The Missing System Theorem

Private efficiency can certify a deal that fails its supporting system

The Missing System Theorem adds one coordinate to party-indexed payoff space: system welfare W. The claim is structural: W is not carried by the payoff vector, even though payoffs continue only while W stays above W₀.

• The failure case is the Hollow Win: (c,a,b)=(0,1,1).
• Both parties gain, yet c=0 because W<W₀.
• The older board can mark the deal efficient but cannot display the system failure.

W is a separate coordinate, not another private payoff

The paper rejects the idea that system welfare can be recovered from u1,...,un by an increasing transformation.

• A2 states there is no increasing g such that W=g(u1,...,un).
• Private gains can be real at the same time the system floor fails.
• The omission comes from the party-indexed payoff space itself.

The theorem tracks payoffs, system welfare, and a survival indicator

An outcome has agent payoffs u=(u1,...,un), system welfare W, and c=1 W≥W₀ . For the two-party display, a and b mark whether each party gains.

• c=1 means the system floor is met.
• c=0 means W has fallen below W₀.
• The Hollow Win cell is visible only after c is carried alongside a and b.

A1 through A3 make the Hollow Win possible

The theorem needs overlapping interests, system independence, and system dependence. Together they separate private improvement from system survival.

• A1: mutually improving moves in u are available.
• A2: W is not a function of the parties' payoffs.
• A3: agent payoffs are sustained only while W≥W₀.

Pareto efficiency over u does not imply c=1

Under A1 through A3, an outcome can be Pareto-efficient in agent payoffs and still have c=0.

• Efficiency over u can coexist with (c,a,b)=(0,1,1).
• The theorem does not claim all efficient deals fail the system.
• It claims standard efficiency certification lacks the coordinate needed to rule that failure out.

The eight-cell board names the missing failure cell

Adding c to the party-gain indicators creates the board where the Hollow Win can be shown directly.

• The visible failure case is system failure plus gains to both parties.
• Without c, the same case appears only as mutual private gain.
• The paper’s teaching entry point is the Hollow Win cell.

The chapter places existing theories on the larger board

MST is framed as a map of reductions, boundaries, restoration switches, and sibling impossibilities, not as a replacement for the canon.

• Nash and CAPM appear as reductions.
• Welfare theorems mark the complete-markets boundary.
• Pigou, Coase, and Ostrom are restoration switches.
• Myerson-Satterthwaite is a sibling impossibility.

Four results do the work beyond the theorem statement

The paper names four load-bearing additions: the eight-cell taxonomy, Conflictoring capture theorem, Decision Accounting report mechanism, and excluded-coordinate return signature.

• The taxonomy displays (c,a,b)=(0,1,1).
• Conflictoring gives one capture-resistant repair path.
• Decision Accounting makes W reportable at decision level.
• The return signature tests where excluded-coordinate domains show up on the return side.

The quantitative claim is a stable ordering, not a dollar total

The paper says the domains where W is most steeply excluded can be ranked, and that rank-ordering is highly stable but not strictly invariant across the choice of consensus shadow price.

• The lead quantitative object is an ordering of excluded-coordinate domains.
• The claim depends on rank stability across shadow-price choices.
• No domain beta-W tile is included in this flagship chapter.

MST is the board for SAPM, Decision Accounting, and Conflictoring

The chapter is presented as the flagship draft theory that connects downstream applications before asking readers to trust domain claims.

• Target journal: JET.
• Status: draft flagship chapter.
• Companion notes cover CAPM, Nash, the externality trilogy, Conflictoring, Decision Accounting, the return signature, and the welfare-theorem / Myerson-Satterthwaite boundary.

The test changes from who gained to whether W stayed above W₀

Once W is on the board, a privately good deal is incomplete until its system condition is checked.

• Economist: test whether W is genuinely excluded from u.
• Regulator: ask which restoration switch can survive capture.
• Teacher: start with the Hollow Win, then reveal why ordinary payoff space cannot show it.