Abstract
Economic systems in multi-agent simulations typically adopt either pure market-based pricing (susceptible to speculative bubbles) or centrally administered pricing (susceptible to misallocation). The Civilization simulation within MARIA OS implements a hybrid approach: every asset is valued at V = 0.5 P_market + 0.5 V_AI, where P_market is the current market price determined by supply and demand and V_AI is the AI-estimated fundamental value computed by the LOGOS system. This paper formalizes the economic dynamics of this hybrid valuation rule. We derive the stability conditions for the three land types (Commercial, Innovation, and Public) as a portfolio optimization problem, showing that the optimal allocation follows a modified Markowitz mean-variance frontier with an additional AI-anchoring constraint. We model bankruptcy cascades as an SIR-type epidemiological process on the economic network and prove that the 50/50 rule reduces the basic reproduction number R_0 of financial contagion by a factor of (1 + rho)^{-1}, where rho is the AI estimation accuracy. Under realistic parameters, this reduces cascade severity by 53%. However, we identify a critical vulnerability: when LOGOS-driven economies increase trading frequency (autonomous cycle pressure), the stability corridor narrows and can collapse if the trading-to-valuation-update ratio exceeds a threshold we derive analytically. Empirical results from 200 simulation runs validate these predictions with < 5% deviation from theoretical bounds.
1. Introduction
Every economic system must solve the valuation problem: how much is an asset worth? Market economies solve it through price discovery — the intersection of supply and demand curves reveals the price at which buyers and sellers agree. Planned economies solve it through administrative assessment — central authorities estimate value based on production costs, social utility, and strategic priority. Both approaches have well-documented failure modes. Market pricing produces speculative bubbles when positive feedback loops amplify noise. Administrative pricing produces misallocation when estimators lack local information.
The Civilization simulation introduces a third approach: hybrid valuation. Every asset — land parcels, business entities, infrastructure — is valued at exactly 50% of its current market price plus 50% of the AI-estimated fundamental value. This rule is embedded in Law 3 (Property Valuation) and cannot be amended. It creates a pricing mechanism that inherits the information-aggregation properties of markets while using AI estimation as an anchor against speculative drift.
This paper analyzes the economic consequences of this rule. We are interested in three questions. First, under what conditions does the 50/50 rule produce stable market equilibria, and when does it fail? Second, how do bankruptcy cascades propagate through the economic network under hybrid valuation, and does the AI anchor reduce contagion? Third, given the three distinct land types — Commercial (revenue-generating), Innovation (R&D and patent-producing), and Public (infrastructure and social services) — what is the optimal portfolio allocation under the 50/50 valuation constraint?
1.1 The Three Land Types
The Civilization simulation defines three land types with distinct economic characteristics:
- Commercial Land: Generates direct revenue through production and trade. Revenue is a function of labor allocation, technology level, and trade agreements. High expected return, high variance. Analogous to equity assets in traditional portfolio theory.
- Innovation Land: Produces patents and technology improvements that increase productivity across all land types. Revenue is indirect and delayed — investment today yields returns 2-3 cycles later. Moderate expected return, moderate variance, but positive externalities to other land types. Analogous to R&D investment or venture capital.
- Public Land: Provides infrastructure, healthcare, education, and social services. Revenue is negative (net cost center), but generates positive externalities that reduce variance of Commercial and Innovation returns. Analogous to government bonds or insurance — negative expected return but negative correlation with risky assets.
2. The 50/50 Valuation Model
2.1 Formal Definition
Let P_i(t) denote the market price of asset i at time t and let V_i^AI(t) denote the LOGOS AI-estimated fundamental value. The official valuation is:
The market price evolves according to standard supply-demand dynamics: P_i(t+1) = P_i(t) + eta * (D_i(t) - S_i(t)), where D_i and S_i are demand and supply at price P_i, and eta is the price adjustment speed. The AI estimate evolves according to a fundamentals model: V_i^AI(t) = f(cash_flows_i, growth_rate_i, risk_premium_i, externalities_i), updated by LOGOS at the end of each cycle.
2.2 Stability Analysis
The stability of the hybrid valuation depends on the correlation between market price deviations and AI estimation errors. Define the market deviation as delta_P(t) = P(t) - V_true(t) and the AI error as delta_AI(t) = V^AI(t) - V_true(t), where V_true is the (unobservable) true fundamental value. The hybrid valuation error is:
The variance of the hybrid error is Var(delta_V) = 0.25 Var(delta_P) + 0.25 Var(delta_AI) + 0.5 Cov(delta_P, delta_AI). Under the assumption that market deviations and AI errors are uncorrelated (a reasonable approximation when LOGOS uses fundamentals-based rather than market-based estimation), the hybrid variance reduces to 0.25 (Var(delta_P) + Var(delta_AI)). If the AI is more accurate than the market (Var(delta_AI) < Var(delta_P)), the hybrid valuation is strictly more accurate than pure market pricing. The stability corridor — the range of prices within which the hybrid valuation remains within one standard deviation of true value — has width 0.34 * sigma under empirical parameters.
2.3 The Autonomous Cycle Pressure Problem
A critical vulnerability emerges when LOGOS-driven economies accelerate trading frequency. In a technocratic nation where LOGOS recommends rapid portfolio rebalancing, the number of trades per cycle can increase by 3-5x. However, the AI valuation V^AI is only updated once per cycle. This creates a temporal mismatch: P_i(t) can drift significantly within a cycle while V^AI(t) remains stale.
Define the trading-to-valuation ratio as TVR = N_trades / N_valuations, where N_trades is the number of trading events per cycle and N_valuations is the number of AI valuation updates. When TVR exceeds a critical threshold TVR* = 2 / (1 - rho^2), where rho is the autocorrelation of market deviations, the stability corridor collapses. At this point, the AI anchor becomes ineffective because intra-cycle price movements overwhelm the correction provided by the stale AI estimate.
3. Bankruptcy Cascade as Epidemiological Contagion
3.1 Network Structure
The economic network of a Civilization nation is a directed graph G = (V, E) where vertices V represent economic entities (businesses on Commercial land, labs on Innovation land, public services on Public land) and edges E represent financial dependencies (supply chains, debt obligations, shared infrastructure). An entity is solvent when its valuation V_i(t) exceeds its debt obligations D_i. It is bankrupt when V_i(t) < D_i.
3.2 SIR Cascade Model
We model bankruptcy cascades using a modified SIR (Susceptible-Infected-Recovered) framework adapted to economic contagion. In this model, S (Susceptible) entities are solvent but have financial exposure to potentially bankrupt neighbors. I (Infected) entities are currently bankrupt and propagating losses. R (Recovered) entities have been restructured through LOGOS-mediated resolution and are no longer contagious.
The transmission rate beta is the probability that a bankrupt entity causes a neighbor to fail, given by beta = E[loss_given_default exposure / (V_neighbor - D_neighbor)]. The recovery rate gamma is determined by the speed of LOGOS-mediated restructuring. The basic reproduction number is R_0 = beta k_avg / gamma, where k_avg is the average degree of the economic network.
3.3 Impact of the 50/50 Rule on R_0
Under pure market pricing, a bankruptcy event depresses the market prices of related assets through panic selling, increasing delta_P and thus increasing beta. Under the 50/50 rule, the AI anchor dampens this effect: even if P_i drops sharply, V_i = 0.5 P_i + 0.5 V^AI_i declines by only half as much (assuming V^AI remains stable). This reduces the loss-given-default in the beta calculation.
Theorem 1 (Contagion Reduction). Under the 50/50 valuation rule with AI estimation accuracy rho (defined as 1 - Var(delta_AI) / Var(delta_P)), the basic reproduction number satisfies R_0^{hybrid} = R_0^{market} / (1 + rho). For rho = 0.7 (empirical LOGOS accuracy), this yields a 41% reduction in R_0, consistent with the observed 87.3% cascade containment rate (vs. 41.2% under pure market pricing) across simulation runs.
3.4 Cascade Phase Diagram
The cascade dynamics exhibit three phases depending on R_0:
| Phase | Condition | Behavior | Typical Outcome |
|---|---|---|---|
| Subcritical | R_0 < 1 | Bankruptcies are isolated, do not propagate | < 3 entities affected |
| Critical | R_0 approximately 1 | Power-law cascade size distribution | Unpredictable, fat-tailed losses |
| Supercritical | R_0 > 1 | Cascades propagate to a finite fraction of the network | Systemic collapse, nation-wide recession |
The 50/50 rule shifts nations toward the subcritical phase. Under pure market pricing, 34% of simulation runs enter the supercritical phase at least once during a 90-day span. Under the 50/50 rule, this drops to 8.2%.
4. Three-Land-Type Portfolio Optimization
4.1 Return and Covariance Structure
Let r_C, r_I, and r_P denote the returns per cycle for Commercial, Innovation, and Public land allocations. Empirical estimates from simulation data yield:
The negative correlations between Public land and the other two types are crucial: Public land acts as a natural hedge, reducing portfolio variance at the cost of expected return. This mirrors the role of government bonds in traditional portfolios.
4.2 Modified Markowitz Frontier
The optimal land allocation solves: max_w (w^T mu - (lambda/2) w^T Sigma w) subject to w_C + w_I + w_P = 1, w_k >= 0.1 for all k (minimum allocation constraint from Law 5), and sum_k |V_k(w) - V_k^AI(w)| <= epsilon (AI-anchoring constraint). The AI-anchoring constraint ensures that the portfolio's aggregate valuation under the 50/50 rule does not deviate too far from the AI estimate, preventing speculative overallocation to volatile land types.
Solving via Lagrangian optimization, the optimal weights under default parameters are w_C = 0.48, w_I = 0.32, w_P* = 0.20, achieving a portfolio Sharpe ratio of 1.42. This represents a significant improvement over naive equal allocation (Sharpe = 0.91) and pure Commercial allocation (Sharpe = 0.73, due to high variance).
4.3 Cycle-Dependent Rebalancing
The optimal allocation shifts across the 9-cycle span. In early cycles (1-3), overweighting Innovation land is optimal because the delayed returns arrive in time to compound. In middle cycles (4-6), the allocation shifts toward Commercial land to harvest accumulated technology improvements. In late cycles (7-9), risk-averse nations increase Public land allocation to lock in gains and reduce variance before the simulation concludes.
5. Empirical Validation
5.1 Valuation Accuracy
Across 200 runs, the 50/50 rule produced valuation errors (measured as RMSE from true fundamental value) that were 38% lower than pure market pricing and 22% lower than pure AI estimation. The hybrid outperforms both components because market and AI errors are approximately uncorrelated (empirical correlation: 0.07), and the averaging effect reduces variance as predicted by the theoretical model.
5.2 Cascade Statistics
| Metric | Pure Market | 50/50 Rule | Improvement |
|---|---|---|---|
| Mean cascade size | 4.7 entities | 1.9 entities | -60% |
| Max cascade size | 23 entities | 8 entities | -65% |
| Supercritical events | 34% of runs | 8.2% of runs | -76% |
| Recovery time | 3.1 cycles | 1.4 cycles | -55% |
5.3 Portfolio Performance
Nations that adopted the optimal 3-land allocation achieved mean terminal CEI_1 (Economic Stability) of 0.72, compared to 0.58 for nations using equal allocation and 0.49 for nations that concentrated in Commercial land. The Sharpe ratio prediction of 1.42 was validated with an empirical value of 1.38 (95% CI: [1.31, 1.45]).
6. Conclusion
The 50/50 valuation rule is a deceptively simple mechanism with profound economic consequences. By anchoring market prices to AI-estimated fundamentals, it creates a stability corridor that prevents pure speculative dynamics while preserving the information-aggregation benefits of market pricing. The epidemiological model of bankruptcy cascades reveals that this anchoring reduces the basic reproduction number of financial contagion by a factor determined by AI estimation accuracy, yielding a 53% reduction in cascade severity under empirical parameters.
The critical vulnerability — autonomous cycle pressure from high-frequency LOGOS-driven trading — identifies a fundamental tension in AI-governed economies: the same AI system that stabilizes valuations can destabilize markets by accelerating trading beyond the valuation update frequency. This finding has direct implications for MARIA OS governance design: AI agents that interact with economic systems must be constrained not only in what they can do but in how frequently they can act. The trading-to-valuation ratio TVR must be monitored and bounded as a first-class governance metric.
Future work will extend the contagion model to inter-nation cascades (where bankruptcy in one nation triggers capital flight to others), analyze the welfare implications of alternative valuation splits (e.g., 70/30 or 30/70), and develop adaptive valuation rules where the market/AI weight ratio adjusts dynamically based on market conditions.
References
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