國外博弈論課件lecture(13)-wenkub.com
2024-10-16 13:57 本頁面
【正文】 Natives ? Only two bars (bar 1, bar 2) in a city ? Can charge price of $2, $4, or $5 ? 6000 tourists pick a bar randomly ? 4000 natives select the lowest price bar ? Example 1: Both charge $2 ? each gets 5,000 customers and $10,000 ? Example 2: Bar 1 charges $4, Bar 2 charges $5 ? Bar 1 gets 3000+4000=7,000 customers and $28,000 ? Bar 2 gets 3000 customers and $15,000 May 20, 2021 73347 Game TheoryLecture 2 15 Example: Tourists amp。 , si+ 1, . .., sn) ui( s1, s2, ... si 1, si , si+ 1, ... , sn) fo r all s1? S1, s2? S2, . . ., si 1? Si 1, si+ 1? Si + 1, ..., sn? Sn. Definition: strictly dominated strategy regardless of other players’ choices si” is strictly better than si’ Prisoner 2 Mum Confess Prisoner 1 Mum 1 , 1 9 , 0 Confess 0 , 9 6 , 6 May 20, 2021 73347 Game TheoryLecture 2 8 Example ? Two firms, Reynolds and Philip, share some market ? Each firm earns $60 million from its customers if neither do advertising ? Advertising costs a firm $20 million ? Advertising captures $30 million from petitor Philip No Ad Ad Reynolds No Ad 60 , 60 30 , 70 Ad 70 , 30 40 , 40 May 20, 2021 73347 Game TheoryLecture 2 9 2player game with finite strategies ? S1={s11, s12, s13} S2={s21, s22} ? s11 is strictly dominated by s12 if u1(s11,s21)u1(s12,s21) and u1(s11,s22)u1(s12,s22). ? s21 is strictly dominated by s22 if u2(s1i,s21) u2(s1i,s22), for i = 1, 2, 3 Player 2 s21 s22 Player 1 s11 u1(s11,s21), u2(s11,s21) u1(s11,s22), u2(s11,s22) s12 u1(s12,s21), u2(s12,s21) u1(s12,s22), u2(s12,s22) s13 u1(s13,s21), u2(s13,s21) u1(s13,s22), u2(s13,s22) May 20, 2021 73347 Game TheoryLecture 2 10 In th e no rm al fo rm g a me { S1 , S2 , ..., Sn , u1 , u2 , ... , un}, let si39
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