The Governing Numbers: Applications of Game Theory and Linear Programming in the Italian Economy
Keywords:
Linear Programming, Game Theory, Nash Equilibrium, Italian Economy, Shadow Prices, Tax Compliance, SME Coopetition, Simplex MethodAbstract
AbstractThis paper examines the structural and strategic dimensions of the Italian economy through the lens of applied mathematics, specifically Linear Programming (LP) and Game Theory. Italy's economic fabric — characterized by a renowned luxury manufacturing sector, a fragmented Small and Medium Enterprise (SME) landscape, and chronic structural challenges including tax evasion and regional agricultural inefficiency — presents an ideal case study for quantitative policy modeling. This study formulates LP models for the "Made in Italy" luxury supply chain and for southern agricultural cooperatives, deriving optimal production mixes and shadow prices for scarce resources via numerical MATLAB implementation. Complementing these, game-theoretic frameworks model the Taxpayer–Revenue Agency interaction as a mixed-strategy non-cooperative game, deriving an equilibrium audit rate of 28.6% against a 4.5% evasion rate, and model SME industrial districts as infinitely repeated Prisoner's Dilemma games, establishing a critical cooperation threshold of δ* = 0.333 that all observed Italian district archetypes comfortably clear. Numerical results reveal that the luxury manufacturing optimum is constrained by carbon-allowance availability rather than artisanal labour — a finding that revises the conventional labour-scarcity narrative and redirects policy emphasis toward emissions-trading flexibility. Taken together, the findings demonstrate that quantitative modeling is not a theoretical luxury but a governance necessity for Italy's economic resilience
References
Allingham, M. G., & Sandmo, A. (1972). Income tax evasion: A
theoretical analysis. Journal of Public Economics, 1(3–4), 323–338.
Becattini, G. (2004). Industrial districts and local development: The
Italian experience. Edward Elgar Publishing.
Boyd, S., & Vandenberghe, L. (2004). Convex optimization.
Cambridge University Press.
Dantzig, G. B. (1947). Linear programming and extensions.
Princeton University Press.
Gibbons, R. (1992). A primer in game theory. Harvester
Wheatsheaf.
Hall, P. A., & Soskice, D. (Eds.). (2001). Varieties of capitalism:
The institutional foundations of comparative advantage. Oxford
University Press.
ISTAT. (2025). Rapporto annuale: La situazione economica del
Paese. Istituto Nazionale di Statistica, Roma.
Kantorovich, L. V. (1939). Mathematical methods of organizing and
planning production. Leningrad State University.
Nash, J. (1950). Equilibrium points in n-person games. Proceedings
of the National Academy of Sciences, 36(1), 48–49.
Von Neumann, J., & Morgenstern, O. (1944). Theory of games and
economic behavior. Princeton University Press.
