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Game Theory 5.0/10

How Many Firms Enter

Identical firms may each pay a fixed entry cost of 50 to produce a homogeneous good with zero marginal cost. The inverse demand is P = 100 − Q. Once n firms have entered, they play the Cournot quantity game. Entry continues as long as one more firm would still earn a non-negative profit net of the fixed cost. How many firms enter?

Related problems & prerequisites

Worth solving first

Source: Original problem written for AxiomIQ, in the spirit of Cournot free-entry models.