Cournot vs. Bertrand Duopoly

Best responses and the equilibrium they determine

Two firms, two competition modes. Cournot sets quantities; the market price follows from aggregate supply. Bertrand sets prices on differentiated goods; customers split. The Nash equilibrium is the intersection of the two best-response curves — toggle modes and watch it move.

Competition mode

Inverse demand:

P = a - b(q_1 + q_2)

Best response:

q_i^{BR}(q_j) = \frac{a - c - b\,q_j}{2b}

Firms set quantities simultaneously; the market clears at the induced price. Nash: the unique fixed point of the best-response map.

a (demand intercept): 20.0

b (slope): 1.00

marginal cost c: 4.0

firm 1 q₁

5.000

firm 2 q₂

5.000

profit firm 1

30.00

profit firm 2

30.00

Drag inside the plot to pick any joint choice. The ringed intersection of the two best-response curves is Nash — the only point where neither firm regrets its move.

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