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Cournot’s model of oligopoly - page 21 / 38

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Direct argument for Nash equilibrium

(m, m) is an equilibrium: if either candidate chooses a different position she loses.

No other pair of positions is a Nash equilibrium:

  • if one candidate loses then she can do better by moving to m (where she either wins outright or ties for first place)

  • if the candidates tie (because their positions are either the same or symmetric about m), then either candidate can do better by moving to m, where she wins outright.

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