In this study, we explore interactions between cancer cells by using the hawk–dove game. We analyze the heterogeneity of tumors by considering games with populations composed of 2 or 3 types of cell. We determine what strategies are evolutionarily stable in the 2-type and 3-type population games and what the corresponding expected payoffs are. Our results show that the payoff of the best-off cell in the 2-type population game is higher than that of the best-off cell in the 3-type population game. When these mathematical findings are transferred to the field of oncology they suggest that a tumor with low intratumor heterogeneity pursues a more aggressive course than one with high intratumor heterogeneity. Some histological and genomic data on clear cell renal cell carcinomas is consistent with these results. We underline the importance of identifying intratumor heterogeneity in routine practice and suggest that therapeutic strategies that preserve heterogeneity may be promising as they may slow down cancer growth.