Game theory is useful for figuring out the best options in situations where your options are dependent on what someone else does, so it's only natural for me to think about applying it to combat. Here are some of the more generally useful concepts I use in swordsmanship to determine if an action is successful or unsuccessful. Think of game theory as a tool designed to solve a scenario in a way that forces either victory or a draw.
To be able to apply this first we have to figure out our goals to determine if we are moving towards them or not, and to understand our goals we have to understand the essence of our art.
As warriors, our role in society is to protect other people, to run towards the danger that threatens the ones we love, and neutralize the threat. However if we simply rush towards danger and die, then we have accomplished nothing. So we must have the skill required to deal with threats without becoming a victim ourselves. This is what originally lead to the development of the art of combat, that is a method of making speed and strength irrelevant in a conflict, or we'd be helpless against a stronger, larger opponent. This is also why weapons were developed.
The core of this becomes two main directives that inform all else we do.
- We must survive.
- We must neutralize the threat.
In other words cut without being cut ourselves in swordsmanship. From these values we can begin to judge an action as enacting those ideals, or going against them.
Here's where we can begin using game theory to help us. There are four main aspects we need to cover, they're known as PAPI, or people, actions, payoffs, and information.
First I'll start with information since it's the simplest to discuss alone. This simply means that you understand what is going on in the game, which moves matter and which ones are irrelevant. In swordsmanship this is essentially the ability to judge timing, distance, and use of perception to determine what your opponent is actually doing rather than guessing. In terms of rock paper scissors, it would be as if your opponent chose their action first and you could see what they had chosen. It is unlikely to know what your opponent does before you act however, or we wouldn't need game theory to deal with the situation, but we'll get to that shortly.
Next let's look at actions and payoffs. Understanding this simply means that we know what to do in a simple situation to get the result we want. So in rock paper scissors we know that if our opponent plays scissors, we can play paper and lose, we can play scissors and draw, or we can play rock and win. It is also important to note when actions don't affect the payoffs in terms of our goals. So whether we decide to count to 3 or 50 before we choose doesn't really affect the game much. Whether we are breathing in or out when we reveal our choice is also irrelevant. By the rules of the game the only determining factor is which action we've chosen.
The aspect of people is the most challenging since it is the main variable. As I wrote earlier, it's uncommon to know what an opponent is going to do before they do it, so we need to get as much of an edge in this area as possible. Fortunately for us though, humans aren't unpredictable, but they are random. By that I mean that we can't predict any specific action that someone will choose, but we can determine trends and assign a probability to them. So in a 100 games of rock paper scissors we may find that one opponent throws scissors 80% of the time, rock 19% of the time, and paper 1%. We don't know what they will throw in any specific game, but there is a clear pattern that usually only becomes more accurate the more information we gather.
In that case we can start to look at how we should defeat this opponent, something like a plan to play rock 80%, paper 19% and scissors 1%. Now this won't ensure victory in every game, but it will greatly increase your odds of winning compared to playing each 1/3 of the time. An even better strategy may be to play rock 99% of the time and paper and scissors 1%, since there's only a 1 in 100 chance that paper will be played, but a 99% chance that either rock or scissors will be played, where playing rock against either results in a draw or win.
To gather this information you usually have to review footage of your opponent, or fight against them directly with the mentality of gathering information to build a better plan. Note though, that this shouldn't simply be a series of abortive attacks, but should be carried through with the intention of success.
The part that makes figuring out your opponents trends tricky is that they will be attempting to recognize your patterns and adapt to them as well. The key is success adapting to them faster. If they realize you are always playing rock, and begin to play paper repeatedly, then change to scissors. The key is to predicting at what point your opponent will actually change their strategy, and this is something that takes judgement that can only come with experience.
The interesting thing about the Kunst des Fechtens is that we don't play in a way that only defeats one action. It would be like playing both rock and paper on one turn, so that the only option to avoid losing is to play paper. Forcing their hand is what is meant by obtaining the Vor, or initiative. They are in our control and we are dictating which moves will allow them to simply not lose. Then if they chose only to defend, the equivalent of choosing paper, we immediately play scissors to defeat them.
However a skilled opponent will also be attempting to get momentum back, and playing paper may be a trap, since they are waiting to reveal that that they've also chosen a rock. This of course is quite metaphorical for choosing one action that will succeed in a variety of situations, either from a defensive position or an offensive one so that you have a series of moves to deal with whatever your opponent does. As you hold the initiative longer, it decreases the options your opponent has until eventually they have none, and you win.
So at a high enough level, once you understand the situation, actions, and payoffs all that's really left is to play against the person. At this point it requires another person with a similar skill level to pose a challenge, since a lack of understanding in the lower levels of play will leave you with an incredible advantage. If you realize that your opponent doesn't know what to do in some situation you should put them into it as often as possible. This is abusing a gap in their understanding of action and payoff, however we should also be prepared for the moment when they finally figure out what to do. This is often what scrubs complain about when they say something isn't balanced. Either they don't know how to deal with the situation, or they are so used to abusing it themselves that when they come across an opponent who renders the tactic useless they assume the game has become broken.
Here's a video that demonstrates brilliant use of game theory to force a mutual victory.