When parties bargain about government formation, they do not do so in an institutional vacuum, rather some parties are endowed with greater institutional resources than others. This paper focuses on the parties of presidents in parliamentary and semi-presidential democracies. Many presidents in these political systems have some influence on assembly dissolution, which enables them to shape government performance and survival. Yet, whether these powers advantage presidential parties in bargaining about government formation remains remarkably poorly understood. To address this gap, we develop a theory of government formation in the shadow of presidential assembly dissolution powers. The parties of presidents who can control assembly dissolution, we argue, are more likely to secure their participation in government than other parties because they enjoy advantages in (i) controlling the bargaining process about coalition formation and (ii) in building a reputation as effective and desirable coalition partners. Our tests of these expectations, using data on 625 government formation opportunities and 428,095 potential coalitions, reveal that the parties of presidents with discretion to dissolve parliament have significantly higher coalition inclusion probabilities than their peers who lack access to this institutional source of bargaining power.