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Cournot’s model of oligopoly - page 18 / 38

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Positions and votes Candidate who gets most votes wins.

(x + x )/2 12

x1

m

x2

vote for 1

vote for 2

In this case, candidate 1 wins.

Best responses

Best response of candidate i to xj:

  • xj < m:

xj

m

any position for i in here wins

candidate i wins if xi > xj and 1 (xi + xj ) < m or in , 2

other words xj < xi < 2m xj. Otherwise she either ties or loses. Thus every position between xj and 2m xj is a best response of candidate i to xj.

  • xj > m: symmetrically, every position between 2m xj and xj is a best response of candidate i to xj.

  • xj = m: if candidate i choose xi = m she ties for first place; if she chooses any other position she loses. Thus m is the unique best response of candidate i to xj.

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