100 Horsemen and the empty city: A game theoretic examination of deception in Chinese military legend
| Published date | 01 March 2011 |
| Author | Christopher Cotton, Chang Liu |
| DOI | 10.1177/0022343310396265 |
| Date | 01 March 2011 |
100 Horsemen and the empty city: A game
theoretic examination of deception in
Chinese military legend
Christopher Cotton
Department of Economics, University of Miami
Chang Liu
Department of Finance, Georgia Institute of Technology
Abstract
We present game theoretic models of two of the most famous military bluffs from history. These include the legend
of Li Guang and his 100 horsemen (144 BC), and the legend of Zhuge Liang and the Empty City (228 AD). In both
legends, the military commander faces a much stronger opposing army, but instead of ordering his men to retreat, he
orders them to act in a manner consistent with baiting the enemy into an ambush. The stronger opposing army,
uncertain whether it is facing a weak opponent or an ambush, then decides to flee and avoid battle. Military scholars
refer to both stories to illustrate the importance of deception in warfare, often highlighting the creativity of the
generals’ strategies. We model both situations as signaling games in which the opponent is uncertain whether
the general is weak (i.e. has few soldiers) or strong (i.e. has a larger army waiting to ambush his opponent if they
engage in combat). We then derive the unique Perfect Bayesian Equilibrium of the games. When the probability
of a weak general is high enough, the equilibrium involves mixed strategies, with weak generals sometimes fleeing
and sometimes bluffing about their strength. The equilibrium always involves the generals and their opponents
acting as they did in the historical examples with at least a positive probability. When the probability of a weak
general is lower (which is reasonable given the reputations of Li Guang and Zhuge Liang), then the unique
equilibrium always involves bluffing by the general and retreat by his opponent.
Keywords
bluffing, deception, deterrence, game theory, signaling game
‘All warfare is based on deception.’
‘The enemy cannot engage me in combat:
I distract him, in a different direction.’
Sun-tzu, The Art of War
Introduction
War has always presented the opportunity for deception.
Some examples, such as the Trojan Horse used by the
Greeks in the 12th or 11th century BC and the Allied
misinformation effort during World War II, were direct
attempts to trick one’s enemy into lowering its guard or
exposing vulnerabilities. In other examples, deception
(by bluffing about one’s own strength) allowed military
commanders to avoid conflict with a more powerful
enemy. We are concerned with this later category of
deception, the military bluff.
This article presents simple game-theoretic models of
two of the most famous examples of military bluffs from
all of history. These include the legend of Li Guang and
his 100 horsemen during the Han Dynasty (144 BC)
and the legend of Zhuge Liang and the Empty City dur-
ing the Three Kingdom period of China (228 AD). In
Corresponding author:
cotton@business.miami.edu
Journal of Peace Research
48(2) 217–223
ªThe Author(s) 2011
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DOI: 10.1177/0022343310396265
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