Pre r,) Prl. 0 Prle Prl.8PI + Prl *For simplicity, we assume two period. If OTSO, clearly p2 becomes 1. IfTT,=0 and g1 is the probability that weak banker strategically choose T,=0(q1 will be determined later), p2 and hence the expected inflation evolve according to the above Bayes Rule P1+9(1-p) W (2) Note that once q1< 1, p2>p, from(1). From (2), one can see the benefit of weak banker pretending to be tough, i. e. reducing the expected inflation. Of course, the cost to play the strategy is the loss caused by the deviation from his best choice at the first period Result: If B is sufficiently large, pooling equilibrium(q,=1). If B is sufficiently small, iF separate equilibrium(q1= 1). Otherwise, the F weak banker plays mixed strategy(0<q< 1).t❖ For simplicity, we assume two period. If π1 > 0, clearly p2 becomes 1. If π1 = 0 and q1 is the probability that weak banker strategically choose π1 = 0 (q1 will be determined later), p2 and hence the expected inflation evolve according to the above Bayes’ Rule. ( ) ( ) ( ) ( ) ( ) ( ) ( ) W W t T T t T T t t T Pt            Pr Pr Pr Pr Pr Pr Pr +  = ( ) (1 ) (2) (1) 1 2 2 1 1 1 1 2 e W p p q p p p  = −  + − = • Note that once q1 < 1, p2 > p1 from (1). From (2), one can see the benefit of weak banker pretending to be tough, i.e. reducing the expected inflation. Of course, the cost to play the strategy is the loss caused by the deviation from his best choice at the first period. • Result: If β is sufficiently large, pooling equilibrium (q1 = 1). If β is sufficiently small, separate equilibrium (q1 = 1). Otherwise, the weak banker plays mixed strategy (0 < q1 < 1)