Even-Split Strategy in Sequential Colonel Blotto Games

We generalize Klumpp, Konrad and Solomon’s model (KKS Model) to multi-contestant sequential Colonel Blotto Games with prize functions where any contestant’s prizes only depend on this contestant’s own number of winning rounds. We show that with weakly monotonic prize functions and CSFs satisfying decreasing success rate condition, there exists a pure strategy Subgame Perfect Nash Equilibrium known as the even-split strategy profile. We also show that with strictly monotonic prize functions and Tullock CSFs with 0 < r ≤ 1, even-split strategy profile is the unique pure strategy Subgame Perfect Nash Equilibrium. We explore the uniqueness of pure strategy Subgame Perfect Nash Equilibrium before any contestant reaches a settled prize when the game is constant-sum. Our work provides a better understanding on the applicability of the simple even-split strategy in Colonel Blotto games where equilibrium strategies (especially for multi-contestant scenarios) are usually complicated