Game Theory and game theory

The Game Meets the Theory

Stephanie's recent missive on attraction (also presented here as a guest post) was interesting for a number of reasons, but from my perspective the best thing about it is its use of the branch of mathematics that we know of as game theory.

Stephanie's basic argument reduces attraction down to a game of mutual cooperation and then presents the use of a tit-for-tat strategy as a method of achieving optimal satisfaction for both parties. It sounds clinical and boring, but in fact, it works, for the exact same reason that developing game (the science of attraction, not the mathematical discipline) works.

To demonstrate why this reasoning is sound, I'll start by looking at the basics of the theory and its applications to games of imperfect and incomplete information. Readers who can't be bothered with the finer points of the theory are welcome to skip this. I'll continue by expanding on Stephanie's original points about the tit-for-tat strategy and showing how it works in human mating behaviour. And I'll finish by showing you how to combine the science of Game Theory with the art of game to provide a deep introvert with the tools needed to achieve what he wants.

A Layman's Introduction to Game Theory

To continue this train of thought will require a digression into the nature of games of imperfect and incomplete information. If you're not of a technical bent, or not particularly interested in the details, skip ahead to the last section; the tl;dr version of this is that game theory applies to relationships as much as it does to arms control negotiations, and for the same reasons.

In a game of perfect information, every player knows exactly what everyone else's incentives are, and the rules of the game are perfectly clear to all- chess, for instance, is an example of a game of perfect information.

One representation of a game of imperfect information
In a game of imperfect information, at least one player's incentives are hidden- think poker or blackjack, where players cannot see each other's cards. The case of blackjack is particularly useful. In this game, the objective is to achieve a hand as close to 21 in value as possible- before the dealer does. Essentially blackjack pits every other player against the dealer first, and then against everyone else. The net result is that because information is imperfect between all players, assigning probabilities to different hands, and correctly judging those probabilities, becomes absolutely critical, even though the final incentives and payoffs are completely known to all.

The way to win at blackjack is to become better than everyone else at figuring out the probability that the dealer has a hand of 21. One of my best friends from college is, among other things, a semi-pro blackjack player who made a LOT of money playing various casinos this year, and has told me that the reason why card-counting is so prevalent (and therefore illegal) in blackjack is that it is the only really useful way in which a player can accurately gauge the probabilities of various outcomes. It is therefore the only method by which a player can derive a probability distribution of events and hence derive an expected value of payoffs.

A game of incomplete information is one in which the incentives themselves are unknown. Games like this, unfortunately, are the most common types of interactions in human society. A great example of a game of incomplete information is an arms-control race. Consider: in such a game, both the risks and rewards available to two nuclear-armed and mutually hostile powers may not be known. If you know anything about the Soviet Union's history, for instance, you know that towards the end of the Cold War, the Soviets were terrified of the fact that their nuclear arsenal was essentially being rendered obsolete by the advent of SDI. Because of this, their incentives went way out of whack. Previously the Soviets had been insistent on maintaining nuclear superiority; but now they had no idea whether they could even maintain parity. Their own payoffs had become unclear even to them- and even more so to American intelligence services.
A representation of a game of incomplete information

Games of this type are very difficult to model and play, because such games perfectly illustrate the difference between risk and uncertainty. Risk is a term to use when the probabilities attached to specific events are unknown, but the events themselves are known; all that is left is to create a probability distribution that can be attached to these events and then test whether that distribution is the right one to use. But uncertainty is where the events themselves are unknown. In such a situation, there isn't even any point in trying to figure out the distribution of probabilities until you first have some idea what the possible outcomes are.

Tit-for-Tat and Trigger Stragies
The basics of a tit-for-tat strategy

In game theory a tit-for-tat strategy involves a response to the other player's original response. As long as the other player sticks to an "honourable" or "beneficial" strategy, you respond in kind. The moment the player responds with a "dishonourable" or "harmful" strategy, again you respond in kind.


Consider the classic Prisoner's Dilemma. The Prisoner's Dilemma is used to demonstrate how rational players in a single-shot game respond to incentives, and thereby achieve outcomes that may not maximise their individual happiness in an unconstrained fashion, but will instead maximise their happiness subject to the constraints of the other person's incentives.
Simple representation of the Prisoner's Dilemma

Now let's see what happens when you turn this into a multiperiod game. Suddenly, it might become optimal for one player to always rat out the other player- provided the second player never responds in kind. Or it might be better for both players to cooperate- provided that both players stick to their original strategies. I've written before about the nature of multiperiod games of competition in a somewhat different context, and this is where the basic idea comes from.


Tit-for-tat is one possible strategy to use in a multiperiod game with a very large number of possible future outcomes. As long as one player cooperates, the other does too. The moment the other player fails to cooperate, the first player does too. And this leads us to the concept of trigger strategies, used to optimise outcomes over long multiperiod time horizons.

Repeated Prisoner's Dilemma
A trigger strategy is a long-term strategy in multiperiod games that dictates how each player will respond to a deviation from an expected pattern of behaviour. Let's say that Prisoner A has cooperated for the last 50 moves of the game, but on the 51st he decides to betray Prisoner 2 and sell him out. Prisoner 2's trigger strategy will then be to respond by always betraying Prisoner 1 in every possible future iteration. If the game goes on long enough, Prisoner 1 will realise that his future will look so bleak that his best option is therefore to cooperate at all times. This particular type of trigger is called, with good reason, a "grim trigger strategy".

Game Theory and Dating

And now we come at last to the meat of the idea. If you've ever seen the movie "A Beautiful Mind" (personally I think you'd be better served reading the book), there is a very brilliant scene in which John Nash demonstrates, through a dating analogy, how to maximise individual happiness via the use of what eventually came to be known as his most famous contribution to the entire field of mathematics (among several). That scene illustrates perfectly how a tit-for-tat strategy, of the kind that Stephanie outlines, would work in real life.

In the context of game, this simply means, "boy meets girl, boy talks to girl, boy figures out whether girl is worth his time"- and vice versa, by the way. When approaching a woman for the first time, you're confronted with imperfect information- you know the list of possible outcomes (rejection, mild interest, moderate interest, clear and heavy interest, physical escalation, sex, relationship, breakup, etc. etc.) but you do not know the probabilities associated with each outcome.

One useful way to get to know those probabilities is through tit-for-tat escalation.

Tit-for-Tat and Introverted Game

Stephanie presents the use of tit-for-tat escalation from a woman's perspective:
The concept is really simple. First you establish an attraction signal to someone you find attractive. The most nonthreatening signal is eye contact. My best trick is to scan a room until I meet eyes with a man who is also scanning the room. Making eye contact is the most effective way of expressing interest. It is the most vulnerable signal in the game of attraction. So much information is processed in a short time frame. Based on how long the eye contact is met depends on initial attraction. If attraction is mutual, curiosity of that signal invites more eye contact between both parties. Frequency and duration of eye contact is the quickest way to evaluate mutual attraction. 
Now with tit-for-tat, once I make eye contact with a man more than once, I wait to gauge his interest. He will either initiate more eye contact or not at all. This is pretty much a pass/fail tactic. If he returns more eye contact, I will return more eye contact. If he advances the eye contact, I will reciprocate further based on his advance. If he changes body positioning and distances himself it sends a clear signal of disinterest.
I present the same set of arguments, from a male introvert's perspective, to establish and gauge mutual interest via an almost algorithmic pattern:

  1. Start with basic eye contact (easy enough for most introverts- the "shy introvert" trope is more of a myth than anything else). If eye contact is weak, break off and move on.
  2. If eye contact is established and strong, move to physical proximity. If she moves slightly away from you, she's not interested. Smile and move on.
  3. If she stays put or leans in slightly, there is potential interest. Maintain eye contact and begin conversation (a weak point for a LOT of introverts and one I'll attempt to address in future posts). If the conversational openings founder or fail, smile and move on.
  4. If the conversation goes well, begin verbal escalation. This is the stage at which you'll begin to get a clear idea of what the probabilities are for friendship (yikes), more conversation, dating, and potentially sex will be. If the conversation begins to fail or fade, or you see clearly that the probability of getting what you really want is going to zero, smile and move on.
  5. If the conversation goes well, begin physical escalation (i.e. touching). This is also a major weak point for a lot of deep introverts- guys like me absolutely hate being touched by strangers, and as a result we don't do much touching ourselves. If she pulls back or brushes you off, walk away.
  6. If the touching goes well, continue escalating until you reach the point where you do in fact get what you want- or you get a signal from her that is negative and therefore you reciprocate.
  7. If at any point you see a strongly negative signal in this set of interactions, maintain frame and move on. Your options are limited only by your willingness to explore them.
A natural question here might be, "where does the trigger strategy come in?" This is where the game concept of "frame" meets the mathematical concept of a grim trigger. Sit back and grab some popcorn, you'll enjoy this.

Let's say you're talking to a girl, having a good time, enjoying yourself, and you move in for physical escalation, and then she pulls the dreaded "I have a boyfriend" card. If you were getting positive signals earlier, then you pull the grim trigger by saying, "goodbye", cutting things off right then and there, and walking away. From your perspective, you punish a bad move instantly.

Or let's say you're trying to make a move on a girl and she pulls back and says, "I just want to be friends". Guys, the friendzone blows. Never ever ever volunteer to be led into it. When this happens, you have one of two options- call her bluff by flatly saying no and walking away, or try the strategies outlined here.

Finally, let's take the scenario where you're over at a girl's place and you're about to try to seal the bang, and she says "no". Now as Vox, Roissy, Roosh, and so many others have pointed out, "no" rarely actually means no. In other words, "no means no- until it doesn't" (straight quote from Roosh's 30 Bangs). Now if this happens, understand well that you are on dangerous ground. If you persist, there is a non-zero and possibly significant probability that you might be hit with a false rape accusation- and that will destroy you unless you are very careful or your game is very, very tight.

Applying tit-for-tat, though, gives you a very nice way out. If she's at your place, kick her out. If you're at her place, walk out. The look on her face will be extremely funny and will almost be worth missing the bang.

(If any of this sounds like standard game advice from any of a dozen sources out there, that's because game is simply yet another aspect of Truth. Mathematics is also Truth, and provides a convenient set of tools by which one might understand that truth. The two are therefore quite compatible, which is why the tools of mathematics can be applied so readily to game. You're not imagining things at all.)

A Game Method for Introverts

This is not your standard PUA approach method. This method doesn't mean dressing up in gaudy outfits and peacocking to pick up phone numbers. It doesn't mean cold-opening women or approaching them from behind or figuring out logistics before an approach the way Roosh outlines in Bang. It doesn't mean going up to a woman wearing headphones in a coffee shop and interrupting what she's doing in order to pull Roosh's Galnuc technique (I'm not criticising it, since it works and is highly effective, I'm just saying that this isn't the same thing), since this is highly disruptive for her and rather difficult for you as a deep introvert. It is applicable to online dating as well as in-person approaches- think about it, if you get a woman to agree to meet you in person, that's already an application of tit-for-tat with successful interactions on both sides.

This method requires that both you and your target are open to approach. It also ensures a somewhat higher probability of success because of that. And the beauty of it is, it works equally well for both men and women; just reverse the roles so that you're looking at things from the point of view of the woman who is on the receiving end of each escalation trigger. And as Stephanie points out, the downsides are limited- an especially important factor for introverts, because our entire lives have been structured around avoiding public exposure and embarrassment. It's one of our most subconscious drives and desires.

Try this stuff out the next time you're at a bar with friends (preferably a quiet one) or in a coffee shop eyeing that cute blonde across the room. If she returns your eye contact and smiles slightly, that's your in. If she flips her hair while talking to you, then make a move. If she's interesting to talk to and gives off the right signals, keep escalating at a pace that feels right to you. And the moment you get a negative signal, respond in kind.

Chances are, if you've done the right things in your life by eating right, developing strength, having interesting hobbies, dressing well, and improving your mind, you're already ahead of the curve. Now you simply have to get out there and do what you've been training for.

Comments

  1. I love this! The only thing I disagree with is using this game theory to hyper escalate. Though it does work to gradually meet goals, trying to throw a girl off with the push/pull dynamic won't work in a man's favor. He may get laid, but it will be followed by the same drama as PUA tactics.

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