Oligopolists choosing quantities: reaction functions and an equilibrium between monopoly and competition.
Warming up the engine…
Oligopoly where firms choose QUANTITIES simultaneously: each firm's best output depends on what rivals produce, and equilibrium sits between monopoly and perfect competition.
Best response: q1 = (a − c − b·q2) / 2b ; equilibrium where best responses cross
If your rival floods the market, the price is low and your best move is to produce less; if they hold back, produce more. Where these reaction curves cross, neither firm regrets its choice: a Nash equilibrium. Add more firms and the outcome slides toward perfect competition, which is why concentration matters for prices.
Total output under Cournot duopoly is BETWEEN monopoly and competitive levels; price is above marginal cost but below monopoly. Deriving one best-response function is usually the whole trick.
Now prove you have it
Move the curve to where you think it lands, and get told exactly which part you got right.
Real-world scenarios on this model
Equilibrium at q₁ 20, q₂ 20.
Equilibrium: q₁* = 20.0, q₂* = 20.0
Current equations
Two firms choose how much to produce, each taking the other's output as given. Your best response falls as your rival grows, where the two reaction lines cross, neither firm regrets its choice. That's Nash equilibriumNash equilibriumA strategy profile where no player can gain by changing their choice alone..
Source: Varian, Intermediate Microeconomics, ch. 28