2 Fases
Fase 1: Will   E1 enter the market?
E1 enters   reaction
  * Accomodate: I: 50 mio $, E1: 10 mio $
  * Fight: I: -40 mio, E1: -40 mio
E1 does not enter the markte   I has a monopoly in the European market: I: 500 mio

Fase 2: Will E2 enter the market?

E2 enters the market reaction: independent of the results from the European market
  * Accomodate: I: 50 mio, E1: 10 mio
  * Fight: I: -40 mio, E1: -40 mio
E2 does not enter the market   I has a monopoly in the American   market : I: 500 mio

4. Further explanation of the scheme.

The benefit of the Incumbent in each situation.
Monopoly in both markets: 1,000 = 500 + 500
Monopoly in the first market, accommodate in the second one:550= 500 + 50
Monopoly in the First market, fight in the second one: 460 = 500 - 40
Both markets accommodate: 100 = 50 + 50
  Accommodate in the First market,   fight in the second one: 10 = 50 - 40
Both markets fight: -80 = -40 – 40

Benefit for   E1 and E2 in each situation:
Accommodate: 10
No enter: 0
Fight: - 40

We can conclude that E2 as -> and E1 as well will enter the market. If we use the technique of backward induction, we can see this easily   considering that both parties will react on a rational basis.
If E2 enters the market than the Incumbent can only maximalise -> maximise his profit by using an accommodate strategy.   The benefit for the Incumbent will than be 50 million $. On the other hand, if the Incumbent had used the fight strategy, the Incumbent would have   had a loss of   -40 million $.
Knowing that the Incumbent will use the accommodate strategy, E2 will enter the market while this decision leads to a benefit of 10 million $.