A Threshold‐Price Approach to Oligopolistic Competition: A Resolution to the Bertrand Paradox

ABSTRACT

In homogeneous‐product markets, changing a price does more than alter a firm's profit margin: it may also determine which competitors can profitably remain active. This paper develops a new static theory of price competition based on this observation. We first establish that, under homogeneous products, unlimited production capacity, and consumer indifference across firms charging the same price, matching a profitable rival price weakly dominates remaining above it (Matching Dominance). Consequently, firms recognize that every feasible price simultaneously determines the corresponding market structure and solve a single optimization problem in which prices and market structure are jointly determined. The solution yields firm‐specific threshold prices that balance operating margins against the profitability of alternative market structures. We then show that competition selects the lowest threshold price as the Nash equilibrium of the game (Competitive Selection). Unlike the classical Bertrand model, equilibrium prices may exceed the relevant competitive benchmark—the common marginal cost under cost symmetry, or the marginal cost of the next most efficient rival under cost asymmetry—without relying on product differentiation, capacity constraints, repeated interaction, or collusion. The conventional Bertrand outcome nevertheless arises as a special case when the exclusion threshold is itself the firm's optimal threshold. The framework characterizes how demand and production costs jointly determine threshold prices and endogenous market structures, and explains how continuous changes in economic fundamentals may generate discrete changes in industry concentration. It also provides a different perspective on market power and merger effects by focusing on the firms capable of determining equilibrium prices rather than on market concentration alone.