static games

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static games with complete information
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Nash equilibrium(definition)
Def Strategy si is a best response to
s-i?S-i if ?i(si,s-i) ? i(si,s-i) for
all si Def A vector of strategies
s(s1,s2,,sN) is a Nash equilibrium if
?i(si,s-i) ? i(si,s-i) for all si and for
all i
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Nash equilibrium(interpretations)

• play prescription
• preplay communication
• rational introspection
• focal point
• trial and error

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example prisoners dilemma
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example coordination gameproblem uniqueness
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example matching penniesproblem existence
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IE(W)DS and Nash equilibria
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IE(S)DS and Nash equilibria
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discussion order of elimination, IE(W)DS and
Nash equilibria
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Nash equilibrium and IEDS(summary)

• Any IE(W)DS solution has to be a Nash
  equilibrium but there may be Nash equilibria
  that are not IE(W)DS solutions.
• Any IE(S)DS solution has to be a Nash
  equilibrium all Nash equilibria survive
  IE(S)DS.
• A dominant strategy equilibrium must be a Nash
  equilibrium the reverse implication does not
  hold.