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CHAPTER 3 OF 18

The eight outcomes

~17 min full text
REVIEWED TEACHING EDITION
This chapter has completed the current author review and public-source checking pass. It remains working-paper teaching material without journal peer review. For the learning sequence, return to the curriculum.
CORE LESSON

There are eight ways a deal can end. Standard analysis can see four. The four it cannot see include the Hollow Win.

~7 min

The payoff space is incomplete

Standard economic analysis of a transaction between two parties, A and B, indexes the outcome space by what each party receives. The result is a two-dimensional payoff vector (a, b). A deal can be privately efficient inside that space and still damage the system that supports the transaction. The Missing System Theory (MST) names the structural reason1: the ordinary two-party payoff space is incomplete because it does not carry the system-welfare coordinate. MST compares that ordinary space with a completed three-coordinate space: Party A, Party B, and system welfare. The theorem’s claim is that the third coordinate cannot be recovered from the first two alone. The outcome space becomes (c, a, b), where c is a binary indicator: c = 1 when system welfare is preserved, c = 0 when system welfare is degraded. This single addition changes what the analyst can see.

Eight outcomes, not four

With three binary coordinates (c, a, b), there are exactly eight possible outcomes. Standard analysis, working with only (a, b), can distinguish four: (1,1) mutual gain, (1,0) A gains and B loses, (0,1) A loses and B gains, and (0,0) mutual loss. The four outcomes that turn on c are invisible to it. Among those invisible outcomes, the Hollow Win (0,1,1) is the key teaching case2 because both parties gain privately while the system they depend on degrades. The deal looks like mutual gain from inside the transaction. It is indistinguishable from a genuine Win-Win-Win (1,1,1) under standard bilateral analysis. The indistinguishability is structural: c cannot be computed from what a and b are.

The eight-outcome taxonomy

The eight outcomes form a complete taxonomy. (1,1,1) Win-Win-Win: all three dimensions positive, no structural tension. (0,0,0) Misery: universal loss. (1,0,0) Stable Misery: the system persists but both parties lose within it, and stability prevents resolution. (0,1,0) Corrosive Win-Lose: A gains at the expense of both B and the system. (0,0,1) Corrosive Lose-Win: B gains at the expense of both A and the system. (1,1,0) Sustainable Win-Lose: B loses for the benefit of the system and A. (1,0,1) Sustainable Lose-Win: A loses for the benefit of the system and B. Each outcome has a name. Most have no name in the existing literature, and they should. The taxonomy maps where private and system incentives align or conflict; it does not rank outcomes by moral judgment.

Why standard analysis cannot see the Hollow Win

The Hollow Win is the natural outcome when private gains are available by degrading a system that is not priced in the transaction. Standard analysis labels both (0,1,1) and (1,1,1) as mutual gain because it carries no coordinate for c. This follows from the structure of the payoff space. The theorem establishes that c is not a function of a and b. No amount of data on what A and B received can reveal whether the system survived. Even when the parties know about some system harms and internalize pieces of them through engineering, insurance, compliance, reputation, regulation, or litigation, the full system-welfare effect still has to be measured separately. The practical consequence is that every claim of mutual gain is ambiguous until the system coordinate is examined on its own evidence.

Examples that make the invisible coordinate visible

The examples that teach the eight-outcome map. A transaction can look like a win-win inside the named-party payoff space while damaging the shared system. A benchmark trade can enrich the desk and satisfy the immediate counterparty while degrading benchmark integrity3. A platform can give consumers a free or convenient service while damaging adolescent mental health, local journalism, or the civic information commons. A tax strategy can benefit mobile capital and its advisers while eroding fiscal capacity and shifting the burden to less mobile taxpayers4. These examples teach the same structural point. The standard payoff map sees the named parties. MST asks whether the support system remains intact. Once that third coordinate is added, the apparent win-win may become a Hollow Win, and the remedy changes from improving bargaining to changing the game.

The relationship to existing landmarks

The Missing System Theory does not replace Nash5, CAPM6, the welfare theorems7, Pigou, Coase, Ostrom, or Myerson-Satterthwaite8.

What changes for the reader

After this chapter, a reader should not read a claim of mutual gain without asking: gain for whom, and at what cost to the system that makes the gain possible? The eight-outcome taxonomy provides a diagnostic grid. Any transaction can be placed in one of eight cells, and the placement requires evidence on all three coordinates. The practical point is narrow and important: the system coordinate must be examined on its own evidence because it cannot be recovered from the parties’ payoffs alone. The chapter does not claim that all private gain degrades the system. Its contribution is structural. It gives a name and a location to outcomes that standard bilateral analysis cannot display.

The eight-outcome taxonomy

Outcome (c,a,b)Namec (System)a (Party A)b (Party B)Structural description
(0,1,1)Hollow Win011Both parties gain while the system degrades. Indistinguishable from Win-Win-Win under standard bilateral analysis.
(1,1,1)Win-Win-Win111All three dimensions positive. No structural tension. The only outcome with no internal contradiction.
(0,0,0)Misery000Universal loss across all dimensions. System, A, and B all degraded.
(1,0,0)Stable Misery100System persists but both parties lose within it. Stability prevents resolution.
(0,1,0)Corrosive Win-Lose010A gains at the expense of both B and the system. Extractive and system-degrading.
(0,0,1)Corrosive Lose-Win001B gains at the expense of both A and the system. Mirror of Corrosive Win-Lose.
(1,1,0)Sustainable Win-Lose110B loses for the benefit of the system and A. Asymmetric sacrifice.
(1,0,1)Sustainable Lose-Win101A loses for the benefit of the system and B. Asymmetric sacrifice.
Why the Hollow Win is a recurring invisible outcome · ~2 min
The Hollow Win (0,1,1) is not a rare edge case. At the theorem boundary, test the three foundational axioms explicitly: (1) Overlapping Interests — the parties have a shared private gain to pursue; (2) System Independence — system welfare W is not a function of the parties' payoffs; and (3) System Dependence — the parties' activity affects W. A Hollow Win additionally requires that the available private gain is associated with system degradation. Pricing, disclosure, or private incentives may reduce that degradation, but those are mechanisms around the theorem boundary rather than substitutes for the three axioms. These structures appear in finance, natural-resource extraction, platform economics, and regulatory arbitrage (structuring an activity to exploit gaps between rules or jurisdictions and dodge a regulation). Standard analysis supplies no C coordinate, so a transaction can continue to read as mutual gain while the system degrades.
  • The Hollow Win is structurally common, not rare.
  • Standard analysis provides no alarm because it cannot distinguish (0,1,1) from (1,1,1).
  • The absence of an alarm is a feature of the payoff space, not a failure of empirical observation.
The relationship between MST and Myerson-Satterthwaite · ~2 min
The Myerson-Satterthwaite (1983) impossibility theorem9 states that no bilateral-trade mechanism can simultaneously satisfy efficiency, individual rationality (no party ends up worse off than its no-deal alternative), incentive compatibility (honesty is each participant's own best strategy), and budget balance (the transfers net to zero, needing no outside subsidy). MST states that system welfare is not a function of the parties' payoffs. These are independent results. Myerson-Satterthwaite concerns the limits of mechanism design under private information. MST concerns the structural exclusion of a coordinate from the payoff space. A mechanism that satisfies all four Myerson-Satterthwaite conditions could still produce a Hollow Win if the system coordinate is missing. A mechanism that carries the system coordinate could still fail the Myerson-Satterthwaite conditions. The two theorems bind on different constraints10, and the taxonomy assigns each a distinct relation to MST.
  • Myerson-Satterthwaite and MST are independent impossibility results.
  • One concerns mechanism design under private information; the other concerns the structure of the payoff space.
  • Satisfying Myerson-Satterthwaite does not prevent Hollow Wins, and carrying the system coordinate does not solve the Myerson-Satterthwaite problem.
Pigou, Coase, and Ostrom as restoration strategies · ~2 min
If the system coordinate is missing from the bilateral payoff space, how can it be restored? The literature contains three distinct strategies. Pigouvian taxation imposes a price on system degradation11, so the private cost reflects the social cost. Coasian bargaining assigns property rights over the system and lets the parties negotiate12. Ostrom's design principles show how communities govern shared resources without top-down pricing or privatization13. Each strategy has a different scope and different failure modes. Pigouvian taxation requires accurate measurement of system degradation. Coasian bargaining requires low transaction costs and well-defined property rights. Ostrom's principles require community stability and shared norms. The Missing System Theory does not choose among these strategies. It shows why all three are responses to the same structural gap: the missing system coordinate.14
  • Pigou, Coase, and Ostrom are three distinct strategies for restoring the system coordinate.
  • Each has different scope conditions and failure modes.
  • MST does not choose among them; it shows why all three respond to the same structural gap.
What the theorem does not claim · ~2 min
The Missing System Theory makes a narrow structural claim. It does not claim that all private transactions degrade the system. It does not claim that the system coordinate is always the most important dimension. It does not claim that the eight-outcome taxonomy replaces existing welfare analysis. It does not claim that the Hollow Win is always the outcome to avoid. The theorem’s claim is that the system coordinate cannot be recovered from the parties’ payoffs alone, and that its exclusion is a property of how the payoff space is built. The practical consequence is that any analysis examining only private payoffs is structurally incomplete. The theorem diagnoses that structure; it does not prescribe what to do about the incompleteness.
  • MST is a structural claim, not a normative prescription.
  • It does not claim all transactions degrade the system.
  • It does not replace existing welfare analysis.
  • It diagnoses the structure of the payoff space.
APPLIED EXERCISE

Classifying a transaction using the eight-outcome taxonomy

~2 min
Select a transaction or business practice that you know well. It could be from your own professional experience, a well-documented industry case, or a regulatory proceeding. Using the eight-outcome taxonomy, classify the transaction on all three coordinates: c (system welfare), a (Party A outcome), and b (Party B outcome). For each coordinate, provide the evidence that supports your classification. Then answer: (1) Which outcome does standard bilateral analysis (a,b) alone show? (2) Which outcome does the full (c,a,b) taxonomy show? (3) If the two classifications differ, what is the practical consequence of the difference? (4) If the transaction is a Hollow Win, which restoration strategy (Pigouvian, Coasian, Ostromian) would be most appropriate, and why?
Answer key
  1. A clear identification of the two parties (A and B) and the system (W) that supports the transaction.
  2. A supported classification for each of the three coordinates, with evidence for each.
  3. A comparison of the standard (a,b) classification with the full (c,a,b) classification.
  4. If the classifications differ, an explanation of what the standard analysis misses.
  5. If the transaction is a Hollow Win, a reasoned choice of restoration strategy with justification.
READING PATH
  1. This is the primary source for the eight-outcome taxonomy and for the structural claim that the system-welfare coordinate cannot be recovered from the parties’ payoffs alone. It establishes the Hollow Win as the outcome standard analysis cannot see.
    Extract the definition of the three-coordinate payoff space (c,a,b), the eight-outcome taxonomy, and the result that c is not a function of a and b.
  2. This source clarifies the relationship between MST and the two fundamental welfare theorems, and between MST and the Myerson-Satterthwaite impossibility theorem. It guards against the common error of treating MST as a replacement for or contradiction of these landmarks.
    Extract the distinct relation each landmark has to MST: the welfare theorems as the boundary where MST's axiom fails, and Myerson-Satterthwaite as an orthogonal impossibility result.
CHAPTER SYNTHESIS
QUESTION
What is the difference between the standard two-dimensional payoff space (a,b) and the extended three-dimensional space (c,a,b)?
ANSWER
The standard space indexes outcomes by what each party receives. The extended space adds a third coordinate c, which indicates whether system welfare W is preserved (c=1) or degraded (c=0). The theorem establishes that c is not a function of a and b.
QUESTION
What do the values c=1 and c=0 represent?
ANSWER
c is a binary indicator on the system coordinate: c=1 when system welfare W is preserved, c=0 when W is degraded. It is added to the party payoffs a and b to form the three-coordinate outcome (c,a,b).
QUESTION
Why is the Hollow Win (0,1,1) invisible to standard bilateral analysis?
ANSWER
Standard analysis works in the (a,b) space, where (0,1,1) and (1,1,1) both appear as (1,1) mutual gain. The system coordinate c is not carried, so the two outcomes are structurally indistinguishable.
QUESTION
Why is the eight-outcome taxonomy described as structural rather than moral?
ANSWER
It maps where private and system incentives align or conflict across the three coordinates. It does not rank outcomes by moral judgment; each cell is a structural position rather than a verdict.
QUESTION
What is the relationship between the Missing System Theory and the two fundamental welfare theorems?
ANSWER
The welfare theorems describe the boundary at which MST's central axiom — system independence — fails. When the system coordinate is priced and traded as a complete commodity, no competitive equilibrium can realize the Hollow Win.
QUESTION
What is the relationship between the Missing System Theory and the Myerson-Satterthwaite impossibility theorem?
ANSWER
They are orthogonal. Myerson-Satterthwaite concerns the impossibility of efficient bilateral trade under private information. MST concerns the structural exclusion of system welfare from the payoff space. They bind on different constraints.
QUESTION
Name the three restoration strategies for bringing the system coordinate back into the transaction, and state the scope condition for each.
ANSWER
Pigouvian taxation (requires accurate measurement of system degradation), Coasian bargaining (requires low transaction costs and well-defined property rights), and Ostrom's design principles (require community stability and shared norms).
QUESTION
What does the Missing System Theory not claim?
ANSWER
It does not claim that all private transactions degrade the system, that the system coordinate is always the most important dimension, that the eight-outcome taxonomy replaces existing welfare analysis, or that the Hollow Win is always the outcome to avoid. It makes a narrow structural claim about the payoff space.
SOURCE
Missing System Theory
SOURCE
welfare-theorem-boundary-ms-sibling
NOTES & REFERENCES
  1. The Missing System Theory — Decision Accounting program paper. Primary source for the three-coordinate payoff space (c,a,b) and the claim that the system coordinate cannot be recovered from the parties' payoffs. summary. ↩
  2. The Hollow Win — Decision Accounting program paper on the (0,1,1) outcome standard bilateral analysis cannot display. summary. ↩
  3. Benchmark Manipulation — Decision Accounting program paper. summary. ↩
  4. Tax Havens — program paper. summary. ↩
  5. Nash, J. F. (1951). Non-Cooperative Games. Annals of Mathematics 54(2): 286–295. link. ↩
  6. Sharpe, W. F. (1964). Capital Asset Prices. Journal of Finance 19(3): 425–442. link. ↩
  7. Arrow, K. J. (1951). An Extension of the Basic Theorems of Classical Welfare Economics. link. ↩
  8. The Welfare-Theorem Boundary — program paper. summary. ↩
  9. Myerson, R. B., and M. A. Satterthwaite (1983). Efficient Mechanisms for Bilateral Trading. Journal of Economic Theory 29(2): 265–281. link. ↩
  10. Why Incentive Compatibility Is Not Welfare Completion — program paper. summary. ↩
  11. Pigou, A. C. (1920). The Economics of Welfare. London: Macmillan. link. ↩
  12. Coase, R. H. (1960). The Problem of Social Cost. Journal of Law and Economics 3: 1–44. link. ↩
  13. Ostrom, E. (1990). Governing the Commons. Cambridge University Press. link. ↩
  14. Pigou, Coase, Ostrom: Limits — program paper. summary. ↩
DIAGRAM NOTES
These notes describe diagrams planned for this chapter. The diagrams are not published yet.
DIAGRAM NOTE
The invisible coordinate: why standard analysis cannot see the Hollow Win
two-panel conceptual diagram
Show that the standard (a,b) payoff space collapses four distinct (c,a,b) outcomes into two visible categories, hiding the Hollow Win and its structural implications.
DIAGRAM INPUTS
Standard payoff space: (a,b) with four quadrants
Extended payoff space: (c,a,b) with eight cells
Mapping: (1,1) in standard space maps to both (1,1,1) and (0,1,1) in extended space
READER CAPTION
The standard two-dimensional payoff space cannot distinguish a Win-Win-Win from a Hollow Win. Both appear as mutual gain in quadrant (1,1). The third coordinate c is required to see the difference. The gap is a structural property of the payoff space rather than a measurement problem.
TEXT FALLBACK
See the eight-outcome taxonomy table for the complete mapping.
Missing System Theory
DIAGRAM NOTE
MST and the welfare-theorem boundary
conceptual map
Show the relationship between MST and the two fundamental welfare theorems: the welfare theorems describe the boundary at which MST's central axiom (system independence) fails.
DIAGRAM INPUTS
MST axiom: system welfare is not a function of the parties' payoffs
Welfare theorem boundary: when the system coordinate is priced as a complete commodity
Result: at the boundary, no competitive equilibrium can realize the Hollow Win
READER CAPTION
The welfare theorems and MST are not in conflict. The welfare theorems describe the conditions under which MST's central axiom is switched off. When markets are complete and the system coordinate is priced, the Hollow Win cannot occur in competitive equilibrium.
TEXT FALLBACK
See the paper summary for the full propositional structure.
welfare-theorem-boundary-ms-sibling
WHAT TO DO NEXT
Restate the chapter claim. For policy triage, open Policy Lab; for measurement, open Domain Tables.
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© 2026 Erik Postnieks · Independent Researcher · Salt Lake City