This paper contributes to a fast growing literature which introduces game theory in the analysis of real option investments in a competitive setting. Specifically, in this paper we focus on the issue of market incompleteness and the practical difficulty of finding a twin security in order to apply real option analysis to real estate projects. We show that an alternative to the standard replicating portfolio approach comes from the use of game theory and mixed strategies. We present some theoretical results and we then present a numerical exercise using the information set obtained on a real estate development in South London. We compare our results to previous analysis based on the standard real options framework.