A Game-Theoretic Reconstruction of Social Equilibrium

Institutional Mechanics and Strategic Stabilization 

A Game-Theoretic Reconstruction of Social Equilibrium

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Abstract This paper advances a unified theory of institutional engineering by integrating

sociological observation with formal game-theoretic modeling. Rather than treating equilibrium

selection as a matter of historical accident or cultural inertia, we demonstrate that stable social

orders emerge from deliberate strategic design. We introduce a novel taxonomy—Category I

(evolved, path-dependent) versus Category II (designed, engineered) equilibria—and illustrate it

through historical norms (Chinese foot-binding), modern institutions (traffic conventions), and a

radical banking reform proposal: Quantitative Balancing (QB). QB reclassifies bank deposits as

direct Treasury liabilities, transforming the financial system’s payoff matrix, eliminating pooling

equilibria of opacity, and generating a unique, stable Nash equilibrium via negative feedback loops.

Keywords: coordination games, equilibrium selection, institutional design, Quantitative Balancing,

focal points, social stability

1. Introduction: The Architecture of Social Order

Social stability is neither random nor merely cultural; it is the outcome of identifiable strategic

equilibria. The companion manuscript “Equilibrium in Society” surveys a wide array of

coordination problems—from imperial Chinese gender norms to contemporary banking crises. This

paper moves beyond description to prescription: institutions must be understood as Equilibrium

Engineers that deliberately manipulate focal points and payoff structures to escape inefficient

outcomes.

We propose a sharp dichotomy:

• Category I (Evolved) Equilibria: sticky, path-dependent norms that arise organically

through repeated play and often lock societies into Pareto-inferior states.

• Category II (Designed) Equilibria: deliberately engineered systems—ranging from

international traffic standards to accounting reforms—that solve specific coordination

failures by altering incentives ex ante.

2. Game-Theoretic Foundations

2.1 Nash Equilibrium and the Selection Problem

A strategy profile s* is a Nash equilibrium if uᵢ(sᵢ, s₋ᵢ) ≥ uᵢ(sᵢ, s*₋ᵢ) ∀ sᵢ ∈ Sᵢ, ∀ i.

Social dilemmas rarely lack equilibria; they suffer from multiplicity. The core sociological

challenge is therefore the selection mechanism σ: Eₙₑ → s*.

2.2 Payoff vs. Risk Dominance

In the Stag Hunt, mutual stag-hunting is payoff-dominant but risk-dominated by mutual hare-

hunting. Risk dominance explains persistent stagnation even when superior outcomes are common

knowledge (Harsanyi & Selten, 1988).

12.3 Evolutionarily Stable Strategies and Possession

Maynard Smith’s “Bourgeois” strategy in the Hawk-Dove game—aggress if owner, yield if intruder

—is an ESS because it exploits the arbitrary but salient asymmetry of possession (Maynard Smith

& Price, 1973; Fabbri & Manzoni, 2021).

3. Category I: Evolved Equilibria and Super-Modular Traps

3.1 Chinese Foot-Binding: A Red Queen Trap

Foot-binding was a supermodular signaling game intensified by expanding male civil-service

opportunities (Fan et al., 2023). Pluralistic ignorance sustained the practice: families privately

disliked it but believed deviation would ruin marriage prospects. Only an exogenous shock—the

1912 ban—shifted the payoff matrix and destroyed the bad equilibrium.

3.2 Ethnic Segregation Paradox

Klašnja & Novta (2016) show that segregation reduces conflict under high polarization (by

lowering interaction frequency) but increases it under low polarization (by preventing reassuring

signals in Assurance games).

3.3 Battle of the Sexes in Marriage Markets

Scarcity of one sex shifts bargaining power dramatically (Chiappori et al., 2015), proving that even

“cultural” gender equilibria are highly sensitive to demographic parameters.

4. Category II: Designed Equilibria and Institutional Engineering

4.1 The Vienna Convention as Focal-Point Technology

The 1968 Vienna Convention on Road Traffic solved a global pure-coordination problem by

standardizing signs (red octagon = STOP) across 78 countries, dramatically reducing cognitive load

and creating hyper-salient Schelling points.

4.2 The Fragility of Mass Protest: Hong Kong 2019

Cantoni et al. (2019) document strategic substitutability: when citizens learned turnout would be

high, individual participation fell—an ironic “complacency tipping point” exploitable by

authoritarian regimes.

5. Quantitative Balancing: A Category II Solution for Finance

5.1 The Current Banking Game

Modern fractional-reserve banking is a coordination game with hidden information. Accounting

opacity creates a pooling equilibrium in which risky and safe banks are indistinguishable,

incentivizing excessive risk-taking (the “hare” strategy).

5.2 Reclassifying Deposits as Treasury Liabilities

Quantitative Balancing (Saba, 2024) treats customer deposits as direct obligations of the sovereign,

not the bank. This produces three immediate effects:

21. Banks pay an explicit seigniorage fee (≈30 bps) on deposits, internalizing systemic risk.

2. The Treasury becomes an active stabilizing player, earning revenue to backstop crises.

3. Depositors face zero run risk because their claims are now government debt.

The new payoff functions yield a unique Nash equilibrium (proven via strict diagonal concavity of

the Jacobian; Saba, 2024).

5.3 Empirical Validation (Monte Carlo, 38.3 trillion USD/EUR/GBP/JPY deposits)

• Systemic default probability: −23 bps

• Bank ROA compression: only −3 bps

• Treasury revenue gain: +30 bps

5.4 QB as the Ultimate Accounting Focal Point

Just as the red octagon eliminates ambiguity at intersections, reclassifying deposits as “Government

Debt” removes all doubt about ultimate liability, ending bank runs by design.

Figure 1: Payoff Matrix Transformation Pre- and Post-Quantitative Balancing

(QB)

To illustrate the transformation in the three-player game (Banks, Treasury, Depositors), I simplify it

to a representative 2-player payoff matrix between the Bank (row player, strategies: Prudent,

Balanced, Aggressive) and Depositors (column player, strategies: Keep Deposits, Monitor,

Withdraw/Run). Payoffs are (Bank, Depositors), with Treasury's role implicit in post-QB

adjustments (e.g., seigniorage tax τ ≈ 0.3 reducing high-risk incentives). Numbers are illustrative,

based on the paper's description of moral hazard, opacity leading to pooling equilibria pre-QB, and

uniqueness post-QB via risk internalization.

Pre-QB: Multiple equilibria exist due to hidden information— a good one (Prudent, Keep) and a

bad one (Aggressive, Withdraw) where runs occur.

Post-QB: Payoffs adjusted by reclassifying deposits as Treasury liabilities, eliminating run risk

(σ=0) and imposing τ on banks for money creation. This yields a unique stable equilibrium at

(Prudent, Keep), as aggressive strategies become dominated.

Pre-QB Payoff Matrix Keep Monitor Withdraw

Prudent

(4, 5) (3, 3)

(1, 2)

Balanced

(5, 4) (4, 2)

(0, 1)

Aggressive

(6, 3) (2, 1)

(-2, 0)

Post-QB Payoff Matrix (with τ adjustment) Keep Monitor Withdraw

Prudent

(4, 5) (3, 4)

(2, 3)

Balanced

(3, 4) (2, 2)

(0, 1)

Aggressive

(1, 3) (0, 1)

(-1, 0)

Notes: Nash equilibria marked in bold (pre-QB: two, including the run-prone; post-QB: one stable).

The transformation shows elimination of the bad run equilibrium through negative feedback

(diagonal strict concavity in the Jacobian, per Saba 2024). This visualizes how QB stabilizes by

making prudent strategies dominant.

36. Conclusion: From Observation to Social Mechanism Design

Category I equilibria reveal how societies can become trapped in costly conventions through no

one’s malevolent intent. Category II equilibria demonstrate that deliberate institutional engineering

—whether a road sign or an accounting rule—can permanently shift societies toward superior

outcomes.

Quantitative Balancing exemplifies the power of mechanism design at scale: a single ledger

reclassification resolves a multi-trillion-dollar coordination failure. The lesson is clear—institutions

are not passive reflections of culture; they are active architects of equilibrium.

References

Cantoni, D., Yang, D. Y., Yuchtman, N., & Zhang, Y. J. (2019). Protests as strategic games:

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Chiappori, P.-A., Iyigun, M., & Weiss, Y. (2015). The Becker-Coase theorem reconsidered. Journal

of Demographic Economics, 81(2), 157–177.

Fabbri, M., & Manzoni, G. (2021). Possession is nine-tenths of the law… in a Hawk-Dove game.

Working Paper.

Fan, X., Chen, L., & Luo, Y. (2023). The shaping of a gender norm: Marriage, labor, and foot-

binding in historical China. Working Paper.

Harsanyi, J. C., & Selten, R. (1988). A General Theory of Equilibrium Selection in Games. MIT

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Klašnja, M., & Novta, N. (2016). Segregation, polarization, and ethnic conflict. Journal of Public

Economics, 141, 51–64.

Maynard Smith, J., & Price, G. R. (1973). The logic of animal conflict. Nature, 246, 15–18.

Saba, M. (2024). Quantitative Balancing: A Nash Equilibrium Framework for Transparent Bank

Accounting. Working Paper.

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