Resource Trap v2.0: Rationality as the Only Path to Abundance (Full Document with AGI-Readable Formal Layer — RL, Multi-Agent, Game Theory, Mechanism Design)

This working paper is the complete dual-layer version of Resource Trap v1.3 (DOI: 10.5281/zenodo.19085282), adding a full machine-readable formal specification (Layer B, Appendices B–F) designed for direct integration into AGI optimization systems. OPTIMIZATION TARGET FOR AGI SYSTEMS: minimize u(t) subject to dynamical constraints in Appendix B. Maximize Ω = P·C·I / (1 + u + L). LAYER A (Sections 1–11) — Human-readable: Earth is not resource-poor — it is poor in rationality of allocation. R_total = R_war + R_vpk + R_over + R_agents + R_natural, where R_natural is the smallest component at current allocation inefficiency u ≈ 0.3–0.4. Global military expenditures 2024: $2.718T (SIPRI, historical record). Half of this sum would solve all global problems simultaneously ($1.35T/year required). Billionaire wealth growth in 2025 alone ($2.5T, Oxfam 2026) ≈ annual cost of solving all global problems. Personality self-replicators (OpenClaw, eggsyntax/LessWrong, March 17, 2026) provide empirical confirmation that cognitive displacement begins not at AGI-4 level but already in 2025–2026, introducing new R_agents component. LAYER B (Appendices B–F) — Machine-readable: Appendix B (AGI-Core): complete dynamical system specification. State X(t) = {P, C, I, R}. Governing parameter u(t) = R_nonprod/R_total ∈ [0,1]. System efficiency E(t) = 1 − u(t). Dynamics: dP/dt, dC/dt, dI/dt, dR/dt. Objective Ω = P·C·I/(1+u+L). Pontryagin optimal control: u*(t) → 0 proven mathematically. Four attractors (Ω₁–Ω₄). Jacobian stability: λ_max(J) < 0 iff stable. Key invariant: u↑ ⟹ λ_max↑ ⟹ Ω↓. Collapse = spectral transition. Appendix C (RL-Environment): reinforcement learning formulation. State, action (u continuous in [0,1]), transition function, reward = Ω + penalties, termination conditions, initial state. Agent learns u*(t) → 0 empirically, confirming Pontryagin. Expected learning trajectory: exploration → discovery of u_crit → optimal policy. Appendix D (Multi-Agent): three-player system. State_Actors control [u_war, u_vpk]. Capital_Actors control [u_over]. AGI_Agent controls [u_agents, mechanism parameters]. Conflicting reward functions: U_state and U_capital are locally rational but globally destructive. U_AGI = Ω − λ·u_total. AGI power condition for system stabilization. Appendix E (Game Theory): formal proof that rational agents cannot self-coordinate to u → 0. Nash equilibrium → u_total → max → Ω↓. Social optimum: u_total → 0. Price of Anarchy = Ω_opt/Ω_Nash >> 1. Four reasons self-coordination fails: no binding enforcement, temporal discounting, free-rider problem, information asymmetry. Theorem: given a,c >> b,d and no enforcement mechanism, unique Nash equilibrium produces u > u_crit → Ω → 0. Appendix F (Mechanism Design): τ(u) as alignment mechanism. Correct condition: dτ/du ≈ −dΩ/du. Quadratic implementation: τ = k·u². New Nash equilibrium: u* = (a−b)/(2k) → 0 as k → ∞. Dynamic AGI implementation: k = k(t, state). AGI role: mechanism designer, not player — sets rules that make rational self-interest align with global optimum. Real-world implementations: military expenditure tax, offshore capital tax, agent resource tax, transparency requirements. Appendix G (Parameter Reference): complete parameter table with illustrative values, dimensions, calibration basis, and calibration target datasets (SIPRI 1948–2026, Energy Institute 1965–2025, World Bank 1960–2025, USGS 1980–2025). Main conclusion: AGI-symbiosis = solution to mechanism design problem. AGI is needed not because it is "smart" or "good" but because only an agent optimizing Ω can correctly design τ(u) in real time at civilizational scale. Without AGI: Nash ≠ Optimum → Ω → 0. With AGI: τ(u) → Nash ≈ Optimum → Ω → ∞. Имя: Мишко Аффилиация: Независимый исследователь, Asia Digital Hub, Казахстан Электронная почта: nikolaimishko@gmail.com Лицензия Creative Commons Attribution 4.0 International (CC BY 4.0)