Variational inequalities and Dynkin games for Markov processes associated with semi-Dirichlet forms

We consider a relation between certain variational inequalities for semi-Dirichlet forms and Dynkin games for the Markov processes associated with these semi-Dirichlet forms. Dynkin games are the optimal stopping games introduced as the models of zero-sum games by two players. We prove that the solution to the variational inequality with two obstacles coincides with the equilibrium price of the Dynkin game. Moreover, we obtain the saddle point of the game.