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The paper considers the interaction between regions during the implementation of a reform, on regional development through a discrete dynamical system based on replicator dynamics. The existence and stability of equilibria of this system are studied. The authors show that the parameter of the local prosperity may change the stability of equilibrium and cause a structure to behave chaotically. For the low values of this parameter the game has a stable Nash equilibrium. Increasing these values, the Nash equilibrium becomes unstable, through period-doubling bifurcation. The complex dynamics, bifurcations and chaos are displayed by computing numerically Lyapunov numbers, sensitive dependence on initial conditions and the box dimension.