The main neurotransmitters in the brain—dopamine, γ-aminobutyric acid (GABA), glutamate, and opioids—are recognized to be the most important for the regulation of aggression and addiction. The aim of this work was to study differentially expressed genes (DEGs) in the main reward-related brain regions, including the ventral tegmental area (VTA), dorsal striatum (STR), ventral striatum (nucleus accumbens, NAcc), prefrontal cortex (PFC), and midbrain raphe nuclei (MRNs), in male mice with 20-day positive fighting experience in daily agonistic interactions. Expression of opioidergic, catecholaminergic, glutamatergic, and GABAergic genes was analyzed to confirm or refute the influence of repeated positive fighting experience on the development of “addiction-like” signs shown in our previous studies. High-throughput RNA sequencing was performed to identify differentially expressed genes in the brain regions of chronically aggressive mice. In the aggressive mice, upregulation of opioidergic genes was shown (Oprk1 in VTA, Pdyn in NAcc, Penk in PFC, and Oprd1 in MRNs and PFC), as was downregulation of genes Opcml and Oprk1 in STR and Pomc in VTA and NAcc. Upregulation of catecholaminergic genes in VTA (Ddc and Slc6a2) and in NAcc (Th and Drd2) and downregulation of some differentially expressed genes in MRNs (Th, Ddc, Dbh, Drd2, Slc18a2, and Sncg) and in VTA (Adra2c, Sncg, and Sncb) were also documented. The expression of GABAergic and glutamatergic genes that participate in drug addiction changed in all brain regions. According to literature data, the proteins encoded by genes Drd2, Oprk1, Oprd1, Pdyn, Penk, and Pomc are directly involved in drug addiction in humans. Thus, our results confirm our earlier claim about the formation of addiction-like signs following repeated positive fighting experience in mice, as shown previously in our biobehavioral studies.