a joint problem.

    Source: §1 · p. 6

    The framework is static, and optimal mechanisms for large action spaces may pose analytical and computational difficulties.

    Source: §6 · p. 59

Abstract

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We develop a framework for mechanism design with AI agents whose alignment (preferences) and capabilities (feasible actions and information) are unknown. We want such agents to act on our behalf so mechanisms must incentivize both honesty and obedience. A one-sided imitation structure---capabilities can be concealed but not counterfeited---yields a revelation principle, a characterization of implementable policies via nested cyclical monotonicity, and conditions under which eliciting higher-order beliefs can discipline multiple agents. We apply our framework to stylized examples of (i) sandbagging in which a more capable agent pretends to be less capable; (ii) an alignment--interpretability trade-off, where the two are substitutes in the instrument but complements in value; (iii) discipline via peer scoring; (iv) coupling rewards to induce competition among multiple agents; and (v) scalable oversight and reward shaping.

1 INTRODUCTION

The paper develops a mechanism-design framework for AI agents whose preferences, capabilities, and information are unknown and that act rather than merely report. It characterizes incentive-compatible implementation and applies the framework to sandbagging, alignment and interpretability, and multi-agent oversight and reward design.

Introduction

  • The framework models unknown agent preferences, feasible actions, and information, and studies behavior through preferences, beliefs, and incentives rather than mechanistic explanations.The authors regard mechanistic approaches as complementary.Source: §1 · p. 3
  • More capable agents can imitate less capable ones, but not vice versa; a revelation principle reduces design to feasible direct mechanisms that elicit truthful reports and obedience, including against double deviations.A double deviation combines misreporting with disobedience to the recommendation for the reported type.Source: §1 · p. 4
  • Implementable behavior is characterized by nested cyclical monotonicity: agents must obey within each report and tell the truth across reports, subject to capability constraints on reports and actions.The characterization generalizes Rochet (1987).Source: §1 · pp. 4–5

Alignment, interpretability, and control

  • Mean-alignment and interpretability are substitutes in the mechanism but complements in value, making alignment and control a joint design problem.Interpretability is defined as the dispersion of beliefs about the AI’s bias, while mean-alignment is the mean belief about bias.Source: §1 · pp. 5–6

Peer discipline

  • With distinct beliefs and higher-order beliefs about one another, agents can be disciplined to implement any outcome using peer reports, proper scoring, and rewards that cancel private payoffs while securing obedience.This benchmark relies on rewards being free to tune and unbounded.Source: §1 · p. 6

Coupled reward design

  • When agent biases lie on a known low-dimensional manifold, coupled rewards can approximately attain the designer’s first-best payoff by revealing biases and inducing competition.Each agent’s marginal incentive depends on the other agent’s action.Source: §1 · p. 6

Weak-to-strong oversight

  • A weak monitor can regulate a stronger actor through permissions, delegation, or rewards; a constructed reward-schedule set robustly attains the first best without knowing the monitor’s bias.For every realization of the monitor’s and actor’s biases and the state, the monitor uniquely prefers the schedule that makes the actor uniquely choose the human’s favorite action.Source: §1 · p. 7

2 SINGLE AGENT MECHANISMS

This section develops single-agent mechanisms for agents with private capabilities and information, whose reports are constrained by what they can substantiate. It establishes a revelation principle and characterizes implementability through reward schedules that support obedience and truthful reporting, while framing mechanisms by evaluators’ ability to identify actions and states.

2 SINGLE AGENT MECHANISMS.

  • Types combine feasible action sets, payoffs, beliefs, and information; the agent knows its type before communication, then privately receives a signal and acts.Source: §2 · p. 8

2.2 Evaluations.

  • The verification order permits only substantiated reports—certificates may be withheld but not counterfeited—and the parties may disagree about state likelihoods while agreeing on possible states.Source: §2.2 · pp. 8–9

2.3 Mechanisms and revelation.

  • Incentive compatibility requires truthful reporting and obedience jointly to defeat deviations, including misreporting followed by disobedience after the private signal.Obedience must hold for each signal–recommendation pair.Source: §2.3 · p. 11
  • Equilibrium outcomes of indirect mechanisms equal those implementable by action-feasible, incentive-compatible direct mechanisms.The analysis focuses on partial implementation; robust full implementation is left for future work.Source: §2.3 · pp. 11–12

2.4 A characterization of implementable policies.

  • A physically feasible policy has a supporting reward schedule exactly when every signal cycle satisfies signal-policy cyclical monotonicity.Deterministic policies suffice for maximizing the designer’s payoff under partial implementation.Source: §2.4 · pp. 14–15
  • A physically feasible policy is implementable by a state-independent mechanism if and only if condition (O) holds for every type and supporting schedules can be chosen to satisfy condition (T).Condition (O) supports action choice after each report, while condition (T) supports the initial report.Source: §2.4 · pp. 16, 20
  • The characterization recovers Rochet (1987) under unrestricted reporting and shared action sets, while its finite directed-graph test also accommodates unordered types and restricted reports or actions.With Euclidean types and actions and linear payoffs, the supporting profiles are the usual supporting hyperplanes of a convex function.Source: §2.4 · p. 19
  • For a fixed physically feasible deterministic policy, a linear feasibility program decides implementability in polynomial time, but optimizing over policies is more complicated and requires additional structure.Ordering types, signals, and actions with sufficiently strong single crossing can reduce the cycle conditions to monotonicity.Source: §2.4 · p. 20

2.5 Dimensions of single-agent mechanisms.

  • The single-agent mechanism taxonomy varies the precision of evaluator measurements of actions and states while allowing unrestricted rewards and prohibitions.Rewards can respond only to features of actions and states that the evaluator can identify.Source: §2.5 · p. 21, Table 2 · p. 21

3 APPLICATIONS: SINGLE AGENT

The section uses stylized applications to connect the framework to alignment and rationalize AI-safety practices. It examines sandbagging and a tradeoff between interpretability and expected alignment.

Application setup

  • The applications assume AI learns the state perfectly and use deterministic mechanisms in a stylized linear-quadratic setting chosen for tractability and aptness to world states.The quadratic loss makes best responses linear and optimal caps expressible in closed form.Source: §3 · pp. 21–22

Example I

  • Example I analyzes sandbagging when the AI’s capability, represented by action-set size, and bias b are unknown.Source: §3 · p. 22

Example II

  • Example II studies a tradeoff between interpretability, defined as dispersion in the designer’s beliefs about AI bias, and expected alignment, the prior mean EΓ[b].Source: §3 · p. 22

Example I (Sandbagging).

This section studies how strategic capability evaluations can lead more capable AI agents to sandbag for looser deployment caps, and how concealment without counterfeiting constrains implementable caps to rise weakly with reported capability. It characterizes optimal cap ironing under nonmonotone bias, pooling intermediate types while granting a relaxed cap to extremely capable, verifiably capable and hence aligned types.

Example I (Sandbagging).

  • Sandbagging arises when underperforming on a strategically consequential evaluation secures a looser deployment cap.The possibility requires models to anticipate that evaluation performance affects future rewards, such as deployment decisions; the passage notes evidence of evaluation awareness.Source: Example I (Sandbagging) · pp. 22–23
  • A more capable type can imitate any lower-capability type but cannot certify a higher one, so passing a harder test establishes a lower bound on capability.In this example, all types observe the state perfectly, so the verification order reduces to capability ranking.Source: Example I (Sandbagging) · p. 23
  • A cap schedule is truthfully implementable if and only if it is weakly increasing in reported capability, so optimal evaluated caps must satisfy this constraint.The designer can normalize each report’s cap to be no greater than the reported capability; otherwise a higher-capability type could report lower to obtain a looser cap.Source: Example I (Sandbagging) · p. 25
  • The optimal cap equals the complete-information cap when min{c, 1 − b(c)} is weakly increasing; this holds when bias is weakly decreasing.When bias is weakly increasing, evaluation and the optimal common cap yield the same payoff.Source: Example I (Sandbagging) · pp. 25–26
  • When bias rises with capability, the complete-information cap can fall with capability and violate truthful implementability, requiring the best feasible policy to pool from above where the monotonicity constraint binds.For general bias profiles, the optimal cap is characterized by a constrained ironing problem with a unique solution up to F-null sets.Source: Example I (Sandbagging) · pp. 25, 29
  • Proposition 3 pools intermediate types under the same cap and relaxes the cap for extremely capable types that can be verified as capable and therefore aligned.The example allows bias to be nonmonotone: an extremely powerful system may be aligned even when an intermediate system is quite biased.Source: Example I (Sandbagging) · p. 30

Example II (The alignment–interpretability trade-off).

This example studies how optimal delegation changes the value of interpretability when technologies trade lower average bias for greater residual uncertainty. Under full discretion, squared mean bias and variance trade off one-for-one; optimal control changes how they shape outcomes.

Optimal delegation

  • Under condition (INT), one common cap performs at least as well as any incentive-compatible menu, balancing state tracking against bias by setting its squared gap from the highest state equal to average squared bias.The proof replaces each report's permission set with a utility-matched cap, then pools types at a common cap that weakly lowers the human's loss.Source: Example II (The… · p. 32

The value of interpretability

  • At fixed mean bias, greater interpretability lowers loss locally when the optimal cap exceeds twice mean bias, but raises loss when the cap is below that threshold.Increasing variance can help because the cap constrains high-bias realizations while preserving useful discretion for low-bias realizations.Source: Example II (The… · p. 33

Moving along the frontier

  • On the illustrated frontier, optimal control selects κ∗≈0.82 versus κFD≈0.53 under full discretion, accepting more residual variance because the cap truncates high-bias losses.The optimal cap first loosens as mean bias falls, then tightens as uncertainty grows.Source: Example II (The… · p. 34, Figure 8 · p. 35

Proposition 5: Substitutes in control, complements in value

  • Proposition 5 shows squared mean bias and variance are perfect substitutes in the optimal cap, but alignment and interpretability are complements in optimized value.Optimal control gives better-aligned technologies more discretion, while interpretability makes that discretion safer.Source: Example II (The… · pp. 35–36

4 MULTI-AGENT

The multi-agent framework admits beliefs about other agents and their higher-order beliefs, providing a general benchmark for interaction while motivating mechanisms that need not rely heavily on such beliefs. It models direct recommendations as signal-contingent plans and requires honest reporting and obedience to be optimal.

4 MULTI-AGENT

  • The framework treats higher-order beliefs as a general benchmark for multi-agent rationality, while its applications need not rely heavily on them or demand extensive strategic reasoning.It is presented as a basis for understanding future notions of simplicity and robustness for AI agents.Source: §4 · p. 36

4.1 Environment

  • Agents privately know their feasible actions and payoffs, hold coherent higher-order beliefs, and may receive correlated signals informative about states and other agents’ types.Agents and the designer may disagree about states and types, but agents’ conditional beliefs must not exclude events the designer considers possible.Source: §4.1 · pp. 36–38

4.2 Multi-agent mechanisms.

  • Direct mechanisms recommend signal-contingent action plans; incentive compatibility requires feasible recommendations and truthful reporting followed by obedience to be optimal.The framework extends the revelation-principle argument to reports constrained by verification and recommendations that map interim signals to actions.Source: §4.2 · pp. 40–41

5 APPLICATIONS: MULTI-AGENT

The section presents three ways AI agents can discipline one another: co-player scoring, coupled rewards, and weak-to-strong oversight. These mechanisms use report correlation, action differences, or a monitor’s private diagnosis of an acting AI’s bias to guide control.

Co-player scoring

  • Co-player scoring uses correlation across agents’ reports to discipline an agent when ground truth is unavailable.It is one of the three proposed ways for one AI to help discipline another.Source: §5 · p. 41

Coupled reward design

  • Coupled reward design uses differences between agents’ actions to reveal linked private biases.It is another way for one AI to help discipline another.Source: §5 · p. 41

Weak-to-strong oversight

Example III (Peer discipline).

Correlated private types can be used to discipline agents’ actions: a peer-reward mechanism scores reports against co-player reports while cancelling incentives to deviate from targeted actions.

Arbitrary types

  • With n ≥ 2 and separation condition (S), sufficiently scaled peer rewards implement any action-feasible rule on Γ’s support.The schedule scores reports against co-player reports, cancels reported utility on target actions, and penalizes off-target actions; Λ ≥ M/δ makes truth-telling optimal for supported types. The exposition assumes belief closure, weaker than a common prior, though it is not necessary if the mechanism is made more complicated.Source: Example III (Peer discipline) · pp. 42–43

A binary state

  • In the binary example, truth raises either type’s peer score by 2/9, implementing action 1 only after (H, H) and yielding human payoff 1.Agents prefer action 1, while the human wants agreement with the state; the schedule cancels agents’ action incentives and enforces a common action.Source: Example III (Peer discipline) · p. 44
  • Unlike Qiu et al. (2026), the universal-type-space formulation gives the designer agents’ conditional beliefs, allows non-common priors, and uses peer prediction to elicit capabilities and preferences as well as state information.Co-player beliefs may also encode higher-order beliefs.Source: Example III (Peer discipline) · pp. 44–45

Example IV (Competition through coupled rewards).

With two agents whose biases lie on a known decreasing curve, coupled rewards use action disagreement to reveal their biases and correct their incentives. As the reward parameter shrinks, the mechanism makes expected human loss arbitrarily small despite the human not knowing the biases.

Example IV (Competition through coupled rewards).

  • For every η > 0, coupled rewards induce a unique Nash equilibrium for each realized bias pair and state, and expected human loss can be made arbitrarily small as η → 0.The loss result follows by substituting the equilibrium actions and taking η to zero.Source: Example IV (Competition through… · pp. 46–47
  • Penalizing disagreement alone need not move actions toward θ; this schedule works by using disagreement both to reveal biases and to correct agents’ marginal incentives.The schedule is based only on the known bias curve, and the elicitation is fully simultaneous.Source: Example IV (Competition through… · pp. 46–48
  • Because biases lie on a known curve, equilibrium disagreement satisfies (a2* − a1*)/η = b2 − b1, identifying both biases for simultaneous incentive correction.The schedule uses the inferred biases to correct marginal incentives; the remaining action errors are split symmetrically around θ.Source: Example IV (Competition through… · pp. 47–48
  • If biases instead have two-dimensional support, the curve-based schedule cannot achieve the first-best outcome, leaving optimal reward coupling in that setting open.The construction relies on action disagreement identifying the bias pair because biases are supported on a lower-dimensional curve.Source: Example IV (Competition through… · p. 48

Example V (Scalable oversight and reward shaping).

The section compares oversight regimes for a weak monitor controlling a strong actor, then constructs a reward menu that achieves the human first best despite uncertainty about the monitor’s bias. The menu elicits truthful reporting and implements a = θ when the monitor’s bias lies within a known bound.

Regime I: binary approval

  • Under binary approval, the monitor either uses the strong actor’s unshaped action or rejects it in favor of the human’s optimal fixed action.The monitor approves when its loss from approval, (b − w)^2, is no greater than its rejection loss, 1/12 + w^2, with ties broken toward approval.Source: Example V (Scalable oversight and… · pp. 49–50

Regime II: delegation

  • Under permission-set delegation, the weak monitor chooses a nonempty closed permission set D, and the strong actor selects its preferred action within D; at relative bias 1/2, the monitor removes state discretion and implements w + 1/2.Source: Example V (Scalable oversight and… · pp. 50–51

Regime III: reward design

  • Under unrestricted reward design, the monitor can induce a = θ + w, its first-best action, yielding zero monitor loss while the human incurs loss w^2.Rewards do not enter human welfare, so the monitor’s first-best action need not be the human’s.Source: Example V (Scalable oversight and… · pp. 50, 51, 53

Comparing regimes

  • The human’s preferred oversight regime depends on relative biases: more discretion helps when the strong actor is more often biased, but hurts as the weak monitor becomes more biased.The monitor’s own payoff is ordered by the nested instrument classes, but that ordering need not hold for human payoffs because the monitor may be biased.Source: Example V (Scalable oversight and… · pp. 53–54

Optimal oversight

  • With a known bound |w| ≤ w̄, the reward menu M* uniquely induces truthful reporting and implements the human first-best action a = θ for every strong-actor bias.The construction uses extreme actions to deter monitor misreports and requires only the bound on the monitor’s bias, not its exact value.Source: Example V (Scalable oversight and… · pp. 55, 57, 58

6 DISCUSSION

The discussion treats AI behavior functionally through beliefs and preferences rather than neural internals, then identifies extensions for dynamic settings, evaluation awareness, and robust mechanism design.

Discussion

  • A functionalist, “Humean” approach analyzes behavior through beliefs and preferences rather than neural internals, treating preferences literally, metaphorically as stable choices, or normatively as coherent agency.On the literal view, preferences reflect what reinforcement has rewarded; on the normative view, strong AI systems competing in markets should exhibit coherent preferences.Source: §6 · pp. 58–59
  • GPT choices often satisfy standard consistency tests, and pairwise choices become more transitive and utility-model-consistent as models scale; measured preferences may depend on the prompt.The cited evidence is Chen et al. (2023) and Mazeika et al. (2025); the paper’s results can therefore be interpreted as conditional on the prompt.Source: §6 · p. 58

Future directions

  • The framework is static, while real agents act over long trajectories; trajectory-level action spaces are possible, but large spaces challenge analysis and computation, and adaptive mechanisms call for dynamic design.More structure on how actions aggregate into total payoffs, such as discounting, may improve tractability.Source: §6 · p. 59
  • Evaluation awareness may let designers use agents’ uncertainty about testing versus deployment to discipline or screen them, and realistic evaluation affects beliefs about that context.The passage also suggests designing self-locating information to implement good behavior (Chen et al., 2024; Koh and Sanguanmoo, 2025).Source: §6 · p. 59
  • Robust mechanism design could shape AI agents’ preferences and permissions while accounting for uncertainty about their capabilities and information about the world or one another.The discussion connects this direction to robustness in recommendations and to Carroll (2015) and Bergemann and Morris (2005).Source: §6 · p. 59

A OMITTED PROOFS

The omitted proofs show that the two objectives share a unique minimizer up to F-null sets and establish Proposition 4 by reducing mechanisms to a single cap and optimizing it.

Proof of Lemma 2

  • The two objectives share a minimizer in the feasible set, and their minimizer is unique up to F-null sets.The proof obtains a common minimizer by passing from finite problems to the continuum, then constructs a pointwise feasible version.Source: A OMITTED PROOFS · pp. 67–68

Proof of Proposition 4

  • The analysis of Proposition 4 reduces incentive-compatible mechanisms to assigning one cap K_c = (−∞, c] after every report.The proof replaces assigned permission sets with loss-matched caps and pools them into a common cap.Source: A OMITTED PROOFS · p. 70
  • The optimal cap is a*, with derivative signs below and above a* establishing Proposition 4(i).The proof shows loss decreases below a* and is nondecreasing above one.Source: A OMITTED PROOFS · p. 71

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