An Achievement Game on a Cycle

Consider the following game played by Maker and Breaker on the vertices of the cycle $C_{n}$, with first move given to Breaker. The aim of Maker is to maximise the number of adjacent pairs of vertices that are both claimed by her, and the aim of Breaker is to minimise this number. The aim of this paper is to find this number exactly for all $n$ when both players play optimally, answering a related question of Dowden, Kang, Mikalacki and Stojakovic.