Narrow Results

We investigate a simple motion pursuit-evasion differential game of one Pursuer and one Evader. Maximal speeds of the players are equal. The Evader moves along a given curve without self-intersection. There is no phase constraint for the Pursuer. Necessary and sufficient conditions to complete pursuit from both fixed initial position and all initial positions are obtained.

We consider pursuit and evasion differential game problems described by an infinite system of differential equations with countably many Pursuers in Hilbert space. Integral constraints are imposed on the controls of players. In this paper an attempt has been made to solve an evasion problem under the condition that the total resource of the Pursuers is less then that of the Evader and a pursuit problem when the total resource of the Pursuers greater than that of the Evader. The strategy of the Evader is constructed.

The compensation received by economic agents reflects their performance. Usually compensation reflects performance measured cardinally, but sometimes ordinal considerations play a role. It is well established that rewards — cardinal or ordinal — can rationally motivate contestants to put forth increased effort. We ask whether rewards, and in particular their cardinal or ordinal nature, can affect agents' strategies. Specifically, if level of effort is fixed and degree of difficulty is the only choice, what strategy is optimal? For example, in a high-jump competition, level of effort is not a meaningful variable; what is of interest is the choice of strategy — the height attempted, or degree of difficulty. We study how optimal strategies reflect reward structure, assuming that rewards may depend on level of difficulty, and go only to successful candidates, or only to candidates who succeed at more difficult tasks. Basing our conclusions in part on simple probabilistic models in which optimal choices can be determined analytically, we show how the structure of competitive rewards alters contestants' rational choices. We adopt a contest-design framework: What combinations of fixed and variable prizes cause contestants to select degrees of difficulty that maximize the contest designer's expected payoff? Our general conclusion is that competition can affect strategic choices, in magnitudes and even directions that are difficult to predict.

Extant studies and my own work show that in US listed corporations, the presence of a firm’s founder adds value to the firm. The incremental value increases with the extent of decision rights controlled by the founder. Furthermore, the value addition is higher if the founder CEO is younger at the time of the initial public offering and decreases with the founder’s tenure in the firm. Further investigation reveals that the founders add value by improving operating performance and being more transparent than similar non-founder firms. Moreover, the founders are more focused on the strategic positioning of the firm in improving operating performance — they improve profit margins in differentiated firms while improving efficiency in firms with cost-leadership strategy. Analysts and investors can benefit by incorporating these insights into their analysis.

Our main focus in this and the next chapter is the application of Cooperative Game Theory (CGT) models to international water resource issues. In this chapter we will justify the use of CGT in water resource problems, and in particular, in international conflict-cooperation cases. The chapter reviews several important CGT concepts and demonstrates their use and calculation. After reading this chapter you will have a good grasp of basic CGT concepts and be able to apply them at both conceptual and empirical levels to simple cases.