A question for the game theorists

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07-01-2010
ddade

A question for the game theorists

I've never once seen an application of the min-max Theorem to a question of military strategy that left me with a warm-and-fuzzy feeling that what I had just taken the time to digest would ever be actually repeated by a commander. My problem is mixed strategies.

Mixed strategies, where a player's strategy is expressed as a vector of probabilities (c.f. pure strategies), are central to min-max Theory, but don't seem like they would be very satisfying to a commander as a solution. The problem is that the optimal strategy predicted by min-max is only "optimal" in the probabilitic sense, i.e. over many runs it will tend not to be outperformed by any other strategy, and that much only if the other player also applies his optimal strategy with a suitable chance mechanism.

But what about one-off interactions like the kind we often face in the real world? What good is a vector of probabilities as a "solution" when a commander must choose a course of action exactly once and it is still possible to select the absolute worst course of action for any one specific interaction? Is min-max Theory not a tool that is used in Military Strategy?
07-02-2010
MikeF

Quote:

Originally Posted by ddade

I've never once seen an application of the min-max Theorem to a question of military strategy that left me with a warm-and-fuzzy feeling that what I had just taken the time to digest would ever be actually repeated by a commander. My problem is mixed strategies.

Mixed strategies, where a player's strategy is expressed as a vector of probabilities (c.f. pure strategies), are central to min-max Theory, but don't seem like they would be very satisfying to a commander as a solution. The problem is that the optimal strategy predicted by min-max is only "optimal" in the probabilitic sense, i.e. over many runs it will tend not to be outperformed by any other strategy, and that much only if the other player also applies his optimal strategy with a suitable chance mechanism.

But what about one-off interactions like the kind we often face in the real world? What good is a vector of probabilities as a "solution" when a commander must choose a course of action exactly once and it is still possible to select the absolute worst course of action for any one specific interaction? Is min-max Theory not a tool that is used in Military Strategy?

Your dillemma is seen throughout social sciences when we try to apply fixed rules, boundaries, and parameters to an open, living system. For instance, in a 2 player min/max game, we assume perfect communication, rational actors, and fair play. In reality, that never happens.

I would suggest looking at Brinksmanship, First Strike games, and Evolutionary Stable Systems (ESS) for better application in the real world.
07-02-2010
ddade

Quote:

Originally Posted by MikeF

Your dillemma is seen throughout social sciences when we try to apply fixed rules, boundaries, and parameters to an open, living system. For instance, in a 2 player min/max game, we assume perfect communication, rational actors, and fair play. In reality, that never happens.

I would suggest looking at Brinksmanship, First Strike games, and Evolutionary Stable Systems (ESS) for better application in the real world.

Thanks for the reply MikeF.

Sure, I'm aware that the model is highly idealized, but the literature often cites the things you mentioned, like perfect knowledge and homo economicus. But I've never read anything that explicitly said that mixed strategies are not useful for figuring out what course of action one should take. I am wondering out loud why not. I'm willing to entertain the possibility that it's me that just doesn't understand something important point, but I don't see it and I'd like someone to point it out to me.

As for brinksmanship, I am currently enjoying Thomas C. Schelling's Arms and Influence. It's qualitative and not rigorous, but man, does it make intuitive sense. The idea that an opponent can threaten to obligate you to do something that you would rather not, is fascinating.

First Strike games and Evolutionary Stable Systems, I've never heard of. Can you please make a recommendation for each?

Thanks for the direction.
07-02-2010
MikeF

Quote:

Originally Posted by ddade

Thanks for the reply MikeF.

Sure, I'm aware that the model is highly idealized, but the literature often cites the things you mentioned, like perfect knowledge and homo economicus. But I've never read anything that explicitly said that mixed strategies are not useful for figuring out what course of action one should take. I am wondering out loud why not. I'm willing to entertain the possibility that it's me that just doesn't understand something important point, but I don't see it and I'd like someone to point it out to me.

As for brinksmanship, I am currently enjoying Thomas C. Schelling's Arms and Influence. It's qualitative and not rigorous, but man, does it make intuitive sense. The idea that an opponent can threaten to obligate you to do something that you would rather not, is fascinating.

First Strike games and Evolutionary Stable Systems, I've never heard of. Can you please make a recommendation for each?

Thanks for the direction.

I can't go too far in-depth b/c I would betray some of my own original work. I dissolved all the assumptions and redid the math.

First Strike- I'm on vacation so I'll give an analogy. Next week, I'll provide some text. Remember the game "Cross-pool" that we'd play during the summer at the pool- one person that was it in the deep end trying to tag others as they dove and swam from one side to the other? Statistically, the first person to go is never tagged out.

ESS- This will probably bore you to death, but this book fascinates me.

Evolution and the Theory of Games- John Maynard Smith.
07-02-2010
William F. Owen

Quote:

Originally Posted by ddade

Is min-max Theory not a tool that is used in Military Strategy?

Almost certainly not because in the real world, Strategy needs a policy, and as you perform your strategy you create costs which can alter the policy.

The best strategy teaching process I know of is fitting out a bathroom with a fixed budget and your wife's ideas as to what she "must have." this = The Policy. Your plan and budget is the Strategy. As you run out of money, your wife will alter the policy and/or increase the budget. As you encounter problems, (lack of plumbing skill, can't tile etc etc) the same will happen.
Strategy is actually simple - in theory. It is extremely "difficult" in practice.
07-02-2010
slapout9

The Original game of Risk. In the old game you not only set up armies around the world but......factories! why this was deleted from the game I don't know but it definitley showed the influence of money on real world wars and politics.
07-03-2010
ptamas

defensible decisions made in ignorance

This thread comes close to something that I'm worrying.
At the end of my undergrad I spent some time studying game theory.

I stopped studying it and went and did a MA in political philosophy when I figured that accumulated uncertainties overwhelmed predictive resolution long before I got to the point I would feel comfortable using the conclusions to support decision making.

These days I'm looking at decision making for interveners in failed and fragile states. At one end there are the COIN folks, which is why I'm on this board, and at the other you have the full spectrum of civvies. They are all trying to work in spaces that overwhelm just about any linear planning model you can think about while having to smile nice for bureaucracies that descend directly from a wet dream of bureaucratic rationality.

What notions are there out there, really, that are workable, again, really, for marrying off environments that overwhelm precisely the imaginary that makes it possible for bureaucracies to flow the money and resources needed to act in those environments?

I don't want to hear the 'more knowledge to inform decisions' argument. My assumption and observation is that decisions in these environments will be knowledge starved when they matter and knowledge-rich when they don't.

I'm looking for discussions of politically passable ways to make operationally responsible decisions when knowledge starved in overwhelmingly complex environments.

-peter
07-04-2010
Steve the Planner

You are on the right road

peter:

I, too, in grad school, played with predictive models, and their inherent limitations and inconsistencies with unbounded realities, unanticipated consequences, and real-life wicked problems.

I just finished a paper for a court case addressing the failures of economic models as a viable tool where certainty and precision are required. They are just not up to the task in many particular applications.

Quick" How many troops are required to take, hold and stabilize Marjah?

Not knowable, and whatever models were applied, did not work.

How many troops are required to take and hold Kandahar to "X" level of stability, with and without AWK? Another unknowable.

Does that mean that any of these objectives are not do-able? No. Does it mean that troop levels are not the critical variable? Yes.

So, the fun of war gaming is to test theories of war, not theories of societal structure and changes within an unstable society, fractured and post-conflict environment.

Better, perhaps, to identify and model the characteristics of a post-conflict fractured society, then test political/societal change theories based on careful delineation of the fractures, faults, parties and paths.

The troop-levl variables will probably fall out of that analysis.
07-04-2010
William F. Owen

Quote:

Originally Posted by ptamas

I don't want to hear the 'more knowledge to inform decisions' argument. My assumption and observation is that decisions in these environments will be knowledge starved when they matter and knowledge-rich when they don't.

There is a body of research that shows that more information does not actually create better decisions, and that even given correct information, decision makers go with what supports their plan, not with what would undermine it. We know how to avoid doing this, but we choose not to do it.

Quote:

I'm looking for discussions of politically passable ways to make operationally responsible decisions when knowledge starved in overwhelmingly complex environments.

If it is overwhelmingly complex then you simply do not understand it. You are doomed to fail out of ignorance. NO situation concerning human affairs is overwhelmingly complex. Saying so, just makes mistakes and inaction forgivable.
We know how to solve all the problems. We just choose not to, because we want to use the solution we want to use, (Protect the population, Governance, development) and not the ones known to work. It may be complex, but it always was, and we deal with it.
07-05-2010
Dayuhan

Quote:

Originally Posted by William F. Owen

We know how to solve all the problems. We just choose not to, because we want to use the solution we want to use, (Protect the population, Governance, development) and not the ones known to work.

I'm not at all sure that we do "know how to solve all the problems", or that there are solutions that are known to work in every situation, everywhere. The problems that arise when governments select goals that require more time or resources than they are willing to commit are particularly intractable, as are those that arise from persistent underestimation of the challenges involved in accomplishing the desired goal.
07-05-2010
William F. Owen

Quote:

Originally Posted by Dayuhan

I'm not at all sure that we do "know how to solve all the problems", or that there are solutions that are known to work in every situation, everywhere. The problems that arise when governments select goals that require more time or resources than they are willing to commit are particularly intractable, as are those that arise from persistent underestimation of the challenges involved in accomplishing the desired goal.

OK, but that really strikes to heart of the debate.

Can the problem be solved by killing those who are killing civilians and soldiers? (YES/NO)
If YES, then do it.
If NO, then it's not a military problem, and the military should not be part of he solution.
Strategy IS the dilemma posed by Ends, Ways and Means. If you don't have the resources to make the idea live, then get another idea and it probably won't work, and will end up costing more.
07-05-2010
Dayuhan

Quote:

Originally Posted by William F. Owen

Can the problem be solved by killing those who are killing civilians and soldiers? (YES/NO)
If YES, then do it.
If NO, then it's not a military problem, and the military should not be part of he solution.

Usually the answer is somewhere between yes and no. Killing some of those who are fighting may be necessary to create the space needed to address the cause of the fight... but if you create the space without addressing the cause, sooner or later that space dries up.

To me it's like treating a patient with a high fever caused by an infection. The fever is a symptom but it's an immediate danger and it has to be treated. The underlying infection that caused the fever also has to be treated. Treating the symptom can give you the space you need to treat the cause, but if you don't treat the cause the symptomatic treatment will ultimately fail.

There are also tasks that we simply can't accomplish. We might be able to send troops to Somalia or Afghanistan to defeat a particular group that we see as a threat. Sending troops to Somalia or Afghanistan to establish a stable functioning central government is like asking a team of ace physicians to reanimate a corpse. They may be really good at what they do, but there are still things they cannot do.
07-06-2010
slapout9

Cross post to war gaming small wars,link discusses BP board game and it's relevance to the current situation in the Gulf.

http://council.smallwarsjournal.com/...430#post102430
07-07-2010
William F. Owen

Quote:

Originally Posted by Dayuhan

Usually the answer is somewhere between yes and no. Killing some of those who are fighting may be necessary to create the space needed to address the cause of the fight... but if you create the space without addressing the cause, sooner or later that space dries up.

Concur

Quote:

There are also tasks that we simply can't accomplish. We might be able to send troops to Somalia or Afghanistan to defeat a particular group that we see as a threat. Sending troops to Somalia or Afghanistan to establish a stable functioning central government is like asking a team of ace physicians to reanimate a corpse. They may be really good at what they do, but there are still things they cannot do.

Concur again. Military force only works when its used against military force to support a policy. Just applying force in isolation, never works.
07-08-2010
slapout9

Bruce Bueno de Mesquita-Game Theory Of Iran

Don't why I didn't think of this guy before,but here is his game theory on the future on Iran.

http://www.ted.com/index.php/talks/b..._s_future.html

Also I posted a paper on politics and game theory from the Air Force but cannot remember the name:( anyway it is the Strategy that the republicans are using against President Obama and it is working!!!!!!all the Republicans have to do is make him fail on one or more of his polices and the Republicans will win the elections, they don't have to offer any solutions just make him fail. Much of the game theory used in the paper was done be de Mesquita.