The two-user linear deterministic interference channel (LD-IC) with feedback is studied under the assumption that each transmitter aims to selfishly maximize its individual achievable rate by tuning its own transmit configuration. More specifically, each transmitter autonomously tunes parameters such as the number of information bits per block, block length, codebook and encoding/decoding functions. To this end, the Nash equilibrium (NE) region of the LD-IC with feedback is fully characterized. The main observations presented in this paper are: (i) The NE region with feedback is strictly larger than the NE region with no feedback. Moreover, all the new rate pairs achieved with feedback are either strictly Pareto or weakly Pareto optimal. (ii) The use of feedback allows the achievability of all Pareto optimal rate pairs of the capacity region of the LD-IC with feedback.