Paper IX — Sociology: References
90 SOURCES · 30 QUESTIONS · ALL FREELY AVAILABLE
Each source carries a technical description and a plain one; authors’ own pages and encyclopaedia entries are linked where they exist. Every address on this page was verified live at publication. The paper itself: Paper IX.
1. Is the market a computer? Say what it computes, and whether the computation is tractable.
The use of knowledge in society
The computational reading at source: dispersed information aggregated by prices — the market as distributed processor.
In plain terms: The free classic that first described the market as a machine for computing with knowledge no one holds whole.
The claim's status examined: idealisation, equilibrium as construct, and what such models assert of the world.
In plain terms: The free scholarly frame for deciding whether the computer talk is theory or metaphor.
Networks, Crowds, and Markets (open copy)
The tractability half made concrete: market equilibria computed in the book's models — and the limits of the computation.
In plain terms: The free standard text where markets are actually run as algorithms, so the question's second half has data.
Background: Economic equilibrium · Computational economics
2. Is a price a measurement? If so, say of what, and with what error.
The use of knowledge in society
The measurement claim's origin: price as a summary statistic of scarcity, transmitting what it does not itemise.
In plain terms: The free essay in which a price is a telegram — short, informative, and silent about its sources.
What measurement requires — a measurand, a scale, an error model — the standard the price must meet or fail.
In plain terms: The free entry supplying the test: if a price measures, it must measure something, on some scale, with some error.
The candidate measurands — marginal valuation, scarcity, expectation — and the noise each account admits.
In plain terms: The free survey of what a price could be measuring, and how far it can be trusted.
Background: Price · Price signal
3. What, exactly, does Arrow’s theorem forbid? State the theorem precisely, and identify which condition each of the standard escape routes abandons.
The theorem exact: unrestricted domain, Pareto, IIA, no dictator — and each escape route matched to the condition it abandons.
In plain terms: The free definitive entry doing precisely the question's audit — the conditions, and the price of relaxing each.
General economic equilibrium: purpose, analytic techniques, collective choice (Nobel lecture)
The theorem in its author's own framing — collective choice within the general-equilibrium programme.
In plain terms: The free lecture from the man himself, placing the impossibility inside his larger picture of economies.
The theorem's home discipline: the aggregation framework, and the result's descendants and generalisations.
In plain terms: The free survey of the field the theorem founded — what forbidding perfection left possible.
Background: Arrow's impossibility theorem · Social choice theory
4. Prove that majority rule between two alternatives can be profitably manipulated by a voter misreporting a preference, or explain why the naïve extrapolation from the Gibbard–Satterthwaite theorem fails here.
May's characterisation of majority rule for two alternatives — including the strategy-proofness the extrapolation overlooks.
In plain terms: The free entry on the two-option case, where honesty turns out to be nobody's loss.
Gibbard–Satterthwaite with its hypotheses — three or more alternatives — marking exactly why two escapes the theorem.
In plain terms: The free survey stating the manipulation theorem precisely enough to see where its reach ends.
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations (open copy)
The proofs in textbook form: single-peakedness, dominance of sincerity on two alternatives, and the general impossibility.
In plain terms: The free standard text where the two-alternative claim can be settled by an actual argument.
Background: Gibbard–Satterthwaite theorem · May's theorem
5. State Condorcet’s jury theorem, and say what becomes of it when the independence of the voters is dropped.
The theorem and its dependence structure: competence and independence, with correlated-voter generalisations and their weakened conclusions.
In plain terms: The free definitive entry — the crowd's wisdom proved, and then re-examined when the crowd talks to itself.
The epistemic reading of voting the theorem underwrites — and its scope conditions.
In plain terms: The free companion on elections as truth-tracking devices, when the theorem's premises hold.
The result located in the aggregation canon, with the deliberation-versus-independence tension made explicit.
In plain terms: The free survey showing why discussion — the very thing juries do — strains the theorem's guarantee.
Background: Condorcet's jury theorem · Wisdom of the crowd
6. Individually transitive preferences can aggregate to a cyclical majority. Locate exactly where transitivity is lost, and explain why McKelvey’s chaos theorem makes the loss consequential rather than curious.
The cycle as the impossibility's seed: transitivity holding for each voter and failing for the profile — located exactly at aggregation.
In plain terms: The free entry pinpointing where the sensible many become an incoherent whole.
Transitivity as a property of individual orderings — the premise that survives intact while its collective analogue dies.
In plain terms: The free account of what each voter keeps, making plain that nothing individual was lost.
The consequence sharpened: agenda control under cycling, and McKelvey's result that majority paths reach anywhere.
In plain terms: The free survey of why the cycle is not a curiosity — whoever sets the agenda can steer the outcome at will.
Background: Condorcet paradox · McKelvey–Schofield chaos theorem
7. A committee votes coherently on each premise and on the conclusion, yet the majority position is inconsistent. State the discursive dilemma precisely, and decide whether it is Arrow’s theorem in disguise.
Belief merging and judgment aggregation
The dilemma stated and generalised: premise-wise consistency with conclusion-wise contradiction, and the List–Pettit impossibility behind it.
In plain terms: The free entry devoted to the committee's paradox — each vote sound, the sum absurd.
The comparison's other term: preference aggregation's impossibility, against which the judgment version is measured.
In plain terms: The free statement of Arrow's result, so the disguise question can be tried on properly.
The epistemic-aggregation setting shared by both results — truth-apt propositions under majority — clarifying what is genuinely new.
In plain terms: The free companion on groups judging facts, where the dilemma's novelty is weighed.
Background: Discursive dilemma · Group decision-making
8. State the revelation principle, and explain why it does not make mechanism design trivial.
Perspectives on mechanism design in economic theory (Nobel lecture)
The principle from its architect: any equilibrium outcome replicated by a truthful direct mechanism — a change of coordinates, not a solution.
In plain terms: The free lecture explaining the great simplification — and why simplifying the search is not ending it.
But who will guard the guardians? (Nobel lecture)
Incentive compatibility at its origin — the constraint set the principle organises but cannot dissolve.
In plain terms: The free lecture from the field's founder on why institutions must be designed against their participants.
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations (open copy)
The principle proved and its residue exhibited: the feasible truthful set still to be optimised over, with its own hard constraints.
In plain terms: The free textbook where the principle is a theorem — and the remaining design problem is the next chapter.
Background: Revelation principle · Mechanism design
9. Two parties would each gain from trade, yet no mechanism can guarantee that the trade occurs. State the Myerson–Satterthwaite theorem with its exact hypotheses, and identify which hypothesis each known escape relaxes.
Perspectives on mechanism design in economic theory (Nobel lecture)
The theorem by its co-author: two-sided private values, interim participation, budget balance — efficiency unattainable together.
In plain terms: The free lecture on the saddest theorem in trade — gains both sides know exist, and no honest procedure that always finds them.
Mechanism design: how to implement social goals (Nobel lecture)
The escapes catalogued from the implementation side: subsidies breaking budget balance, ex-ante participation, correlation, large markets.
In plain terms: The free companion lecture on which assumption each known loophole quietly gives up.
Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations (open copy)
The proof accessible in full, hypotheses labelled — the exactness the question demands, free of charge.
In plain terms: The free text where every hypothesis can be checked against the statement, line by line.
Background: Myerson–Satterthwaite theorem · Bargaining
10. The Vickrey–Clarke–Groves mechanism makes truth-telling dominant and the outcome efficient. Explain why it is nonetheless rarely used, on grounds internal to the mathematics.
The lovely but lonely Vickrey auction
The internal indictment itself: low and non-monotonic revenue, collusion and shill vulnerability, complement-driven failures — all from the mathematics.
In plain terms: The free classic on why the perfect auction is almost never held — its flaws are theorems too.
Auction research evolving: theorems and market designs (Nobel lecture)
What replaced it in practice — designs trading dominant-strategy purity for robustness the VCG mathematics cannot supply.
In plain terms: The free lecture from the designer of real spectrum auctions on why theory's favourite lost the job.
Networks, Crowds, and Markets (open copy)
The mechanism itself taught cleanly — truthfulness and efficiency proved — so the indictment has its exact object.
In plain terms: The free textbook chapter establishing the loveliness before the loneliness is explained.
Background: Vickrey–Clarke–Groves auction · Auction theory
11. State the revenue equivalence theorem, and identify the assumption whose failure best explains why real auctions are not all alike.
Auction research evolving: theorems and market designs (Nobel lecture)
The theorem and its undoing: equivalence under independent private values and risk neutrality — and affiliation as the failure that ranks formats.
In plain terms: The free lecture naming the assumption whose breakdown makes English and sealed-bid auctions genuinely different.
Auctions: theory and practice (survey and materials)
The equivalence's scope surveyed — risk aversion, budgets, correlation — each departure assigned its predicted asymmetry.
In plain terms: The free survey collection cataloguing exactly how the real world breaks the tie.
Perspectives on mechanism design in economic theory (Nobel lecture)
The theorem's deepest form: revenue pinned by allocation and lowest-type utility — the optimal-auction machinery it falls out of.
In plain terms: The free lecture from the author of the general theorem the classroom version specialises.
Background: Revenue equivalence · First-price sealed-bid auction
12. Prove that a stable matching always exists in the marriage problem, explain in what sense the proof is an algorithm, and say whom deferred acceptance favours.
College admissions and the stability of marriage
The original: deferred acceptance defined, termination and stability proved — existence by construction, favouring the proposing side.
In plain terms: The free seven-page classic that solved the problem by describing a courtship — the proof is the procedure.
The theory and practice of market design (Nobel lecture)
The algorithm in the field: doctors matched, the proposing-side optimality confirmed at national scale.
In plain terms: The free lecture on the theorem that runs real markets — and whom its favouritism actually helps.
Networks, Crowds, and Markets (open copy)
The result in teaching form: matching markets, stability, and the algorithmic reading of the existence proof.
In plain terms: The free textbook treatment, where the proof's double life as an algorithm is made explicit.
Background: Stable marriage problem · Gale–Shapley algorithm
13. The top trading cycles algorithm delivers the unique core allocation of the housing market and cannot be profitably manipulated. Prove one of the two properties, and account for the rarity of so clean a result.
The theory and practice of market design (Nobel lecture)
The algorithm's career: from Shapley–Scarf housing to kidney exchange — core uniqueness and strategy-proofness in deployment.
In plain terms: The free lecture where the clean theorem saves lives — cycles of kidneys traded exactly as the mathematics prescribes.
Stochastic games and other Nobel-recognised contributions (Nobel lecture)
The co-inventor recognised: the Shapley–Scarf market whose core the cycles compute, in the prize record.
In plain terms: The free lecture page for the mathematician behind the housing model the question names.
The rarity accounted for: core existence and uniqueness as exceptional — indivisibility and single-unit demand doing quiet work.
In plain terms: The free survey explaining why so few problems reward honesty and stability at once — and what makes this one special.
Background: Top trading cycle · Strategyproofness
14. Sperner’s lemma guarantees an envy-free division of a cake among any number of claimants. Explain how a combinatorial lemma about labelled triangulations comes to say anything about envy, and why existence here outruns procedure.
The combinatorial engine exact: proper labellings force a fully-labelled cell — the discrete fixed point beneath the fairness.
In plain terms: The free mathematical statement of the triangle lemma that somehow ends arguments about cake.
Papers on fair division and Sperner's lemma (author's page)
The bridge at source: preference labellings on the simplex of divisions, Sperner cells as approximate envy-free points — existence without a bounded procedure.
In plain terms: The free home of the rental-harmony argument — how colouring corners of triangles divides rent and cake without envy.
A discrete and bounded envy-free cake cutting protocol for any number of agents
Procedure finally catching existence: a bounded protocol — at tower-of-exponentials cost — measuring how far ahead the lemma ran.
In plain terms: The free breakthrough showing what it took to actually do what the triangle lemma promised — and at what astonishing price.
Background: Sperner's lemma · Envy-free cake-cutting
15. The Shapley value is the unique division of a coalition’s surplus satisfying four axioms. State them, decide which is the least innocent, and defend the choice.
Notes on the n-person game II: the value of an n-person game
The construction at source: efficiency, symmetry, null player, additivity — and the unique value they jointly force.
In plain terms: The free original RAND paper where four fairness rules turn out to leave exactly one way to split the gains.
Stochastic games and other Nobel-recognised contributions (Nobel lecture)
The value in its author's honoured corpus — the axiomatics recognised alongside the rest.
In plain terms: The free prize record of the mathematician whose name the division bears.
The axioms interrogated — additivity's independence-of-context as the standard suspect — with the debate's terms.
In plain terms: The free survey where the least innocent axiom is put on trial, as the question demands.
Background: Shapley value · Cooperative game theory
16. Exhibit a cooperative game whose core is empty, state the Bondareva–Shapley condition that diagnoses the emptiness, and say what emptiness means for the players.
The framework exact: characteristic functions, the core as unblocked imputations, balancedness as its existence criterion.
In plain terms: The free mathematical reference for coalitions, their demands, and the condition that decides whether all can be met.
Emptiness interpreted: three-player majority division as the canonical empty core, and instability as its meaning.
In plain terms: The free survey with the classic example — three splitting a prize by majority, and no split that some pair won't overturn.
Stochastic games and other Nobel-recognised contributions (Nobel lecture)
The diagnosing theorem's co-author in the prize record — balanced covers as the exact price of a non-empty core.
In plain terms: The free lecture page for the man whose condition tells the players whether peace is even possible.
Background: Core (game theory) · Bondareva–Shapley theorem
17. Prove that every finite game has a Nash equilibrium in mixed strategies, identifying what each hypothesis of the fixed-point theorem corresponds to in the game.
Equilibrium points in n-person games
The one-page original: best-reply correspondence into Kakutani — convexity from mixing, continuity from expected payoffs, a fixed point as equilibrium.
In plain terms: The free founding note, barely a page long, in which every finite game acquired a resting point.
The work of John Nash in game theory (Nobel lecture)
The result in the prize record, with the simplex-and-continuity architecture of the argument recounted.
In plain terms: The free lecture materials honouring the theorem the question asks to be re-proved.
The fixed-point machinery itself: compact convex domains and continuous maps — each hypothesis the game must supply.
In plain terms: The free statement of the topological theorem doing the hidden work — and the checklist the game answers to.
Background: Nash equilibrium · Kakutani fixed-point theorem
18. Computing a Nash equilibrium is PPAD-complete. State what this means, and what it implies for the claim that players, or markets, actually reach equilibrium.
Publications on the complexity of equilibria (author's page)
The completeness result in its author's open corpus: Nash computation captured by end-of-line arguments — existence without efficient search.
In plain terms: The free home of the proof that finding the equilibrium is the hard part — the theorem promises it exists, not that anyone can reach it.
Settling the complexity of computing two-player Nash equilibria
The sharpening: two players suffice for PPAD-completeness — the hardness is not a large-game artefact.
In plain terms: The free companion proof that even the simplest case resists — two players, and still no fast path to balance.
Computational complexity theory
What completeness for a total-search class means — and licenses — for claims that agents or markets reach the fixed point.
In plain terms: The free philosophical entry translating the hardness into its consequence: equilibrium as description, not prediction.
Background: PPAD (complexity) · Algorithmic game theory
19. State a folk theorem for infinitely repeated games precisely, and explain why a result that permits almost everything is nonetheless not empty.
The theorem by its master: any feasible, individually rational payoff sustained at high discount factors by credible punishment.
In plain terms: The free lecture on repetition as the mother of cooperation — and of every other durable arrangement besides.
Mechanism design: how to implement social goals (Nobel lecture)
The perfect version's co-author: subgame-perfect punishments making the permissiveness credible, not cheap.
In plain terms: The free lecture from the man who made the anything-goes theorem answer for its threats.
The theorem's content demonstrated on the canonical game: cooperation among the sustained equilibria — the non-emptiness the question requests.
In plain terms: The free entry showing what the permissive theorem actually delivers — the dilemma escaped, lawfully, through patience.
Background: Folk theorem (game theory) · Repeated game
20. Account for the persistence of cooperation among self-interested agents without invoking the word “trust”.
Five rules for the evolution of cooperation
The mechanisms without the word: kin selection, direct and indirect reciprocity, network and group structure — each with its threshold inequality.
In plain terms: The free classification of cooperation's engines — five mathematical reasons the selfish help, none named trust.
The strategic core: repetition, reputation, and conditional strategies sustaining cooperation among payoff-maximisers.
In plain terms: The free survey of how the dilemma is escaped in theory and tournament — by structure, not sentiment.
The population dynamics: cooperation as an attractor of replication under the right interaction structure.
In plain terms: The free entry where helping persists because it breeds, in agents that never deliberate at all.
Background: Reciprocal altruism · Tit for tat
21. Define an evolutionarily stable strategy, relate it exactly to Nash equilibrium, and say what the refinement buys in a population that does not reason.
The definition and the exact relation: every ESS a Nash equilibrium, the converse failing — with invasion-resistance as the surplus.
In plain terms: The free entry on stability for the unreasoning — what a strategy must survive when nobody is calculating.
Five rules for the evolution of cooperation
The refinement earning its keep: stability conditions selecting among equilibria in populations under selection.
In plain terms: The free paper showing what the sharper concept buys — predictions about which behaviours persist.
The evolutionary sections: strategies as replicators, tournaments as selection — equilibrium reached without reasoning.
In plain terms: The free companion where the refinement is watched at work in populations of simple rules.
Background: Evolutionarily stable strategy · Replicator equation
22. Hamilton’s rule, rb > c, is a theorem, an approximation, or a tautology, depending on how its terms are defined. Adjudicate.
The adjudication's terrain: rb > c as exact theorem under regression definitions, approximation under others, tautology under careless ones.
In plain terms: The free entry laying out how one small inequality can be all three things, depending on what its letters are made to mean.
Five rules for the evolution of cooperation
The rule in working form: relatedness thresholds derived alongside four siblings — the approximation reading in practice.
In plain terms: The free paper using the rule as a tool, which is its own answer to what kind of statement it is.
The definitional substrate: fitness, covariance, and the Price-equation formalism on which the rule's status turns.
In plain terms: The free companion on the underlying bookkeeping — where the adjudication is finally settled.
Background: Kin selection · Inclusive fitness
23. Agents who share a common prior and commonly know one another’s posteriors cannot agree to disagree. State Aumann’s theorem, and identify the assumption bearing the most weight.
The theorem in its two pages: common priors plus common knowledge of posteriors forcing equality of posteriors.
In plain terms: The free original — among the shortest famous papers in social science — proving that open disagreement cannot survive full openness.
The load-bearing assumptions weighed — the common prior above all — with the theorem's partition machinery unpacked.
In plain terms: The free entry identifying which premise carries the surprising conclusion, and how much it must carry.
The theorem's author in the prize record, the interactive-epistemology programme it seeded acknowledged.
In plain terms: The free lecture from the theorem's author — the two-page result grown into a field.
Background: Aumann's agreement theorem · Common knowledge (logic)
24. Distinguish mutual knowledge from common knowledge, and exhibit a coordination problem in which every finite depth of mutual knowledge fails where common knowledge would succeed.
The hierarchy exact: mutual knowledge to every finite depth against the infinite conjunction — with the coordinated-attack failure at each level.
In plain terms: The free definitive entry where 'I know that you know that I know' is climbed rung by rung — and shown never to reach the top.
Epistemic foundations of game theory
The consequence for play: which solution concepts need which epistemic conditions — coordination demanding the full tower.
In plain terms: The free entry on what players must know about each other's knowledge before acting together is rational.
The formal apparatus: K-operators, iteration, and the fixed-point definition separating common from merely mutual.
In plain terms: The free logic entry supplying the symbols in which the distinction becomes a theorem.
Background: Coordination game · Two Generals' Problem
25. State the independence axiom of expected utility, exhibit the Allais pattern that strains it, and decide whether the pattern refutes the axiom or only the theory’s descriptive ambitions.
The axiom stated and stressed: independence, the Allais pattern violating it, and the normative-versus-descriptive verdict options.
In plain terms: The free entry housing the exact confrontation — the clean axiom, the stubborn choices, and what each may claim.
The theory's architecture: representation theorems resting on independence — what falls, and what stands, if it is dropped.
In plain terms: The free survey of the whole edifice, showing which floor the paradox actually shakes.
Choice under uncertainty: problems solved and unsolved
The empirical adjudication: fanning-out documented, non-expected-utility responses surveyed — the descriptive verdict in the field's own journal.
In plain terms: The free classic survey of how economics absorbed the paradox — keeping the norm, amending the description.
Background: Expected utility hypothesis · Allais paradox
26. A book of bets is Dutch when it guarantees its holder a loss. State the Dutch book theorem, and say whether it grounds the probability calculus or merely reprices it.
The theorem and its converse, with the grounding question itself: pragmatic self-defeat versus dramatised incoherence.
In plain terms: The free definitive entry asking exactly what the sure-loss argument proves — foundation, or vivid illustration.
The argument among its rivals — accuracy-domination and representation theorems — competing to ground the same calculus.
In plain terms: The free survey of the other roads to the probability axioms, against which the bets are judged.
The betting framework itself — credences as prices — on which the argument's force, or mere repricing, depends.
In plain terms: The free entry on treating belief as willingness to bet, the assumption the whole book is written in.
Background: Dutch book · Probability interpretations
27. The Sonnenschein–Mantel–Debreu theorem shows that aggregate excess demand is essentially arbitrary. State the result precisely, and say what, after it, general equilibrium theory remains a theory of.
The theorem's philosophical weight: individual rationality imposing almost nothing on aggregate demand — and what survives as theory.
In plain terms: The free entry on the result that humbled the grand system — and the question of what it still explains.
Economic theory in the mathematical mode (Nobel lecture)
The co-author's own account of the axiomatic programme — existence secured, uniqueness and stability surrendered.
In plain terms: The free lecture from the man who proved both the system's existence and, in effect, its silence.
General economic equilibrium: purpose, analytic techniques, collective choice (Nobel lecture)
What general equilibrium remains a theory of, by its other founder: consistency and existence, not dynamics or forecast.
In plain terms: The free companion lecture stating the enterprise's honest purpose — the purpose the theorem leaves intact.
Background: Sonnenschein–Mantel–Debreu theorem · General equilibrium theory
28. Adding a road to a congested network can lengthen every driver’s journey at equilibrium. Exhibit Braess’s paradox, locate the failure — in the network, in the equilibrium concept, or in the drivers — and state the sense in which such inefficiency is nonetheless bounded.
On a paradox of traffic planning (translation of the 1968 original)
The paradox at source: the four-node network where the new link degrades every equilibrium journey.
In plain terms: The free original example, hosted by its discoverer — the road that made all the traffic worse.
The bound the question requests: equilibrium cost within 4/3 of optimal for linear latencies — anarchy priced exactly.
In plain terms: The free landmark proving the selfish outcome is bad by at most a third — the paradox bounded.
Networks, Crowds, and Markets (open copy)
The diagnosis taught: Wardrop equilibrium as the failure's location — the network innocent, the solution concept indicted.
In plain terms: The free textbook chapter locating the fault — not in the road, nor quite the drivers, but in what balance among them means.
Background: Braess's paradox · Price of anarchy
29. City sizes, word frequencies, and firm sizes obey Zipf’s law. State the regularity precisely, give two generative mechanisms that produce it, and say whether their multiplicity undermines the demand for a single explanation.
Power laws, Pareto distributions and Zipf's law
The regularity exact and the mechanisms plural: preferential attachment, multiplicative growth, criticality — each yielding the same tail.
In plain terms: The free standard survey — one law, many machines that manufacture it.
Power laws in economics: an introduction
The economic instances — cities, firms — with random growth plus friction as the generative account, and its unification claim.
In plain terms: The free survey by the economist who explained the cities — and argues the many mechanisms share one skeleton.
Power-law distributions in empirical data
The statement's precision enforced: estimation and testing that separate true power laws from look-alikes — discipline for the explananda.
In plain terms: The free methodological classic ensuring the law is stated, and verified, before it is explained.
Background: Zipf's law · Power law
30. Why does this paper contain no macroeconomics? Answer from the mathematics.
Whom or what does the representative individual represent?
The mathematical answer: aggregation destroys the rational-agent structure — the representative agent unlicensed by SMD.
In plain terms: The free classic explaining, from the theorems, why the whole economy is not a big person — and macro-as-theorem therefore scarce.
Economic theory in the mathematical mode (Nobel lecture)
The standard the paper enforces — theorem, proof, counterexample — and the aggregate level's failure to meet it, by his own results.
In plain terms: The free lecture setting the bar of rigour, beneath which macroeconomics, through no idleness, cannot yet pass.
General economic equilibrium: purpose, analytic techniques, collective choice (Nobel lecture)
The admissible remainder: existence and consistency results at the economy scale — what of macro is theorem, and how little.
In plain terms: The free lecture marking the boundary this paper respects — where proof gives out, the syllabus ends.
Background: Representative agent · Microfoundations