The paper investigates the impacts of random household participations in a transactive open energy market (TOEM) in residential microgrids. The strategic decision making procedures of different households with diverse renewable energy portfolios are analyzed by formulating a non-cooperative game for neighborhood energy transactions. In the proposed TOEM, houses with energy excesses initiate the energy trading process while houses with energy shortages act as followers to meet their demands by purchasing energy at competitive prices. Moreover, there are flexibilities for participants for energy transactions in the TOEM, i.e., individual households are free either to participate or not. The impacts of random participations of different households for energy trading in residential microgrids with the TOEM are analyzed in this paper in terms of utilities of sellers and buyers. Several case studies are conducted using residential house level data for energy generations and consumptions by considering Australian scenarios in order to show how the proposed energy trading game achieves cost savings as well as how random participations of different households affect individual rationalities.