Theory Model & Proof Architecture (aejmic-theory-model)

This is the central skill for AEJ: Micro. The journal is theory-first: the deliverable is a clean, general, well-motivated result — a theorem, characterization, or impossibility — that a broad microeconomics audience finds illuminating. Get the model and the proof right before anything else.

When to trigger

• The primitives (players, actions, information, timing, payoffs) are not yet pinned down
• The equilibrium / solution concept is unstated or mismatched to the question
• A result is conjectured but the proof strategy is unclear or fragile
• You are trading generality against tractability and cannot decide where to cut
• A referee questions which assumption the result actually depends on (then pair with aejmic-identification)

The AEJ: Micro modeling bar

AEJ: Micro wants the economics to be the point: the model should be the simplest environment in which the mechanism is visible, and the result should travel beyond the example. It sits between JET/GEB (specialist, often maximal generality) and AEJ: Applied (empirical). Aim for a result that a non-specialist micro theorist can state in one sentence and that a specialist finds non-obvious.

1. Model setup — make primitives minimal and motivated

• State players, action sets, information structure, timing, and payoffs explicitly; flag every assumption that is substantive vs. WLOG.
• Prefer the minimal environment that exhibits the mechanism; add structure only when it earns its keep in the result.
• Motivate each non-standard assumption economically (an institution, a friction), not just for tractability.

2. Equilibrium / solution concept — name it and justify it

• Pick the concept that matches the question: Nash / subgame-perfect / sequential / PBE; dominant-strategy or Bayesian incentive compatibility (mechanism design); stability / core (matching, market design); rationalizability or level-k (behavioral).
• State existence and, where it matters, uniqueness (or characterize the equilibrium set). Refinements should be justified, not invoked to rescue a result.

3. Proof strategy — choose the architecture before writing it

• Common architectures: construction (exhibit the object), revelation principle then optimize over direct mechanisms, fixed-point / monotone-comparative-statics (Topkis, single-crossing), duality / LP (information design, Bayesian persuasion), induction on type/stage, variational / first-order arguments, impossibility by contradiction.
• For a characterization, prove both directions; for an optimum, verify the candidate is global (not just a local/first-order point).

4. Generality vs. tractability — decide deliberately

• A finite/binary type space that exposes the mechanism cleanly often beats a continuum that buries it. State the cost: what does the simplification rule out?
• If the general case is the contribution, prove it generally; if the insight is the contribution, prove it where it is cleanest and discuss extension in aejmic-robustness.

5. Where proofs live

• Short, illuminating proofs (or proof sketches) in the main text; long or routine proofs in the appendix. The main paper should be self-contained for the key results — do not hide a load-bearing proof in supplementary material.

Checklist

• [ ] Primitives stated explicitly; each assumption marked substantive vs. WLOG, with economic motivation
• [ ] Solution concept named, matched to the question, with existence (and uniqueness/characterization where relevant)
• [ ] Main result stated as a numbered Proposition/Theorem in words a non-specialist can parse
• [ ] Proof architecture chosen and stated; candidate optima verified global, both directions of a characterization proved
• [ ] Generality-vs-tractability call made deliberately, with the cost of any simplification stated
• [ ] Key proofs in main text; appendix carries the rest; main paper self-contained

Anti-patterns

• A model loaded with assumptions, several only for tractability, none flagged — the mechanism is invisible
• Asserting an equilibrium without existence, or invoking a refinement only to rescue the result
• "It can be shown that…" standing in for a proof of a load-bearing claim
• Maximal generality that obscures the economic point (reads as JET, not AEJ: Micro), or a one-off example with no result that travels
• A first-order condition presented as if it established a global optimum

Worked vignette: a screening result (illustrative)

A monopolist screens buyers with private values. A weak setup throws in a continuum of types and three frictions at once; the optimal-contract characterization becomes a thicket. The AEJ: Micro move: start with two types, derive the standard "no distortion at the top, downward distortion below" characterization as a clean Proposition, prove it by the relaxed-program-then-verify-monotonicity architecture, then in aejmic-robustness show the continuum case preserves the qualitative result. The two-type model is the simplest environment where the distortion is visible — and the result travels.

Output format

【Model】players / actions / information / timing / payoffs (substantive vs. WLOG flagged)
【Solution concept】[Nash/SPE/PBE/IC/stability/…] + existence/uniqueness
【Main result】Proposition stated in words
【Proof architecture】[construction / revelation+optimize / fixed-point / duality / induction / impossibility]
【Generality call】where proved + cost of any simplification
【Proofs live】main text: [...]; appendix: [...]
【Next step】aejmic-identification (what makes it tight) or aejmic-robustness (extensions)

Supplementary resources

• ../../resources/worked-examples/01-introduction.md — a theory-paper intro arc (puzzle → model → proposition → driving assumption)
• ../../resources/exemplars/library.md — real AEJ: Micro theory papers by area