# 100 Horsemen and the empty city: A game theoretic examination of deception in Chinese military legend

## Author Info

• 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.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://jpr.sagepub.com/content/48/2/217.abstractFileFormat:text/html

## Bibliographic Info

Article provided by Peace Research Institute Oslo in its journal Journal of Peace Research.

Volume (Year): 48 (2011)
Issue (Month): 2 (March)
Pages: 217-223

as in new window
Handle: RePEc:sae:joupea:v:48:y:2011:i:2:p:217-223

Contact details of provider:
Web page: http://www.prio.no/

## Related research

Keywords: bluffing; deception; deterrence; game theory; signaling game;

## References

No references listed on IDEAS
You can help add them by filling out this form.

## Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

## Corrections

When requesting a correction, please mention this item's handle: RePEc:sae:joupea:v:48:y:2011:i:2:p:217-223. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (SAGE Publications).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.