Signaling games

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Signaling games
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• 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

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• payoff matrix

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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) gt0
• w gt 2/3
• so oldstar fights if it has a prior
  information that nova is weak

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signaling

• nova can give information by
• display
• dont display

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• strong nova

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• weak nova , c is the cost for displaying

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• so if w lt2/3 , then oldstar retreats if it sees
  the display.
• so for weak nova , if c lt2 then it should
  challenge and display, since oldstar retreats
  pooling equilibrium

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how does oldstar react

• Oldstar draws conclusion whether or not nova
  displays according to Bays rule

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semi - separation

• so Old stars payoff from fighting conditional on
  oberving a display is
• 1(wp/(1-wwp)) (-2)(1-w)/(1-wwp)
• wp 2(1-w)/(1-wwp)
• nova chooses p to keep oldstar perfectly
  indifferent
• p 2(1-w)/w

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Mixed strategy

• Old stars strategy of fighting q , weak novas
  expected payoff form challenging a display
• q(-2-c) (1-q)(2-c) 2-c-4q
• weak novas payoff for not challenging 0
• q (2-c)/4