First, Taiwan liberalizes and China does not coerce, thus revealing China to be economics-first.
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).
This, however, is a politics-first Taiwan's least preferred outcome, for, if it perceives that it is likely to be coerced by China, it would rather restrict trade (01) than have a politics-first China coerce and then punish it (05), but it would prefer to fight and lose on the political issue (05) than to acquiesce willingly when coerced (03).
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.
In one, Taiwan will restrict trade only if it is politics-first; in the other, China will coerce only if it is politics-first.
If a politics-first Taiwan believes that China is unlikely to coerce, it will risk trading with China.
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.
Taiwan first chooses whether to trade or not, after which China decides whether to exploit the trade relationship and coerce Taiwan.