Are you talking about the Prisoner’s Dilemma?
When I was taking an into class for computer science, we found that the best strategy was:
Cooperate.
If, during the last turn, your opponent has competed against you, compete.
This method yields the most points over the course of a game (which, to be statistically sensible, should consist of at least 30 turns).
In most games I play I use a “defensive” strategy. The idea is to set up battle grounds for your opponent to come play on. I like to have some naval gunfire and artillery waiting for him. Let your opponent beat himself to death on your defenses while you build an overwhelming force to crush him.
/hijack
From SimonX
I didn’t even know there WAS a PC version to be honest. 
Is it fairly new or old?
On the PC I’m pretty well addicted to Total War: Medeval. To me its the best war game on the PC I’ve ever played. It has a combination of turned based strategy, technology trees galore, and a real time tactical fighting element. I’m STILL playing hours a day and have had the game well over a year now. I can’t wait for their Rome version. 
/hijack
From adaher
No, you have to attack, no doubt. I think what most people (well, what I’m saying anyway) is you have to have balance. Most of the time I play a defensive opening game, where I protect my resource base, or perhaps heavily fortify an area I WANT to get attacked, all the while building up attackes of my own from these fortified positions. Also, there is the difference between strategically defensive but tactically agressive. I think though that the OP has been answered…all out attack is almost NEVER a good thing, unless you are so superior to your enemy that you can get away with it.
-XT
See, for a while I was having my doubts about this MssgBoard. I was wondering whether I should be spending (I think I used the word, “wasting”) my time sifting through these pages and asking questions.
Looking at the quality of the answers/responses to the OP (particularly xtisme, Dissonance, glee, SimonX and specially Taran) I realise what it is that makes me come back again and again and again.
To clarify some points:
I think you’re argument is better summed up by this:
And I’m sorry, I realize it does have an extremely broad-backed base (for this I apologize). But I wanted my argument to be applicable to all sorts of “games” that produce a competitive environment (e.g. You vs Me or Us vs Them). I didn’t want to rob the answers of the sort of range that (for example) Taran has provided with his “Marriage-Model”.
So basically, for two reasons:
a) It is interesting to hear about the development and usage of strategy for “games” outside of warcraft and business (though I appreciate these will be the primary examples)
b) I thought that by doing so, I could try to identify the key factor(s) in a situation (or “game”) that require a particular strategy (whether attacking/defensive) or mix of strategies (as mentioned by xtisme). Even just having a glimpse of understanding for what the contrasts between these (admittedly) highly diverse “games” do for the underlying strategy that is employed would be great.
For example, I think a partial answer to part b) can go something like this:
Go read Sun Tzu.
I was involved in a very active board gaming group in graduate school. And we were a bunch of eggheads who were interested in exactly questions like these.
One of the players in our group, call him “Byron” (OK, just call him Byron, that was his name) was extremely agressive, and would regularly take the task of discovering if constantly attacking was a benefit.
In most cases (in games), it isn’t. In two player games, it might well be. However, in multi-player games, it is often most] beneficial to avoid conflict (provided that doesn’t mean retreating) whenever possible. Constantly attacking is often a recipe to stunt your own growth as well as the opponent you are attacking.
I wonder if the OP can be amended to make the best/optimal strategy to avoid being attacked. For two player games, this might amount to being the attacking player, but for multi-player games it is more subtle.
I agree with Taran that if you can identify a scenario where there is little or no difference in cost to attack vs the cost to defend, then attacking (or agressiveness) is the only way to make gains. Typically, agressivness involves projecting your resources beyond the zone within which they are comfortable. So, armies must leave fortifications, businesses must develop new and untried products, and interpersonally, you must be willing to make yourself vulnerable to another. I heard one time (It may have been from the “Myth” series of books by Aspirin, so forgive me if I get the wrong) that a “mini max” theory applies to the situations we are discussing. That is you want to choose actions which provide the minimum risk for the maximum gain. Again, Sun Tsu said it better, but I cannot find my copy so I’ll leave it at that.
I doubt that there’s any one optimal strategy for so many diverse situations.
“If ten times the enemy’s strength, surround them; if five times, attack them; if double, divide them; if equal, be able to fight them; if fewer, be able to evade them; if weaker, be able to avoid them. Therefore, a smaller army that is inflexible will be captured by a larger one”
…those skilled in warfare make themselves invincible and then wait for the enemy to become vulnerable. Being invincible depends on oneself, but the enemy becoming vulnerable depends on himself…
Sun Tzu - The Ancient Art of War
Sun Tzu believed that flexibility and deception were key to fighting a war. Whether on the offense or the defense, you set the pace and timing of the battle. You pick and choose when and where to attack. Attack places where he is weak. Goad him into attacking you where you are strong. An ill-planned and equiped attack can fail and sap your army of its strength, leaving you vulnurable to counterattack.
Everyone who has played Age of Empires, Command & Conquer or Total Anihilation knows that you can get the upper hand if you can attack first and make your enemy go on the defensive. Attack too soon however and you can end up without an army to defend yourself.
I’ve read Sun Tsu and highly recommend him. Another far eastern (well, from Japan at least) book on philosophy of war is Book of 5 Rings (The classic guild to strategy), by Miyamoto Musashi. The book is very deep, but it also is a must read for people who enjoy both strategy and tactics (not just in combat but in business or any other forum). And of course, one should always read the Master…Nicolo Machiavelli.
I think Newton meter’s summation of the difference between having a single opponent and having multiple opponents is very relevant as well. In a contest of 2 opponents, you have a lot more offensive strategic flexability than in a contest where there are multiple opponents, shifting alliances and threats.
In the later situation (which happens OFTEN in the Total War games), I usually play a very cautious game, fortifying my provences, building my infrastructure and resource base, building up my technologies and modestly building a field army…which I use mainly if attacked. When attacked my general response is to fortify my fronteer and destroy the aggressor that has attacked me (resources and the frigging Pope willing…I absolutely HATE excommunications :)). Once that is accomplished I try and rebuild my trade routes (especially the sea ones) and sit back again to build. My games generally last from the early 1100’s to just about the 1400’s because of how I play…but I usually win no matter which country I start off with.
-XT
Assuming that you must attack to win* (to capture, to destroy, etc.) the question beccomes when to attack. As it was pointed out, the only way to do it is to attack at a point at a time of your choosing, not to do it blindly, or worse yet, forced by your opponent(s).
glee,
I must posit that taking an enemy pawn is an attack, or at least a counterattack.
SimonX,
The best opening for Russia is to attack Ukraine, though.
Taran,
It seems that the meta-strategy of that algorithm for men is to go to big groups while for women is to go to very small groups.
*In some games, scenarios, and real life situations all you need to do to win is to deny your opponent(s) their victory conditions, in which case attacking is not necessary.
Also, it’s possible to look like you’re going on the defensive to fake out your opponent. In fencing, where speed is everything, if I find that my opponent is faster than I am, I’ll let him attack, then either parry, step slightly aside or lower my body to take a low line, and thrust, or just parry and thrust, the key being to be able to time this just right. I find it highly effective against fencers who are better than I am but too aggressive for their own good.
Allegedly, there’s a scene in Seven Samurai where a younger fencer challenges an older one, and the older one takes this tack and kills the younger one. Haven’t seen that movie, so I can’t say if that’s true, but it sounds like what would happen in real life. Age and treachery always overcomes youth and skill.
Also works in chess, I’ve found, especially on the Internet. For some reason lots of players on the Net are extremely aggressive.
Who says it is impossible to defend and attack at the same time? What, we only have one arm an no legs?
All things being equal, an offensive position presents the best option. All things are not usually equal in practice, but that’s life. There is an advantage in taking an offensive posture, but it depends and can be revrsed by the specifics of the situation.
I would argue the OP is generally wrong.
I would place far more importance on initiative and work from there. You can be on the defensive but retain the initiative by refusing to commit yourself first, you can seize the initiative by attacking and as long as you can maintained the initiative and make the opposition dance to your tune, react to your threats (be the passive “fleet in being” threats or active “kick ass” threats) then you will end up on top.
It is the loss of initiative that leads to defeat, not being on the defensive for a period.
It would say this counts in warfare, wargames, most sports, chess and probably life.
I can only speak as a veteran RTS gamer. I agree with notquitekarpov about initiative and tempo. The key question is whether taking an initially defensive strategy will allow me to gain some sort of military/economic advantage. Defense is not a strategy if it’s the default position from being attacked. It must be a choice. The benefit of going on the defensive (turtling) is that your opponent get’s chewed up in the static defenses and the garrisoned troops which get offensive and defensive bonuses. You can consequently make a much smaller force and put resources into increasing productive capacity. Many RTS opponents (and I’m sure Generals) lack the discipline to make a tactical retreat. Even after they know well that they’ve lost the battle they will still allow the last 1/3 of their army to be destroyed. They move focus to the creation of their next army. Bad idea. It takes more discipline to attack intelligently than to defend intelligently. If you know you’re opponent lacks discipline you can wait for them to make the mistake.
I agree with the OP.
Offense is always the surest way to win.
This applies to most things, from my take on things, specially combat (both personal and warfare).
The examples are out there in history books for you 
Here’s a couple of comments from Master Sigmund Ringeck (A medieval fencing master to the Duke of Bavaria) :
He warns about staying on the defensive:
“All fencers that rely on displacing will be deceived and defeated…”
And
“When you are in the zufechten close with your opponent do not try to avoid his strikes and do not wait for what he intends to do against you. Swordsmen who only wait for the opponents strikes and do nothing other than avoid them have little success. They are usually defeated.”
His concept of the art refers to certain timings in combat. The before, the after, and simultaenous action. To be on the defensive is to always be in the after, which is seldom good.
Similarly, you can’t win wars by barricading yourself in a fortress or underground. Eventually you will be driven out, or you’ll be stuck waiting for the bunker buster to find your particular hole in the ground.
Take it from a Vikings fan. Offense is NOT the surest way to win.
Tell it to the Germans on the Eastern front. NO one strategy is the best way to go. Sometimes the best thing to do is defensive, sometimes offensive. Personally I usually favor a counter punching stategy from a grand stategic perspective, and an agressive offensive on the tactical level. Even at the tactical level, MANY times its better to hold ground or manuver, than simply attack.
-XT
Being a fencer, I have to take serious exception to Master Sigmund, Kinthalis.
I have on numerous occasions defeated fencers who were on paper far better than I simply by allowing them to attack, sidestepping that attack in one way or another, and then thrusting home for the kill. I shocked my fencing master by defeating his best pupil the first time I faced that pupil by doing this. The pupil couldn’t figure out what was happening. The master, of course, knew exactly what was going on. Afterwards, he said to me in the locker room “I don’t know what you’re doing, but whatever it is, keep doing it.”
I’ve been defeated the same way more often than I can count including, of course, by this same guy. Didn’t take him long to figure me out. If the other guy has a plan and you go in blindly attacking, well, you won’t be long for this world.