We consider two agents interacting under the RSP-game. First, we analyse the case of perfect memory and equal adaptation rates: both agents keep track of the information about all past events and use it equally to change their future actions. The game state space is a 4-dimensional manifold corresponding to the product of two 2-dimensional simplices. We prove the existence on that manifold of a heteroclinic network connecting the 9 equilibria that correspond to the different possible plays (pairs of actions). The analysis of the discretization of the flow in the neighbourhood of the heteroclinic network reveals switching dynamics: every path on the network is followed by a trajectory for the dynamics of the play. Moreover, depending on initial conditions and the reward or penalty for ties, there is a preference for a particular sequence of plays. This relates to the relative asymptotic stability of the heteroclinic cycles in the network. We then analyse the consequences for the dynamics of the game of different adaptation rates. The main conclusion is that the above dynamics is preserved with an increase in the sequences of play where the agent with higher adaptation rate wins more often. Finally, we apply the RSP-game to economic's reality. We use the adaptation rate as a proxy for an economic agent that has more information about the market, and so is able to better respond to the different