Barriers and dispersal surfaces in minimum-time interception

Minimum time interception of a target moving in a horizontal plane is analyzed as a one-player differential game. Dispersal points and points on the barrier are located for a class of pursuit evasion and interception problems. These points are determined by constructing cross sections of the isochrones and hence obtaining the barrier, dispersal, and control level surfaces. The game solution maps the controls as a function of the state within the capture region

Optimal feedback strategies for pursuit-evasion and interception in a plane

Variable-speed pursuit-evasion and interception for two aircraft moving in a horizontal plane are analyzed in terms of a coordinate frame fixed in the plane at termination. Each participant's optimal motion can be represented by extremal trajectory maps. These maps are used to discuss sub-optimal approximations that are independent of the other participant. A method of constructing sections of the barrier, dispersal, and control-level surfaces and thus determining feedback strategies is described. Some examples are shown for pursuit-evasion and the minimum-time interception of a straight-flying target

A formulation and analysis of combat games

Combat is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives. With each opponent is associated a target in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously or in neither, a joint capture or a draw, respectively, is said to occur. Resolution of the encounter is formulated as a combat game; namely, as a pair of competing event-constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero-sum differential game. Otherwise the optimal strategies are computed from a resulting non-zero-sum game. Since optimal combat strategies frequencies may not exist, approximate of delta-combat games are also formulated leading to approximate or delta-optimal strategies. To illustrate combat games, an example, called the turret game, is considered. This game may be thought of as a highly simplified model of air combat, yet it is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit-evasion games

A formulation and analysis of combat games

Combat which is formulated as a dynamical encounter between two opponents, each of whom has offensive capabilities and objectives is outlined. A target set is associated with each opponent in the event space in which he endeavors to terminate the combat, thereby winning. If the combat terminates in both target sets simultaneously, or in neither, a joint capture or a draw, respectively, occurs. Resolution of the encounter is formulated as a combat game; as a pair of competing event constrained differential games. If exactly one of the players can win, the optimal strategies are determined from a resulting constrained zero sum differential game. Otherwise the optimal strategies are computed from a resulting nonzero sum game. Since optimal combat strategies may frequently not exist, approximate or delta combat games are also formulated leading to approximate or delta optimal strategies. The turret game is used to illustrate combat games. This game is sufficiently complex to exhibit a rich variety of combat behavior, much of which is not found in pursuit evasion games

A Study of Corporate Diversification and Restructuring Activities in the 1980s and 1990s Using Multiple Measures

Using popular/common measures of diversification employed by industrial organization scholars (Jacquemin-Berry entropy measure) and strategy scholars (size of the primary business segment), this study examines the corporate diversification and restructuring activities of American firms (sample from the Fortune 250 list) in the 1980s and 1990s. There is empirical support for the widespread notion that in the 1980s and 1990s, firms underwent major restructuring efforts by divesting unrelated (unprofitable) businesses and strengthening their core business units and related segments. Additionally, the results illustrate the consistencies and discrepancies between the above measures