Game Theory 2-7-12

Game Theory 2-7-12 - GameTheory 2712 PartnershipGame o...

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Game Theory 2-7-12 Partnership Game o Si   [0, 4]   can choose any number between 0 & 4 including decimals o Profits = 4[s1 + s2 + (b)(s1)(s2)] o 0 b 1/4  o Both players choose simultaneously o Utilities  U1(s1,s2) =  ½  (4[s1 + s2 + (b)(s1)(s2)] – s1^2 U2 (s1,s2) =  ½  (4[s1 + s2 + (b)(s1)(s2)]– s2^2 o What to do? Find best response functions by taking partial derivatives U1=  ½  (4 + 4(b)(s2)) – 2s1 U2=  ½  (4 + 4(b)(s1)) – 2s2 Second order condition = -2, it’s a maximum Ŝ 1= 1 + (b)(s2)   best response for player 1: Br(1) Ŝ 2= 1 + (b)(s1)   best response for player 2: Br(2) o Graph Will be assuming that b=  ¼   Truncated version of graphs, assumes rationality, now you are assuming you  know that the other person is rational Eventually you keep eliminating till you find the result because of common
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