As it is known the values of different states in parity games (deterministic parity games, or stochastic perfect information parity games or concurrent parity games) can be expressed by formulas of µ-calculusa fixed point calculus alternating the greatest and the least fixed points of monotone mappings on complete lattices. In this paper we examine concurrent priority games that generalize parity games and we relate the value of such games to a new form of fixed point calculus -the nearest fixed point calculus.