POL-UA 700 Lecture Notes - Lecture 18: Master Of Business Administration, Bayes Estimator
21 Nov 2016
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Used for incomplete information, within the realm of expected payoff calculations (& therefore probability). Must define both strategy pair and beliefs, and then verify that it is consistent with bayes" rule. Beliefs on equilibrium path have to be consistent with strategies as per bayes" rule. Both players are playing best responses i. ii. i. (enter|strong, stay out|weak; cooperate|enter; p(strong|enter)=1) General formula: p (a | b) = [ p (b | a) * p (a) ] / [p (b | a) * p (a) + p (b | not a) * p (not a)] P (strong | enter) = [p (enter | strong) * p (strong)] / ([p (enter | strong) * p (strong)] + [p (enter | weak) * p (weak)]) He will enter given he is strong, will not if he is weak. Therefore, p (strong | enter) = (1 * . 5) / [(1 * . 5) + (0 * . 5)] = 1 ii. iii. iii.
