Gemini surfactants are a relatively new type of surface active material, characterized by multiple hydrophilic head groups. The phase behavior of a Gemini surfactant lattice model is studied by Monte Carlo simulations and quasichemical (QC) calculations. The predictions of these methods are in excellent agreement, justifying use of the analytical QC theory. The dependence on temperature, surfactant solubility, surfactant rigidity, and oil chain length of the global phase behavior of ternary mixtures of Gemini surfactant, oil, and water is investigated. Three-phase equilibrium exists only at low temperatures, with a transition to two-phase equilibrium as temperature is increased. Surfactants with moderate solubilities (i.e., those which do not have a strong preference for either solvent) exhibit three-phase equilibrium at low temperatures, while surfactants with extreme solubility preferences yield two-phase equilibrium only. When a flexible surfactant exhibits three-phase equilibrium, imposing rigidity promotes a transition from three- to two-phase equilibrium. Increasing molecular size of the hydrophobic solvent (oil) causes a transition from two- to three-phase equilibrium, and finally back to two-phase equilibrium, but with reversed relative surfactant solubility in the oil and water phases.