As in many countries, Ireland’s incoming governments needs to win a vote of investiture in the lower chamber of the Oireachtas in order to take office. The process is formally a sequential game, with the chamber first electing a prime minister who later returns to the chamber to seek the support for her choices of cabinet and sub-cabinet ministerial appointments. This paper investigates the theoretical consequences of this system design, playing particular account to the formal and informal institutional structures that have developed since the foundation of the state. We then assess the investiture game using examples from recent rounds of government formation.