# 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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