  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 cells. We determine what
strategies are evolutionarily stable in the 2-type and 3-type population games
and the corresponding expected payoffs. 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. Translating these mathematical findings to
the field of oncology suggests that a branching-type tumor pursues a less
aggressive course than a punctuated-type one. Some histological and genomic
data of clear cell renal cell carcinomas are consistent with these results.
