Equilibrium in a two-sided market represented by network platforms on the plane and heterogeneous agents is investigated. The advocated approach is based on the duopoly model which implies a continuum of agents of limited size on each side of the market and examines the agents’ heterogeneous utility with the Hotelling specification. The exact values were found for the equilibrium in the case of duopoly in a two-sided market with two platforms on the plane. The dependence of the platforms’ benefits on network externalities was investigated. The problem of the optimal location of platforms in the market was considered.