Economics 650

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Economics 650

• Game Theory

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Homeworks 1

• Notice there are four basic proper subgames.
• Taking turns will resolve this problematic game.

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Homeworks 2 Hot Dogs

• Since the game has a definite end after 5 weeks,
  the two will choose the noncooperative strategy
  -- the low price -- on each repetition.

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Homeworks 3-1 Pressing

• Yes. If Nicholas adopts a TfT strategy rule, and
  Neighborhood experiments with a single defection
  by playing no care, then Neighborhood faces the
  following payoff sequence
• 3,0,2,2,2,
• whereas if they do not defect the sequence is
• 2,2,2,2,2,
• As usual the difference is only in the two first
  periods, so Neighborhood will be deterred if
  2?(2) gt 3 ?(0) 3, that is, ?gt1/2. For this
  problem, ?.979.98/1.00094, so Tit for Tat
  should be effective.

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Homeworks 3-2

• Notice that Nicholas best response is always to
  press whenever he can anticipate that
  Neighborhood will take care, so it shouldnt be
  necessary for Neighborhood to adopt any
  retaliatory strategy to encourage him to bring
  his shirts! If, nevertheless, we suppose
  Neighborhood were to adopt a Tit-for-Tat strategy
  we find Nicholas will be deterred from skipping
  provided that ? gt -2/3. Since ? is always
  positive, Tit-for-Tat will always bring Nicholas
  in to the cleaner.

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Homeworks 4 Hot Dogs

• Its not so clear, since we dont know the value
  of ?. Suppose ?0.75.
• Will a Grim Trigger Strategy bring about a
  cooperative equilibrium in this game?
• If one keeps charging higher price p2, his
  profit is 1212?...12?t12/(1-?)48
• If one deviates to lower price p1.5, his profit
  is 18 10?...10?t 810/(1-?)48
• Since the payoffs are identical, players are
  indifferent whether cooperate or not.