Differential game theoretic analysis of a problem of warfare

Chattopadhyay, R.

doi:10.1002/nav.3800160314

Cited by 3 publications

(1 citation statement)

References 1 publication

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“…I n particular, althougR the planning horizon for the problem a t hand is of fixed length, one camot invoke the sufficient conditions based on convexity of Mangasarian [24] or Funk and Gilbert [ll] because the right-hand sides of the differential equations (9) are not concave functions of r c and (6, . As we have discussed elsewhere [31-33, 35,401, however, the optimality of an extremal trajectory may be proven via citing the appropriate existence theorem for an optimal control; for the problem a t hand there are two further subcases: (1) if the extremal is unique, then it is optimal, or (2) if the extremal is not unique and only a finite number exist, then the optimal trajectory is determined by considering the finite number of corresponding values of the criterion functional.…”

Section: Determination Of the Optimal Fire-support Policymentioning

confidence: 99%

An examination of the effects of the criterion functional on optimal fire‐support policies

Taylor

Brown

1978

Naval Research Logistics

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This paper examines the dependence of the structure of optimal time-sequential fire-support policies on the quantification of military objectives by considering four specific problems, each corresponding to a different quantiiication of objectives (i.e. criterion functional). We consider the optimal time-sequential allocation of supporting fires during the "approach to contact" of friendly infantry against enemy defensive positions. The combat dynamics are modelled by deterministic Lanchester-type equations of warfare, and the optimal fire-support policy for each one-sided combat optimization p~oblem is developed via optimal control theory. The problems are all nonconvex, and local optima are a particular di5culty in one of them. For the same combat dynamics, the splitting of supporting &es between t*o enemy forces in any optimal policy (i.e. the optiality of singular subarcs) is shown to depend only on whether the terminal payoff reflects the objective of attaining an "overall" military advantage or a "local" one. Additionally, switching times for changes in the ranking of target priorities are shown to be different (sometimes significantly) when the decision criterion is the difference and the ratio of the military worths (computed accolding to linear utilities) of total infantry survivors and also the difference and the ratio of the military worths of the combatants' total infantry losses. Thus, the optimal fie-support policy for this attack scenario is shown to be significantly influenced by the quantification of military objectives.

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Section: Determination Of the Optimal Fire-support Policymentioning

confidence: 99%

An examination of the effects of the criterion functional on optimal fire‐support policies

Taylor

Brown

1978

Naval Research Logistics

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Chapter 29 Game theory models of peace and war

O’Neill

1994

Handbook of Game Theory With Economic Applications

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Embedded Game Analysis of a Problem in International Relations

Gillespie

Zinnes

Tahim

1978

IEEE Trans. Syst., Man, Cybern.

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The use of game theoretic models for understanding international relations has been widely criticized. In this paper we suggest that the theory of embedded differential games with optimal control is a productive methodology for responding to the critics. Several noncooperative differential game models with embedded objective functions are formulated. Concepts for obtaining undominated solutions based on the game structure, the quadratic objective functions and linear differential kinematic equations are discussed. The paper concludes that models with rich empirical reference can be formulated and productively used in understanding international conflict. @ tions, embedded games analysis, game theoretic analysis, mathematical models.

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Differential game theoretic analysis of a problem of warfare

Abstract: The present article considers a problem of missile warfare. It is formulated as a problem of economics and treated as a differential game. Some optimal strategies of targeting and firing of missiles are derived. Conditions under which such a war can be prevented are also developed.

Cited by 3 publications

References 1 publication

An examination of the effects of the criterion functional on optimal fire‐support policies

An examination of the effects of the criterion functional on optimal fire‐support policies

Chapter 29 Game theory models of peace and war

Embedded Game Analysis of a Problem in International Relations

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