The Welfare-Theorem Boundary and the Myerson-Satterthwaite Sibling

Welfare theorems mark the point where MST no longer applies

The paper separates two relations that can be blurred by calling everything a special case: welfare theorems are MST's complete-markets boundary, while Myerson-Satterthwaite is a separate bilateral-trade impossibility.

• Proposition W.1: when W is priced and tradable, A2 fails and no competitive equilibrium realizes a Hollow Win.
• Proposition W.2: Myerson-Satterthwaite binds on private information; MST binds on the excluded system coordinate.
• The placement is boundary for welfare theorems, sibling for Myerson-Satterthwaite.

A2 excludes system welfare from the bilateral payoff space

MST depends on system independence: the bilateral traders can evaluate their own gains without W entering the payoff space.

• A2: the system coordinate W is not part of the bilateral payoff space.
• A Hollow Win is the outcome (c,a,b)=(0,1,1): both traders gain while the system coordinate fails.
• If W enters the priced commodity vector, the missing-coordinate premise is gone.

Priced and tradable W makes the Hollow Win impossible at equilibrium

With complete markets in W, Pareto efficiency is evaluated over the full commodity vector, including the system condition.

• W is a priced, tradable commodity, so A2 fails.
• At any competitive equilibrium, the paper states c=1.
• An allocation degrading W below W₀ is not efficient when a Pareto-improving alternative preserves W.

The first welfare theorem certifies equilibrium only after W is internal

The first fundamental theorem does not rescue a missing coordinate. It certifies competitive equilibrium in the complete economy where W is already inside the efficiency criterion.

• Complete markets and no externalities are the relevant assumptions.
• Every commodity, including the system condition, has a price and is traded.
• The equilibrium is certified including the system dimension, not outside it.

The second welfare theorem also lives in the complete-coordinate regime

The paper treats both welfare theorems as operating in the regime where every Pareto-efficient allocation can be supported because the system coordinate is already part of the commodity space.

• The second theorem covers Pareto-efficient allocations for some endowments.
• That claim is made in an economy with complete markets.
• MST starts where the system coordinate has been excluded, so this is the complement rather than a case inside MST.

MST names the missing market as the excluded coordinate

The paper connects MST to the Arrow-Starrett missing-market idea by indexing the missing market as W, the system coordinate excluded from bilateral payoffs.

• Welfare theorems hold when the relevant system coordinate is internalized.
• The Hollow Win requires failure of that completeness condition.
• The relationship is two-way in the paper: complete W means no MST; excluded W means the welfare-theorem boundary has been left.

Myerson-Satterthwaite and MST bind on different axes

Both results concern bilateral exchange, but their binding constraints differ. Myerson-Satterthwaite concerns unverifiable private valuations; MST concerns a system loss outside the bilateral payoff space.

• Myerson-Satterthwaite: no mechanism simultaneously satisfies efficiency, individual rationality, incentive compatibility, and budget balance when valuations are private.
• MST: the system coordinate is structurally excluded by A2.
• M-S lost surplus accrues to the two traders; MST loss accrues to third party C.

Complete information can remove M-S while MST still produces a Hollow Win

The paper's first separating case is a common-value bilateral exchange with full information and a system externality.

• No private information is present, so Myerson-Satterthwaite does not bind.
• The paper uses the common-pool construction with n=2.
• The Hollow Win remains the dominant-strategy outcome because W never enters the bilateral payoff space.

Private-value bilateral trade can trigger M-S while MST is vacuous

The second separating case removes the system coordinate entirely. Then the Myerson-Satterthwaite impossibility applies, while MST has no W over which to bind.

• Private valuations are present.
• No system coordinate is present.
• M-S binds; MST is vacuous.

Solving incentive compatibility does not price the missing system coordinate

The mechanism-design lesson is narrow: a mechanism can solve the informational problem in the bilateral payoff space and still permit system degradation outside that space.

• Efficient, IR, IC, budget-balanced trade can still leave W excluded under A2.
• Internalizing W removes the MST problem but does not solve the Myerson-Satterthwaite private-information barrier.
• The paper's claim is placement: boundary for welfare theorems, sibling for M-S.

CAPM and Nash reduce MST; welfare theorems bound it; M-S sits beside it

The paper's canon map assigns different relation types to different landmarks rather than folding them into one special-case label.

• Reduction: the coordinate is switched off, as in the paper's placement of CAPM and Nash.
• Boundary: the coordinate is complete, priced, and tradable, as in the welfare theorems.
• Sibling: the impossibility is on another axis, as in Myerson-Satterthwaite.

Do not invoke MST where enforceable claims on W are complete

The paper narrows MST's use. If the domain has complete, enforceable, tradable claims on system welfare, the missing-coordinate explanation should stop there.

• No empirical beta-W tile is claimed for this paper.
• The target is theory placement above applied domain ranking.
• The stated contribution is boundary discipline, with peer review still pending.