On phase coordinate restrictions in differential games of fixed duration

Kamran Haji-Ghassemi, Purdue University

Abstract

Using Berkovitz's definition of a differential game, we examine the existence and regularity of the value in differential games of fixed duration in which phase coordinate restrictions are imposed on one or both of the players. For games with phase restrictions on only one of the players, we show the existence of the value and the existence of a saddle point in a restricted sense when the phase set is a given closed subset of $\IR\sp{\rm n}$. For special types of sets we give sufficient conditions for the value to be finite, continuous or Lipschitz continuous. We, further, characterize the value as the "constrained" viscosity solution of the Hamilton-Jacobi-Isaacs equation with proper terminal values. Games with phase restrictions on both players are reduced, under appropriate hypothesis, to a finite sequence of games with phase restrictions on only one player. Thus the results on existence and regularity of the value are deduced from those described above. The results are applied to the games of "War of Attrition and Attack" and "Battle of Bunker Hill."

Degree

Ph.D.

Advisors

Berkovitz, Purdue University.

Subject Area

Mathematics

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