RDP 2009-02: Competition Between Payment Systems Equation (1)

\begin{array}{l} Ω_{i}^{c} = Ω_{i, ~ j}^{c} \cup Ω_{i, j}^{c} & , & Ω_{j}^{c} = Ω_{j, ~ i}^{c} \cup Ω_{i, j}^{c} \end{array}