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Two theoretical approaches appropriate for two-dimensional plasma photonic crystals reveal dispersions of propagating waves including photonic (electromagnetic) band gaps and multiflatbands. A modified plane-wave expansion method yields dispersions of collisional periodical plasmas, and the complex-value solution of a wave equation by a finite difference method enables us to obtain dispersions with structure effects in an individual microplasma. Periodical plasma arrays form band gaps as well as normal photonic crystals, and multiflatbands are present below the electron plasma frequency in the transverse electric field mode. Electron elastic collisions lower the top frequency of the multiflatbands but have little effect on band gap properties. The spatial gradient of the local dielectric constant resulting from an electron density profile widens the frequency region of the multiflatbands, as demonstrated by the change of surface wave distributions. Propagation properties described in dispersions including band gaps and flatbands agree with experimental observations of microplasma arrays.