Groupoidal 2-quasi-categories and homotopy 2-types

We define a notion of groupoidal 2-quasi-categories and show that they are the fibrant objects of a model structure on the category of ${\mathrm{\Theta }}_2$-sets. We show that this model category is Quillen equivalent to the Kan-Quillen model category of simplicial sets and that 2-truncated groupoidal 2-quasi-categories are models for homotopy 2-types.