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7.3hwpage2 - I113 Ema—11 GAMES(com—uaci 40 The matrix...

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Unformatted text preview: I113 Ema—11% GAMES (com—uaci.) 40. The matrix of the dynamical system is A = [E 2] so fA()l) = (a — A)” — ha. Hence, A1; = a :l: b, and the respecLive eigeuvecturs are [i] and [—1] . . e 3 1 ”1 e 1 5 1 Smce 12(0) = lg] = i [1] —§[ 1],byFa£:l; 7.2.3. 3(1) = :I-(a—l—b)‘ [1]+;Le—b)‘ [_1]. Note that a. —b is between 0 and 1, so that the second eununand in the formula above goes to 0 as it goes tn infinity. Qualitatively different outcomes occur depending on whether a + b exceeds 1, equals 1, or is less than 1. 'See Figure 7.20. a+b>l The Spending of both nations The Spending of both nations The spending of both nations grows: an arms race stabilizes at an equal level of decreases to zero: disarmament $11.75. Figure 7.20: for Problem 7.3.40. ...
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