To bluff, or not to bluff? That is the question

May 23, 2011

Economist Christopher Cotton from the University of Miami (UM), uses game theory to explore two of the most famous military bluffs in history. The findings are published in the current issue of the Journal of Peace Research.

The study is one of the first to use game theory to assess the Chinese military legends of Li Guang and his 100 horsemen (144 BC), and Zhuge Liang and the Empty City (228 AD). The stories appear in modern day translations of Sun Tzu's fundamental book on military strategy "The Art of " to explain what is meant by deception.

Both legends involve a military that faces a much stronger opposing force. Instead of retreating, the commander of the weaker army orders his men to act as if they were preparing to bait the enemy into an ambush. The stronger army unsure of whether they are facing a weak army or an ambush decides to retreat and evade combat. In other words, the stronger opponent falls for the bluff.

The legends have been used for the past two-thousand years to illustrate military deception. What is new about this study is that it explains why their strategies were successful, says Christopher Cotton assistant professor in the Department of Economics at the UM School of Business Administration, and principal investigator of the study.

"With this study we gain insight about these legends that nobody had before. For example, bluffing doesn't work because it convinces an opponent that you are strong. It works because your opponent can't tell whether you are really strong, or whether you are only acting strong. This uncertainty is all that's needed," says Cotton. "The generals chose strategies that left their opponents uncertain, and this uncertainty was enough to avoid confrontation."

Game theory is a field of mathematics that started to gain ground in the 1940's. It provides a way to model strategic situations, in which the success of an individual's choices depends on the choices of his opponent(s), explains Cotton. "The theory basically says that what I want to do depends on what you do, and what you want to do depends on what I'm doing. We ask what strategy people should follow in such situations."

Cotton modeled the military legends as signaling games, where one player has all the information about the situation and the other does not. Equilibrium is achieved when the participants or "players" adopt strategies or "actions" that bring about the best outcome, or "payoff." These optimal strategies can be described as a situation where "what I'm doing should be consistent with what you have chosen to do, and given what you have chosen to do, I should not want to go do something else," says Cotton. In the case of the military legends, the researchers found that bluffing arose naturally as the optimal strategy in each situation.

The study says that "when the probability of a weak general is high, the equilibrium involves mix strategies, with weak general sometimes fleeing and sometimes bluffing….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."

What the researchers are showing is that these famous generals were acting according to optimal strategy, as defined by modern-day strategic reasoning. "They are playing in a way that is consistent to what we would recommend them doing today, even though they were doing it two-thousand years before any of the modern tools for strategy were developed," Cotton says.

The paper is titled "100 Horsemen and the empty city: A game theoretic examination of deception in Chinese military legend," The co-author is Chang Liu, (PhD Student) in the Department of Finance, at the Georgia Institute of Technology. The study adds to the literature in which is used to gain insight of historic events, it increases understanding on the role of deception in military and defense strategies and explores the logic used by experienced professionals, who unknowingly play strategic games to create innovative solutions to everyday problems.

Explore further: A two generation lens: Current state policies fail to support families with young children

add to favorites email to friend print save as pdf

Related Stories

Economic game theory studied by Haas professor

Jan 06, 2011

You are running a political campaign with limited resources. How should you spend your money to beat your rival? You are a military commander trying to win a battle. How should you deploy your soldiers to gain an edge? You ...

Recommended for you

Scholar tracks the changing world of gay sexuality

Sep 19, 2014

With same-sex marriage now legalized in 19 states and laws making it impossible to ban homosexuals from serving in the military, gay, lesbian and bisexual people are now enjoying more freedoms and rights than ever before.

User comments : 11

Adjust slider to filter visible comments by rank

Display comments: newest first

spectator
not rated yet May 23, 2011
These optimal strategies can be described as a situation where "what I'm doing should be consistent with what you have chosen to do, and given what you have chosen to do, I should not want to go do something else," says Cotton. In the case of the military legends, the researchers found that bluffing arose naturally as the optimal strategy in each situation.


Yall don't play much Real Time Strategy games do you?

Scouting and intelligence is actually more important than strategy itself. After all, you cannot make a decent strategy unless you know what your opponent is doing.

If all you can do is guess about what your opponent is doing, and especially if they have half decent intelligence on what you are doing, then you will inevitably build into a technology or maneuver which is hard countered by whatever the opponent is doing technologically or positionally.
spectator
not rated yet May 23, 2011
Anyway, it's not possible to scout too much in a Real Time Strategy game, nor is it possible to scout enough. No matter how much you scout, you want to scout more.

When watching replays of Starcraft 2 at the professional level, some of the biggest blunders are caused by one guy, for what ever reason, making a mis-understanding about what his opponent is doing, because he either scouted poorly, or interpreted what he saw incorrectly.

Statistically, in Starcraft and Starcraft 2, a marginal tech advantage beats a marginal numbers advantage around 9 times out of 10.

However, a scouting advantage beats a marginal tech advantage probably around 70% of the time. Knowing what your opponent is doing is that important.
antialias
not rated yet May 23, 2011
Scouting and intelligence is actually more important than strategy itself.

This goes for 'games' where you can scout. Most real life situations involve incomplete information for both sides (e.g. business decisions) or no information (e.g. poker - unless you know someone's tells)

What the researchers are showing is that these famous generals were acting according to optimal strategy,

The problem is that onece you knwo that your opponent will act according to an 'optimal' strategy you can usually devise a counter. In a way if you know how the choice of strategy is made that in itself will be information which can be used.

spectator
not rated yet May 23, 2011
The problem is that onece you knwo that your opponent will act according to an 'optimal' strategy you can usually devise a counter. In a way if you know how the choice of strategy is made that in itself will be information which can be used.


Optimal strategies take optimal counter measures into consideration.

Metagames evolve based on what technology is available. Some strategies are so good that it does not matter if your opponent knows about it ahead of time, they can't stop it anyway. In collectible card games, this usually results in banning one or more cards. In other games it results in rebalancing or rules changes.

An example of this is in Tic Tac Toe. If the first player uses optimal strategy, he is guaranteed to tie at worst. Whereas if the second player uses optimal strategy, he is still at a disadvantage in tempo, and can only win if the first player makes a mistake. Of course, this is a turn based game, so it's not the greatest example.
spectator
not rated yet May 23, 2011
Any turn 1 kill in a turn based game, such as a CCG like Magic: The Gathering, would be an uncounterable optimum strategy. It does not matter if your opponent knows your strategy, you win anyway. This eventually results in bans and rules changes.

Another example was in Starcraft, pre-version 1.07, the Zerg race had the "virtually uncounterable" 4th pool zergling rush. The game had to be patched to increase the build cost of the Spawning Pool tech structure to fix this imbalance.

In the real world, an uncounterable strategy or technology makes you the super power.

In practial terms, nothing in the real world is "truly" uncounterable, but some things are hard enough to counter as to be "virtually uncounterable". Rail guns and lasers, or some other means of having an absurd range advantage would be a good example of a "virtually uncounterable" technology, because the only way to counter it is to have better rail guns and lasers of your own. Even then, whoever attacks first wins..
ennui27
not rated yet May 23, 2011
Doesn't Eisenhower's use of Gen Patton fit in here somewhere. The German overflights showed a considerable accumulation of equipment, Patton was a known General - but it was not known there was a Potemkin army and George P. was not to be involved in the D Day activities.
hush1
not rated yet May 23, 2011
Doesn't Chaos Theory supersede all strategy? Regardless of information (flow)?
"...uncertainty is all that's needed" says Cotton.
Yes, indeed. As long as the value of uncertainty is positive, asserts Chaos Theory, the paths(or outcomes)become unpredictable.
Au-Pu
not rated yet May 24, 2011
What a waste of time energy and money.
The researchers are clearly not the brightest.
antialias
not rated yet May 24, 2011
Optimal strategies take optimal counter measures into consideration.

That's why most successfull (computer)games are based on a rock-paper-scissors approach where no single strategy is optimal.

In the real world, an uncounterable strategy or technology makes you the super power.

Not entirely. Technology that is ever more prevalent (ever easier to manufacture by individuals) and even a smidgeon of terrorism can - at the least - end in total distruction. While this is not a 'win' for terrorism it is certainly also not a 'win' for the technology favoring society.

This is something that games theory does not take sufficiently into account. Oftentimes a draw or a postponement is considered a 'winning situation' by one side (because of the hope/expectation taht a winning strategy will eventually develop in a dynamic environment where currently none is available)
ennui27
not rated yet May 24, 2011
"Technology that is ever more prevalent (ever easier to manufacture by individuals) and even a smidgeon of terrorism can - at the least - end in total distruction. While this is not a 'win' for terrorism it is certainly also not a 'win' for the technology favoring society."

Isn't that called asymmetrical warfare?
antialias
not rated yet May 24, 2011
Yes. It's a perfect example that being best/overly specialized (or overwhelmingly powerful) breeds its own kind of weakness.