國外博弈論課件lecture(13)-文庫吧資料
2024-10-25 13:57本頁面
【正文】 ayer’s strategy is best for her, given that all other players are playing their equilibrium strategies May 20, 2021 73347 Game TheoryLecture 2 21 In th e no rm al fo rm g a me { S1 , S2 , ..., Sn , u1 , u2 , ... , un}, a bi natio n of strategies ), . . . ,(**1 nss is a Nas h equ ilib rium if , f or ever y p l ay er i , ), . . . , . . . ,(), . . . , . . . ,(**1*1*1**1**1*1niiiiniiiisssssusssssu????? fo r all ii Ss ?. Th at is, *is so lv es Ma x imize ), . . . , . . . ,(**1*1*1 niiii sssssu ?? Sub ject to ii Ss ? Definition: Nash Equilibrium Given others’ choices, player i cannot be betteroff if she deviates from si* Prisoner 2 Mum Confess Prisoner 1 Mum 1 , 1 9 , 0 Confess 0 , 9 6 , 6 May 20, 2021 73347 Game TheoryLecture 2 22 2player game with finite strategies ? S1={s11, s12, s13} S2={s21, s22} ? (s11, s21)is a Nash equilibrium if u1(s11,s21) ? u1(s12,s21), u1(s11,s21) ? u1(s13,s21) and u2(s11,s21) ? u2(s11,s22). 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 23 Finding a Nash equilibrium: cellbycell inspection 1 , 0 1 , 2 0 , 1 0 , 3 0 , 1 2 , 0 Player 1 Player 2 Middle Up Down Left 1 , 0 1 , 2 0 , 3 0 , 1 Player 1 Player 2 Middle Up Down Left Right May 20, 2021 73347 Game TheoryLecture 2 24 Summary ? Dominated strategies ? Iterated elimination ? Nash equilibrium ? Next time ? Nash equilibrium ? Best response function ? Reading lists ? Sec and of Gibbons and Sec of Osborne 。 , si+ 1, . .., sn) ? (b ut n ot alway s =) ui( s
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