Consider the above game (question 1) but suppose that the decision to enter
by the competitor is reversible in the following sense: after it has entered,
and after the monopolist has chosen to accommodate or fight, the competitor can
choose to remain in the industry (and receive either the $5M profits or $5M loss)
or to exit. Suppose that exiting at this point results in a loss to the entrant
of $1M, and the monopolist regains its $10M profit.
The new game is represented by the following tree:
What is the rollback equilibrium of the above game?
The intuition here is that, by not being able to commit to entry, the competitor will be worse off.
Start by working at the end:
- If the monopolist fights entry, the competitor will exit (out3) since losing $1M is better than losing $5M.
- If the monopolist accommodates, the competitor will stay in the industry (in2), earning $5M.
- Rolling back to the monopolist's decision: accommodating leads to the competitor staying in, and each earning $5M, while
fighting leads to the entrant leaving and the monopolist reclaiming $10M, so the monopolist fights.
- In the first period, the competitor now recognizes that entry leads to eventual withdrawl and losses of $1M,
so the entrant stays out (out1).