Colonel Blotto Games with Two Battlefields

35 Pages Posted: 11 Feb 2019

See all articles by Dong Liang

Dong Liang

Tsinghua University

Yunlong Wang

Chinese Academy of Sciences (CAS) - University of Chinese Academy of Sciences

Zhigang Cao

Beijing Jiaotong University - School of Economics and Management

Xiaoguang Yang

Chinese Academy of Sciences (CAS)

Date Written: January 18, 2019

Abstract

The Colonel Blotto Game is one of the most classical zero-sum games, with diverse applications in wars, auctions, political elections and anti-terrorists etc. We consider the two-battlefield Colonel Blotto Game, a basic case that has not been completely understood yet. We study three variant scenarios where at least one player's resources is indivisible, and compare them with the benchmark scenario where the resources of both players are divisible. We present the equilibrium values for all three scenarios, and provide a complete equilibrium characterization for the scenario where both players' resources are indivisible. Our main finding is that, more or less surprisingly, the difference between divisible and indivisible resources generally has no effect on players' equilibrium values. In some special cases, however, the larger continuous strategy space when resources are divisible does bring the corresponding player a higher equilibrium value than when resources are indivisible, and this effect is more significant for the stronger player who possesses more resources than for the weaker player.

Keywords: Allocation Game, Colonel Blotto Game, Nash Equilibrium

JEL Classification: C72

Suggested Citation

Liang, Dong and Wang, Yunlong and Cao, Zhigang and Yang, Xiaoguang, Colonel Blotto Games with Two Battlefields (January 18, 2019). Available at SSRN: https://ssrn.com/abstract=3318291 or http://dx.doi.org/10.2139/ssrn.3318291

Dong Liang

Tsinghua University ( email )

Beijing, 100084
China

Yunlong Wang

Chinese Academy of Sciences (CAS) - University of Chinese Academy of Sciences ( email )

Building 7, NO. 80 Zhongguancun Road
Beijing, Beijing 100190
China

Zhigang Cao (Contact Author)

Beijing Jiaotong University - School of Economics and Management ( email )

China

Xiaoguang Yang

Chinese Academy of Sciences (CAS) ( email )

52 Sanlihe Rd.
Datun Road, Anwai
Beijing, Xicheng District 100864
China

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