Romance and other relationships - a game theory analysis (Aspie, what me?)
Considering the significance of relationships such as romance and friendship to most people, it's odd they don't make more use of all the conflict analysis paid for by the US government during the Cold War. Admittedly that analysis produced the worrying strategy of Mutually Assured Destruction, but even that relationship pattern works well for some people.
Much of game theory is devoted to zero-sum games such as chess, where any benefit to one player is exactly matched by a cost to the other. Relationships of this type where, for example, one player gains self-esteem by reducing their opponent's supply of it, are probably more in need of therapy than tactical tips, so we'll skip quickly over those.
In real life most game situations are non-zero-sum, meaning that both players might win, or they might both lose, and they may win or lose quite different amounts of whatever they're playing for. Several decades of study of this type of game (the Prisoners' Dilemma type) have mainly shown that the length of the game is crucial to deciding the best strategy.
If you're only going to play with someone once, then it's best to rip them off for whatever you can get, but if you're going to play with the same people many times, it's much better to co-operate and work together to each gain the biggest prizes. The first case, various forms of one night stand, isn't a tactically interesting game, so we'll only consider the optimum strategies for forming and maintaining long-term mutually beneficial relationships.
The Payoff Matrix
The basic move, particularly in the early stages, is to offer some information and see how the other player responds. The value of information relates to how private/embarrassing/secret it is, on a scale from "I like pizza" (worth almost no points) through "I like Abba" (mildly embarrassing if it came out more widely) up to "I'm a Nithling still on the run from the Icelandic Secret Police" (a potentially damaging secret representing a gamble worth many points).
The player offering the information is risking points in the sense that they make themselves vulnerable in the hope of increasing rapport and building up mutual trust. Initial moves should be kept to low value information, not only to minimise the risk of heavy losses (e.g. if the opponent responds with jeering), but because people's grasp of how to play the game is so instinctive that they find bad play (starting by revealing big secrets) to be disturbing and creepy in itself.
The player given some information then chooses a response from three types of counter-move: fold, match or raise.
Fold, meaning offer nothing in return for the information, appears to win that round in the sense of collecting a profit without paying any of their own private information for it, but that would be zero-sum thinking. In practice it tends to end the game, especially if repeated over time, with both sides losing. This is the strategy to adopt only if the game is going badly and needs to be abandoned: it's unfortunate when players choose this option only by carelessness, not realising it's the losing move.
It loses because, while people mostly don't analyse the exchange of information in such precise terms, they certainly get a message from the primate social game engine in their brain, feeling lack of fair exchange of information as disappointment, rejection or confusion.
Match, meaning the second players offers some of their own information of roughly equivalent value, maintains the trading cycle and keeps both players feeling that they're doing something worthwhile. In the long-run it may not be enough, in that if the same player has to start every trade cycle they'll realise they're driving the relationship and might want the other to be a more active player.
This is a waiting strategy, to be used when the relationship looks promising enough that the player wants to stay in the game and see whether it's worth committing higher stakes in later rounds when they know more.
Raise, meaning responding with somewhat more valuable information than the first player provided, fuels the spiral of increasing mutual profit which we call whirlwind romance. It can't be sustained in the long term as there's not an unlimited supply of increasingly valuable information available, but can usually run long enough to get the relationship up to a high plateau.
This is the most fun strategy in many ways, and the one that leads to the biggest prizes when it works. When it doesn't work, it's not so good.
The semantic algebra of touch
The value of each specific information offer may vary between players, and if their ideas of what each secret is worth vary greatly then the game will be short and bewildering. This effect also applies to symbolic touch, but is easier to analyse there as there are relatively few moves available.
Most people assign about the same intimacy values to each level of touch, documented by Desmond Morris in a 12 step model from looking to mating, which might need some updating for internet courting, but has some traps even in real life use.
One is that a few people use a significantly different sequence, so if your opponent suddenly jumps to head touching (step 8, the one before foreplay), it's best to check they really meant to go past the hand holding, cuddling and kissing steps. Otherwise they may just be a nit nurse, or culturally accented in their gesture language, or otherwise idiolectic.
The other odd effect some people exhibit is not to be able to see the gradation of intimacy at all, and interpret a low level gesture such as holding hands as a demand for level 12 sex. The gradation is not an intellectually difficult idea, so the trick is to involve higher brain functions in processing sensory input. First convert touch to symbolic form, and then process the meaning of that symbol. Games only work if all players are using the same rules.
The Backgammon doubling cube
In that zero sum game the doubling cube is a mechanism which sometimes allows one player to offer to double the stakes, with the other player forced to either accept the higher risk or concede and lose the current stake.
In the non-zero-sum version of relationships it's an offer to double the stakes in the sense of increasing the profit or loss for both players, depending on how things turn out later. Examples include meeting the other's parents/children, having sex, getting married, and jointly buying a cat (in whatever order people do these things nowadays).
When to offer a double is an interesting question, and the Backgammon answer (when you have at least a 67% chance of winning) is not obviously applicable to love. It's sometimes used to force a crisis, in the Backgammon way of hoping the opponent will decline and concede the game if they're not expecting to win, but that's potentially an expensive way to find out the other's expectations. (E.g. they might have to decline now, but would have accepted later when they've acquired more information and confidence of a successful result.)
The Backgammon answer for when to accept a double is when you have at least a 25% chance of winning, which is intriguing from the point of view that 25% + 67% isn't 100% - there's a gap when doubling up is good (or at least better than the alternatives) for both players even in that zero-sum game. And the benefits are much stronger in the non-zero-sum world of course.
The sunk cost fallacy trap
This strategic error applies in many areas of life but is particularly confusing in relationships, because it's a bad idea which overlaps with good ideas.
The fallacy is that the value of continuing to do something increases with how long you've already been doing it. Zoologists have been searching increasingly desperately for any example of animals doing this, and there aren't any, because they've been tuned by natural selection not to do anything so bad for them as making an investment for illogical reasons.
Humans, uniquely because our intelligence lets us override long-tuned instincts, are able to do stupid things, and the sunk-cost fallacy is one of our favourites. Specifically in this case, whether a relationship is worth continuing depends only on the future benefits - not on the effort already put in or on the past benefits.
The complication in implementing this strategic decision correctly is that future benefits can't be measured, but must be estimated based on past experience, and having been together a long time can itself produce future benefits. The trick is to clearly distinguish logical expectations of future good things from sentimental attachment to old things.
Just as every peace-time army is fully prepared to re-fight the previous war, it's tempting to plan on re-living the last n years, but this may not be practical.
When to mate for life
The curious, but still popular, practice of monogamy and its extreme form of mating for life, has its own special problems and solutions. A big question for new players is at what age to marry, or put another way, what is the optimum number of failed courtships to carry out before choosing The One and settling down forever.
The simple answer from game theory is the 37% rule, often described in terms of a submarine with a single torpedo being passed (once each) by enemy ships of different sizes: what's the best way to target one of the biggest ones? Statistically it's easy to show that on average the best result comes from watching 37% of the targets go by and then shooting at the next one that is bigger than any of those first 37%.
Of course in real life the poly/cheating/divorce options give us more than one torpedo, but it's good to have mathematical proof that puppy love (contrary to the young Donny Osmond's theory) is for surveying the available field, rather than marriage. The best strategy under the most unrealistic romantic restrictions is to date 37% of all the datable people you're ever going to meet, then propose to the next one after that who is better than the first 37%.
An interesting variation is to remove the restriction of only being able to date each other player once, so it's possible to return to a previous good one if they're not already married to someone else by the time you have enough data to know they were the best bet. The best strategy then is to nag - keep proposing to still available previous partners, in order of suitability, until one accepts, and add a new one to the list each time they all refuse.
This is difficult for many players as their previous partners tend to become unavailable for another game merely by their previousness, but it's a good argument against burning your bridges before you come back to them. As potential new mates, exes are statistically a more valuable resource than strangers, because they've already been filtered and selected as candidates once.
Summary
So the optimum strategies for each stage in relationships are:
Getting to know someone: co-operate and be nice to them.
Increasing the stakes: co-operate and be nice to them.
Communicating intimacy: co-operate and be nice to them.
Ending relationships: co-operate and be nice to them.
Radical stuff.
Much of game theory is devoted to zero-sum games such as chess, where any benefit to one player is exactly matched by a cost to the other. Relationships of this type where, for example, one player gains self-esteem by reducing their opponent's supply of it, are probably more in need of therapy than tactical tips, so we'll skip quickly over those.
In real life most game situations are non-zero-sum, meaning that both players might win, or they might both lose, and they may win or lose quite different amounts of whatever they're playing for. Several decades of study of this type of game (the Prisoners' Dilemma type) have mainly shown that the length of the game is crucial to deciding the best strategy.
If you're only going to play with someone once, then it's best to rip them off for whatever you can get, but if you're going to play with the same people many times, it's much better to co-operate and work together to each gain the biggest prizes. The first case, various forms of one night stand, isn't a tactically interesting game, so we'll only consider the optimum strategies for forming and maintaining long-term mutually beneficial relationships.
The Payoff Matrix
The basic move, particularly in the early stages, is to offer some information and see how the other player responds. The value of information relates to how private/embarrassing/secret it is, on a scale from "I like pizza" (worth almost no points) through "I like Abba" (mildly embarrassing if it came out more widely) up to "I'm a Nithling still on the run from the Icelandic Secret Police" (a potentially damaging secret representing a gamble worth many points).
The player offering the information is risking points in the sense that they make themselves vulnerable in the hope of increasing rapport and building up mutual trust. Initial moves should be kept to low value information, not only to minimise the risk of heavy losses (e.g. if the opponent responds with jeering), but because people's grasp of how to play the game is so instinctive that they find bad play (starting by revealing big secrets) to be disturbing and creepy in itself.
The player given some information then chooses a response from three types of counter-move: fold, match or raise.
Fold, meaning offer nothing in return for the information, appears to win that round in the sense of collecting a profit without paying any of their own private information for it, but that would be zero-sum thinking. In practice it tends to end the game, especially if repeated over time, with both sides losing. This is the strategy to adopt only if the game is going badly and needs to be abandoned: it's unfortunate when players choose this option only by carelessness, not realising it's the losing move.
It loses because, while people mostly don't analyse the exchange of information in such precise terms, they certainly get a message from the primate social game engine in their brain, feeling lack of fair exchange of information as disappointment, rejection or confusion.
Match, meaning the second players offers some of their own information of roughly equivalent value, maintains the trading cycle and keeps both players feeling that they're doing something worthwhile. In the long-run it may not be enough, in that if the same player has to start every trade cycle they'll realise they're driving the relationship and might want the other to be a more active player.
This is a waiting strategy, to be used when the relationship looks promising enough that the player wants to stay in the game and see whether it's worth committing higher stakes in later rounds when they know more.
Raise, meaning responding with somewhat more valuable information than the first player provided, fuels the spiral of increasing mutual profit which we call whirlwind romance. It can't be sustained in the long term as there's not an unlimited supply of increasingly valuable information available, but can usually run long enough to get the relationship up to a high plateau.
This is the most fun strategy in many ways, and the one that leads to the biggest prizes when it works. When it doesn't work, it's not so good.
The semantic algebra of touch
The value of each specific information offer may vary between players, and if their ideas of what each secret is worth vary greatly then the game will be short and bewildering. This effect also applies to symbolic touch, but is easier to analyse there as there are relatively few moves available.
Most people assign about the same intimacy values to each level of touch, documented by Desmond Morris in a 12 step model from looking to mating, which might need some updating for internet courting, but has some traps even in real life use.
One is that a few people use a significantly different sequence, so if your opponent suddenly jumps to head touching (step 8, the one before foreplay), it's best to check they really meant to go past the hand holding, cuddling and kissing steps. Otherwise they may just be a nit nurse, or culturally accented in their gesture language, or otherwise idiolectic.
The other odd effect some people exhibit is not to be able to see the gradation of intimacy at all, and interpret a low level gesture such as holding hands as a demand for level 12 sex. The gradation is not an intellectually difficult idea, so the trick is to involve higher brain functions in processing sensory input. First convert touch to symbolic form, and then process the meaning of that symbol. Games only work if all players are using the same rules.
The Backgammon doubling cube
In that zero sum game the doubling cube is a mechanism which sometimes allows one player to offer to double the stakes, with the other player forced to either accept the higher risk or concede and lose the current stake.
In the non-zero-sum version of relationships it's an offer to double the stakes in the sense of increasing the profit or loss for both players, depending on how things turn out later. Examples include meeting the other's parents/children, having sex, getting married, and jointly buying a cat (in whatever order people do these things nowadays).
When to offer a double is an interesting question, and the Backgammon answer (when you have at least a 67% chance of winning) is not obviously applicable to love. It's sometimes used to force a crisis, in the Backgammon way of hoping the opponent will decline and concede the game if they're not expecting to win, but that's potentially an expensive way to find out the other's expectations. (E.g. they might have to decline now, but would have accepted later when they've acquired more information and confidence of a successful result.)
The Backgammon answer for when to accept a double is when you have at least a 25% chance of winning, which is intriguing from the point of view that 25% + 67% isn't 100% - there's a gap when doubling up is good (or at least better than the alternatives) for both players even in that zero-sum game. And the benefits are much stronger in the non-zero-sum world of course.
The sunk cost fallacy trap
This strategic error applies in many areas of life but is particularly confusing in relationships, because it's a bad idea which overlaps with good ideas.
The fallacy is that the value of continuing to do something increases with how long you've already been doing it. Zoologists have been searching increasingly desperately for any example of animals doing this, and there aren't any, because they've been tuned by natural selection not to do anything so bad for them as making an investment for illogical reasons.
Humans, uniquely because our intelligence lets us override long-tuned instincts, are able to do stupid things, and the sunk-cost fallacy is one of our favourites. Specifically in this case, whether a relationship is worth continuing depends only on the future benefits - not on the effort already put in or on the past benefits.
The complication in implementing this strategic decision correctly is that future benefits can't be measured, but must be estimated based on past experience, and having been together a long time can itself produce future benefits. The trick is to clearly distinguish logical expectations of future good things from sentimental attachment to old things.
Just as every peace-time army is fully prepared to re-fight the previous war, it's tempting to plan on re-living the last n years, but this may not be practical.
When to mate for life
The curious, but still popular, practice of monogamy and its extreme form of mating for life, has its own special problems and solutions. A big question for new players is at what age to marry, or put another way, what is the optimum number of failed courtships to carry out before choosing The One and settling down forever.
The simple answer from game theory is the 37% rule, often described in terms of a submarine with a single torpedo being passed (once each) by enemy ships of different sizes: what's the best way to target one of the biggest ones? Statistically it's easy to show that on average the best result comes from watching 37% of the targets go by and then shooting at the next one that is bigger than any of those first 37%.
Of course in real life the poly/cheating/divorce options give us more than one torpedo, but it's good to have mathematical proof that puppy love (contrary to the young Donny Osmond's theory) is for surveying the available field, rather than marriage. The best strategy under the most unrealistic romantic restrictions is to date 37% of all the datable people you're ever going to meet, then propose to the next one after that who is better than the first 37%.
An interesting variation is to remove the restriction of only being able to date each other player once, so it's possible to return to a previous good one if they're not already married to someone else by the time you have enough data to know they were the best bet. The best strategy then is to nag - keep proposing to still available previous partners, in order of suitability, until one accepts, and add a new one to the list each time they all refuse.
This is difficult for many players as their previous partners tend to become unavailable for another game merely by their previousness, but it's a good argument against burning your bridges before you come back to them. As potential new mates, exes are statistically a more valuable resource than strangers, because they've already been filtered and selected as candidates once.
Summary
So the optimum strategies for each stage in relationships are:
Getting to know someone: co-operate and be nice to them.
Increasing the stakes: co-operate and be nice to them.
Communicating intimacy: co-operate and be nice to them.
Ending relationships: co-operate and be nice to them.
Radical stuff.