ДВУСТОРОННЯЯ ЛОВУШКА НЕДОИНВЕСТИРОВАНИЯ В ИИ-КОМПЕТЕНЦИИ: ФОРМАЛЬНАЯ МОДЕЛЬ

Abstract:
The paper develops a formal two-agent model of investment in marketing training under accelerated AI-driven depreciation of human capital. The starting point is the empirical observation by Brynjolfsson et al. that relative employment of workers aged 22–25 in AI-exposed occupations declined by approximately 13%; we interpret this labor-market signal as quantitative rather than price-based. In the model, employer and worker simultaneously choose training investment shares for competencies with depreciation rate δ and payback horizon T. An analytic profitability condition δ·T ≤ ln 2 is derived. Within this region the individually rational equilibrium coincides with the social optimum, while in the intermediate zone ln 2 < δ·T ≤ ln 2 + ln(1+γ/α) strategic complementarity generates a coordination trap: joint investment benefits both agents, yet neither moves first. For three levels of marketing competencies formalized in the present paper (level 1 with δ₁ ≈ 0.6, level 2 with δ₂ ≈ 0.25, level 3 with δ₃ ≈ 0.08) the trap exclusively affects the first level at standard T ≈ 1.5 years, explaining the empirical concentration of underinvestment in platform-specific training. Comparative statics in δ, T, and public-funding share θ are obtained; trap boundaries T_crit = ln 2 / δ are derived for each taxonomy level. A numerical illustration using public McKinsey data matches observed retraining deficits. The results justify coordination mechanisms: in the trap zone a modest subsidy to one party suffices to escape the trap, since complementarity ensures entry of the second agent.