Bacterial infections are the second largest cause of mortality in shrimp hatcheries. Among them, bacteria from the genus Vibrio constitute a major threat. As the use of antibiotics may be ineffective and banned from the food sector, alternatives are required. Historically, phage therapy, which is the use of bacteriophages, is thought to be a promising option to fight against bacterial infections. However, as for antibiotics, resistance can be rapidly developed. Since the emergence of resistance is highly undesirable, a formal characterization of the dynamics of its acquisition is mandatory. Here, we explored the co-evolutionary dynamics of resistance between the bacteria Vibrio sp. CV1 and the phages V1G, V1P1, and V1P2. Single-phage treatments as well as a cocktail composed of the three phages were considered. We found that in the presence of a single phage, bacteria rapidly evolved resistance, and the phages decreased their infectivity, suggesting that monotherapy may be an inefficient treatment to fight against Vibrio infections in shrimp hatcheries. On the contrary, the use of a phage cocktail considerably delayed the evolution of resistance and sustained phage infectivity for periods in which shrimp larvae are most susceptible to bacterial infections, suggesting the simultaneous use of multiple phages as a serious strategy for the control of vibriosis. These findings are very promising in terms of their consequences to different industrial and medical scenarios where bacterial infections are present.