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Signaling games

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. equilibrium without signaling.

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Signaling games

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  1. Signaling games

  2. 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

  3. payoff matrix

  4. 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

  5. signaling • nova can give information by • display • don’t display

  6. strong nova

  7. weak nova , c is the cost for displaying

  8. 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

  9. how does oldstar react • Oldstar draws conclusion whether or not nova displays according to Bays rule

  10. 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

  11. 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

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