In this paper, we study two game models of rent-seeking competition under two behavior rules by use of difference equation, one is a competition game model between two myopic rent-seekers with bounded rationality, the other is an evolution game model between the myopic rent-seeker, who can make choice of its behavior rule, and Nash rent-seeker with complete rationality, and then give the Nash equilibrium conclusion and its stability. The conclusion shows that under certain condition the myopic rent-seeker will trend to Nash equilibrium after repeated games. The game model selecting behavior rule shows that the simple myopic rule can?t be washed out by complicated Nash rule, and instead the rent-seekers will select myopic rule, under certain condition whose rent-seeking input x_t* will trend to Nash equilibrium input gradually.