If Taiwan chooses to liberalize trade, then China decides whether or not to coerce Taiwan.
Unlike the first two moves of the game, the moves following China's decision to coerce depend solely on each player's type.
The longer China takes to coerce Taiwan once trade has been liberalized, the more it signals that China is economics-first, in which case a politics-first Taiwan might be willing to sustain liberalized trade without fearing political vulnerability.
If China chose not to coerce, then eventually we would have to conclude that both China and Taiwan are economics-first, and economic interdependence would result in a new peaceful status quo.
If it did not believe Taiwan's politics-first reputation, it would try to coerce in an effort to achieve gains both from economic interdependence and on the sovereignty issue.
The extended-form version (Figure 2) shows that a politics-first China will always coerce and then punish if given the chance, but an economics-first China will never punish if Taiwan refuses to comply.
And, China will coerce always, even if it is economics-first.
Equation (2) implies that an economics-first China will coerce Taiwan when (a) it perceives that Taiwan is more likely to be economics-first (the value of p is high), (b) the utility derived from attaining political concessions from Taiwan outweighs China's gains from cross-strait trade (y1-y2 is high), and (c) China does not suffer a high cost if Taiwan chooses not to comply and China does not punish Taiwan (y2-y3 is low).
China's strategy remains unchanged from El; it will coerce, even if it is economics-first.
E3 is another separating equilibrium, because although Taiwan will liberalize trade even if it is politics-first, China will only coerce if it is politics-first.
Equation (5) implies that an economics-first China will not coerce and a politics-first China will coerce if (a) China perceives that Taiwan is more likely to be politics-first (p is low), (b) there is little gain from attaining a political concession from Taiwan (y1-y2 is low), and (c) China suffers a high cost if it chooses not to punish Taiwan when Taiwan does not comply.
First, Taiwan liberalizes and China does not coerce, thus revealing China to be economics-first.