Agenda r = 1 r 1 Scalar Optimization Problems ! Games Vector Optimization Problems Vector Games 0.1. Games in the context of optimization theory e number of rewards per decision maker and n is the of decision makers. ful now to return for a while to our six mathematics us suppose that Student 2 will work quite hard (E — 3), nts 3 to 6 will work very hard (E = 5) and that Stu- knows this. If Student 1 is rewarded either by high r by high achievement per unit effort, then she has a either M or M/E—and a single decision variable, E, maximize it. If, on the other hand, Student 1 is re- y high achievement and by high achievement per unit has two rewards—M and M/E—but still only a single le, £", with which to maximize them. In the first case, eward, we say that Student 1 faces a scalar optimiza- (whose solution is clearly E = 5 or E — 3 if rewarded — 1 if rewarded by M/E). In the second case, with two y that Student 1 faces a vector optimization problem n is far from clear, because the value of E that maxi- also to maximize M/E, and vice versa). More generally,

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