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In this paper we are concerned with a class of mathematical problems that arise when modeling dynamic competition among conflicting agents may reach a dynamic equilibrium. We call this class of problems differential variational inequalities. We present a numerical method to solve differential variational inequalities, so-called the fixed point algorithm very briefly. We are further interested in the application of models belonging to this class of problems to the study of problems appearing in service management. As an example, we introduce a dynamic pricing model in service providers' competition.