For many economic problems facing large-scale strategic interactions between large groups and when strategic interactions occur participants may cooperate to seek higher benefits. Studying the existence of cooperative equilibrium in population games provides a unified analytical framework for these situations. In this paper we first introduced the model of population games and the definition of cooperative equilibrium in these games. Secondly under the condition that the population state function was pseudo continuous an auxiliary preference mapping was constructed. With the aid of the property of pseudo continuity an existence theorem for cooperative equilibrium of population games was established and an example was given to illustrate its advantages. When solving cooperative equilibrium in population games there may be deviations in the collection of original data model data may be disturbed and the approximate solution sequence may not be feasible. Studying the well-posedness of cooperative equilibriums of population games provides a theoretical basis for numerical calculation. The concepts of Hadamard well-posedness and Levitin Polyak well-posedness of cooperative equilibrium of population games were introduced. By the semicontinuity and compactness of cooperative equilibrium mappings sufficient conditions of Hadamard well-posedness were established. At last by the pseudo-continuity of the population state function sufficient conditions of Levitin-Polyak well-posedness were established.