Even-split Strategy in Sequential Colonel Blotto Games
50 Pages Posted: 25 Oct 2021 Last revised: 20 Jun 2023
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Even-split Strategy in Sequential Colonel Blotto Games
Even-Split Strategy in Sequential Colonel Blotto Games
Date Written: October 22, 2021
Abstract
We propose a multi-contestant sequential Colonel Blotto Game with ``more wins, higher reward'' prizes, showing that in the equilibrium, all the contestants adopt the even-split strategy, paying an equal amount of efforts regardless of history or score. The results reveal the relationship between prize setting and equilibrium behavior in a contest, showing that weakly monotonic prize functions correspond to the existence of equilibrium and that strictly monotonic prize functions correspond to the uniqueness of equilibrium. We further prove that when the game is constant-sum, the equilibrium exhibits quasi even-split features. We propose ``Decreasing Success Rate Condition'' for the contest success function, enlarging our conclusions to a large class of scenarios. Our work provides a better understanding of the monotonic prize setup as well as the applicability of the even-split strategy in Colonel Blotto games, where equilibrium strategies (especially for multi-contestant scenarios) are usually complicated.
Keywords: Even-split strategy, Colonel Blotto Game, Prize Function, Sequential contest, Multiple battles
JEL Classification: C72, D72, D74
Suggested Citation: Suggested Citation