How Game Theory Predicts Firm Entry in Unlimited Markets

In a Nash equilibrium scenario with unlimited firm participation, the number of firms (n) remains stable even as the number of games (t) approaches zero. This stability stems from the fact that in a Nash equilibrium, no individual firm has an incentive to alter its strategy, irrespective of the number of games played.

However, when the ratio of population density (s) to the cost of entry per firm (f) trends towards positive infinity (s/f → ∞), the number of firms (n) will surge. A higher population density implies a larger customer base for each firm, making market entry more lucrative. Furthermore, as the cost of entry per firm diminishes relative to the population density, it becomes simpler and more profitable for new firms to enter the market, ultimately driving an increase in the total number of firms (n).