15.6 Entry Game with Withdrawal
In the text, we considered a sequential-move game which an entrant was considering entering an
industry in competition with an incumbent firm (Figure 15.1). Consider now that the entrant, if
fought, has the possibility of withdrawing from the industry (at a loss of 1 for the entrant and a
gain of 8 for the incumbent), or staying (at a loss of 5 for each player). What is the equilibrium of
this game? Discuss if the entrant is better off with or without the ability to withdraw.
Answer:
In the sequential-move game illustrated in Figure 15.1, an entrant is deciding whether to enter an
industry in competition with an incumbent firm.
The entrant would not enter in this case.
If he were to enter his only options (if fought) would be a loss of 1 or a loss of 5. Meanwhile, the
incumbent firm would certainly fight because there is a gain of 8, a favorable outcome over a loss of
5.
Knowing this outcome, the entrant would not enter and choose a profit of $0 over a loss of any
amount, making the equilibrium outcome (0,10)
The entrant is better off without the option to withdrawal. If you recall from the text, one of the
available options before was in/accommodate with a gain of 5. With the ability to withdrawal, the
scenarios all lead to a loss.
Entrant
Out
In
0, 10
Incumbent
Fight
In the text, we considered a sequential-move game which an entrant was considering entering an
industry in competition with an incumbent firm (Figure 15.1). Consider now that the entrant, if
fought, has the possibility of withdrawing from the industry (at a loss of 1 for the entrant and a
gain of 8 for the incumbent), or staying (at a loss of 5 for each player). What is the equilibrium of
this game? Discuss if the entrant is better off with or without the ability to withdraw.
Answer:
In the sequential-move game illustrated in Figure 15.1, an entrant is deciding whether to enter an
industry in competition with an incumbent firm.
The entrant would not enter in this case.
If he were to enter his only options (if fought) would be a loss of 1 or a loss of 5. Meanwhile, the
incumbent firm would certainly fight because there is a gain of 8, a favorable outcome over a loss of
5.
Knowing this outcome, the entrant would not enter and choose a profit of $0 over a loss of any
amount, making the equilibrium outcome (0,10)
The entrant is better off without the option to withdrawal. If you recall from the text, one of the
available options before was in/accommodate with a gain of 5. With the ability to withdrawal, the
scenarios all lead to a loss.
Entrant
Out
In
0, 10
Incumbent
Fight
