Even-split Strategy in Sequential Colonel Blotto Games

50 Pages Posted: 25 Oct 2021 Last revised: 20 Jun 2023

See all articles by Xinmi Li

Xinmi Li

Tsinghua University - Department of Physics

Jie Zheng

Shandong University - Center for Economic Research

Multiple version iconThere are 2 versions of this paper

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

Li, Xinmi and Zheng, Jie, Even-split Strategy in Sequential Colonel Blotto Games (October 22, 2021). Available at SSRN: https://ssrn.com/abstract=3947995 or http://dx.doi.org/10.2139/ssrn.3947995

Xinmi Li

Tsinghua University - Department of Physics ( email )

Beijing, Beijing 100084
China

Jie Zheng (Contact Author)

Shandong University - Center for Economic Research ( email )

Jinan, Shandong 250100
China

HOME PAGE: http://https://meetecon.com/jie/

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