Signaling games. consider two firms –Oldstar ( old, set in the market) –Nova (new) if fight happens,oldstar can beat weak nova but not the strong, the.

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Presentation transcript:

Signaling games

consider two firms –Oldstar ( old, set in the market) –Nova (new) if fight happens,oldstar can beat weak nova but not the strong, the winner has the market to itself. for oldstar 3,for nova 4 and cost of fighting is -2

payoff matrix fightrefrain strong2,-24,0 weak-2,10,3

equilibrium without signaling let ‘w’ be probability that nova is weak in absence of any signals from nova, the payoff function for fighting is (w)1+(1-w)(-2) >0 w > 2/3 so oldstar fights if it has a prior information that nova is weak

signaling nova can give information by –display –don’t display

strong nova fightrefrain challen ge 2,-24,0 don't challen ge 0,3

weak nova, c is the cost for displaying fightrefrain challen ge and display -2-c,12-c,0 challen ge but don't display -2,12,0

so if w <2/3, then oldstar retreats if it sees the display. so for weak nova, if c <2 then it should challenge and display, since oldstar retreats – pooling equilibrium

how does oldstar react Oldstar draws conclusion whether or not nova displays according to Bays rule displ ay no displ ay sum of col stron g 1-w0 wea k wpw(1- p) w sum of row 1- w+w p w(1- p)

semi - separation so Old stars payoff from fighting conditional on oberving a display is 1(wp/(1-w+wp)) + (-2)(1-w)/(1-w+wp) = [wp – 2(1-w)]/(1-w+wp) nova chooses p to keep oldstar perfectly indifferent p = 2(1-w)/w

Mixed strategy Old stars strategy of fighting q, weak nova’s expected payoff form challenging a display q(-2-c) + (1-q)(2-c) = 2-c-4q weak nova’s payoff for not challenging = 0 q = (2-c)/4