Lecture 9 Reputation Formation 14.123 Microeconomic Theory III Muhamet Yildiz Centipede Game 1 2 1 12 12 100 1 0 2 98 979998 1 3 2 98 10099 101 … 100 1Centipede Game – with doubt 197 5 4 3 2 1= n{.999}1 2 2 12 12 100 100 … 1 0 96 98 979998 1 3 99 98 10099 101 12 21 21 20 {.001} 100μ5 μ3 μ1 … -1 0 0-10-10 1 3 99 98 10099 101 Facts about SE in Centipede 2 always goes across with positive probability. Every information set of 2 is reached If 2 strictly prefers to go across at n, then she must strictly prefer to go across at n+2, her posterior at n is her prior. For any n > 2, 1 goes across with positive probability. If 1 goes across w/p 1 at n, then 2’sposterior at n -1 is her prior. If 2 is mixing at n, then (1- μn) pn-1= 1/2 μn = μn-2/2 μ ≥μn-2/2n 2Centipede Game – with doubt 197 5 4 3 2 1= n{.999}1 2 2 12 12 100 100 … 1 0 96 98 979998 1 3 99 98 10099 101 12 μ52 1 μ32 1 μ12 0 {.001} 100 … -1 0 0-10-10 1 3 99 98 10099 101 0 20 40 60 80 100 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 Go Across Mix 3MIT OpenCourseWarehttp://ocw.mit.edu 14.123 Microeconomic Theory III Spring 2010 For information about citing these materials or our Terms of Use, visit:
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