Approximations and empirics for stochastic war equations
ABSTRACT The article develops a theorem which shows that the Lanchester linear war equations are not in general equal to the Kolmogorov linear war equations. The latter are time-consuming to solve, and speed is important when a large number of simulations must be run to examine a large parameter space. Run times are provided, where time is a scarce factor in warfare. Four time efficient approximations are presented in the form of ordinary differential equations for the expected sizes and variances of each group, and the covariance, accounting for reinforcement and withdrawal of forces. The approximations are compared with “exact” Monte Carlo simulations and empirics from the WWII Ardennes campaign. The band spanned out by plus versus minus the incremented standard deviations captures some of the scatter in the empirics, but not all. With stochastically varying combat effectiveness coefficients, a substantial part of the scatter in the empirics is contained. The model is used to forecast possible futures. The implications of increasing the combat effectiveness coefficient governing the size of the Allied force, and injecting reinforcement to the German force during the Campaign, are evaluated, with variance assessments. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005.
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ABSTRACT: Jack Hirshleifer (1925–2005) contributed to investment theory, information economics, conflict, and bioeconomics, clarified the foundations of investment and capital theory in the spirit of Fisher, and made basic contributions to the analysis of covariance risk, gambling and insurance, the Modigliani–Miller Theorem, and public investment through a focus on time, uncertainty and information. He formulated new models of public goods, added to understanding of contest success functions, and explained the paradox of power. He developed a general equilibrium approach to conflict jointly encompassing production, exchange, appropriation and defense. He analyzed the emotions as guarantors of threats and promises, proposed alternatives to the tit-for-tat strategy, considered the bioeconomic causes of war, and investigated the truthful signaling hypothesis. Jack Hirshleifer was a leading scholar and original thinker of the 20th century. His scientific contributions have left a Nobel Prize unbestowed.European Journal of Political Economy 02/2006; · 1.44 Impact Factor