Equilibrium Existence Results for Simple Economies And Dynamic Games
Equilibrium Existence Results for Simple Economies And Dynamic Games
Paul R Kleindorfer
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For all (x, y) e x" X Y. This assumption implies, in particular, ^^^^ k^i^n^'i) = k^i for all (^x, i) e ^X X Y, which, as will become clear below, corresponds to the case where the feasible control region is fixed. 17 where n*^a • n^ '^ X "^ [n^^J is defined for each a e A and (^x°, ^) G ^x"x Y by In order to facilitate discussion we introduce the follov/inrr terminology. 2. 1. Terminology; From here on, whenever we speak of a "dynamic game", we will always mean a s. D. G.. Let S be as in 2. 0.... The elements of S will be referred to as follows. 2. 1. 0, n will be called the planning horizon . 2. 1. 1. X^ (^x^) will be called the g-control space (a-plan space), and x^ (^x^) will be called an d-control ( g-plan ) iff x. E X. ( x. E X ) ' ^ ' a anana X (^X") will be called the g-exclusive control space (g-exclusive plan space). And x" (^x") will be called ^^ a-exclu5ive control ( a-exclusive plan ) iff x'' t X" (^x" E J"). X (^X) will be called the control scace (U lan space ), and x (^x) will be called a control ( plan ) iff X e X ( X e X) .
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