To Deter or Not to Deter

Market demand is $P = 100 - Q$, where $Q$ is total quantity, and producing costs nothing. An incumbent first commits to a quantity $q_1 \ge 0$ (any real number). A potential entrant observes $q_1$ and then decides whether to enter. Entering costs a fixed amount of $49$, after which the entrant chooses his own quantity $q_2$ and the two firms sell at the resulting price. An entrant who is indifferent between entering and staying out stays out. The incumbent maximises his own profit and both are rational. What is the incumbent's profit in the subgame-perfect equilibrium?

• combinations
• nash equilibrium
• oligopoly

Source: Entry deterrence by commitment, after Spence (1977) and Dixit (1980), in a linear-demand Cournot setting. Statement written for AxiomIQ.