哈佛博弈論課件section-預覽頁
【正文】 major types of equilibria: – Pooling: the types behave the same—updated beliefs=old beliefs – Separating: the types of behave differently ? Useful for sequential games of inplete information Perfect Bayesian Equilibrium ? 2 players, each contemplating nuclear war ? Neither knows if the other is about to strike ? Each can attack (A, a) or delay (D, d) ? If war, there‘s a 1st strike advantage ? Outes: – No war results in (0, 0) – The oute of being the firststriker in war is –a – The oute of NOT being the firststriker in war is –r ? Assume 0 a r Nuclear Deterrence Example A A 189。 N 1 D a 1 d 2 2 a d D (a, r) (r, a) (0, 0) (0, 0) (a, r) (a, r) Such that 0 a r Player1 forms beliefs over and Player 2 forms beliefs over and Equilibrium will look like: p = Prob(Player 1 plays D), m = Prob( ) q = Prob(Player 2 plays d), n = Prob( ) 1 Play D: m*[q*0+(1q)*(r)]+(1m)*0 = m*(1q)*(r) 1 Play A: m*(a)+ (1m)*(a) = a Always play A if m = 1, q = 0, else play D PBE: (A, a, 1, 1)…though Nature goes (189。)… again, by symmetry, and because beliefs are consistent w/ play. PBE outes are consistent w/ players‘ PBE beliefs Only 1 more PBE: When m*(1q)*(r) = a and m = (18
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