Approximations and empirics for stochastic war equations

Faculty of Social Sciences, University of Stavanger (UiS), Stavenger, Rogaland, Norway
Naval Research Logistics (Impact Factor: 0.72). 10/2005; 52(7):682 - 700. DOI: 10.1002/nav.20105


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.

5 Reads
  • Source
    [Show abstract] [Hide abstract]
    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; 22(2-22):251-276. DOI:10.1016/j.ejpoleco.2006.02.004 · 1.44 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: Many authors have used dynamical systems to model asymmetric war. We explore this approach more broadly, first returning to the prototypical models such as Richardson’s arms race, Lanchester’s attrition models and Deitchman’s guerrilla model. We investigate combinations of these and their generalizations, understanding how they relate to assumptions about asymmetric conflict. Our main result is that the typical long-term outcome is neither annihilation nor escalation but a stable fixed point, a stalemate. The state cannot defeat the insurgency by force alone, but must alter the underlying parameters. We show how our models relate to or subsume other recent models. This paper is a self-contained introduction to 2D continuous dynamical models of war, and we intend that, by laying bare their assumptions, it should enable the reader to critically evaluate such models and serve as a reminder of their limitations.
    Journal of the Operational Research Society 12/2013; 66(2):191-201. DOI:10.1057/jors.2013.178 · 0.95 Impact Factor
  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper develops a version of the stochastic salvo combat model in which the exchange of fire is sequential, rather than simultaneous. This sequential-fire version is built by modifying the equations in the original simultaneous-fire version. The performance of the sequential model is tested by comparing its outputs with those of a Monte Carlo simulation. The fit between the model and the simulation is very close, especially for the mean and standard deviation of losses. The model is then applied to the Battle of the Coral Sea. The results suggest that attacking first would have given the American force a larger advantage than that provided by an extra aircraft carrier.
    Journal of the Operational Research Society 10/2014; 65(10). DOI:10.1057/jors.2013.115 · 0.95 Impact Factor