All is fair in love and war, on Zero-sum games in life

by Ratios4 min read17th Apr 202121 comments


Social StatusWorld Modeling

Crossposted from my blog: Dark Rationality

Why can’t we all just get along? Is a good question to ask, even if you won’t like the answer. Naval Ravikant posted on Twitter that people should avoid playing zero-sum games and focus on the positive-sum game of wealth creation, the irony is quite amusing considering twitter is a zero-sum-silicon-valley-engineered status game that causes many of its participants to become utterly obsessed with their follower counts. In this case, the medium is the message.

The case I’m going to be making in this post is that for humans zero-sum games are not only unavoidable but are actually very important and that these truths are being suppressed and denied because of their dire implications.

Zero-sum games in life

The most famous and clear-cut zero-sum game in life is wars, two or more sides fighting over some scarce resource, may it be oil, land, or trade routes.

The entire human history was filled with wars, in many cases wars can be considered even a negative-sum game as the aggregate loss from both sides in many cases is larger than the utility gain of the winning side. A contrarian reader would probably mention world war 2 and the positive influence it had on the development of many technologies like computation or nuclear power. But I would argue that the price we paid in economic destruction and suffering was quite high, and it’s unclear if on aggregate the result was positive. But even if it was the case this is the exception and not the norm.

But wars are not what they used to be, it seems that nuclear weapons and the MAD doctrine have made wars somewhat obsolete so an argument can be made that while wars used to be a significant problem in the past their importance in human life seems to be heavily declining.

The second big zero-sum game in life is status, here things start to become unpleasant. Because it’s quite hard to deny that status is zero-sum and while wars are becoming rare it doesn’t seem that status-wars follow suit. And if you believe the ideas of Peter Turchin about the overproduction of elites they might have even become worse with time. Judging by revealed preferences, social status is very important to people – many spend a large number of resources on Veblen goods and signaling (the broke individual who still splurges on clothes is a trope for a reason). The elephant in the Brain by Robin Hanson and Kevin Simler claims that many very basic facets of our life are actually related to signaling and status maneuvers.

The third bid zero-sum game is competing for sexual partners (long and short term). One objection that I sometimes encounter against viewing intrasexual competition as a zero-sum game is different preferences. Imagine that Alice is dating Bob and Charles is dating Dina but in reality, Alice and Charles are way more compatible, and so are Bob and Dina. So if they would switch you would get a Pareto improvement which means it’s actually not a zero-sum game. And while this argument is theoretically correct in practice most people are looking for the same qualities, men usually put emphasis on youth while women tend to appreciate power, but both men and women prefer attractive and healthy mates. So in practice, the competition for partners can mostly be described as zero-sum [1]. Important to note that the zero-sum game is not between the partners in the relationship, because if the relationship is healthy it’s definitely a positive-sum game. The zero-sum game is the intrasexual competition, think of the stories of Helen of troy or Bathsheba as archetypical representations of this phenomenon.

The fourth category of zero-sum games is more subtle but still happens quite frequently and these are zero-sum games that are hidden in positive-sum games, few examples:

  • While employment at large is a positive-sum game – salary negotiations are a zero-sum game, every extra dollar the employee is a dollar that the employer could have and vice versa.
  • While the government could be described as a positive-sum game (at least if you agree with the Hobbesian view). The election process is a zero-sum game for the parties that participate.
  • While marriage is a positive-sum game, a specific argument about who is the one who needs to get up to care for the crying baby at 4 am is zero-sum.

These are not the only examples, it seems that most interactions have some kind of a zero-sum in them: even if you work together to increase the size of the pie, the question of how the pie will be divided always stays pressing and relevant.

The grim implications

Two questions that are worth asking: How important are the results of these games are to our well-being? can someone lead a happy life while consistently finding himself on the losing side of these games?

The answer to both of these questions seems to be complex. Losing a war can be a matter of death or enslavement, while we can easily imagine someone who utterly sucks at salary negotiations but yet still lives a perfectly good life.

While there is a significant variance in the importance of different games, in aggregate, doing well in zero-sum games is extremely important for thriving and happiness.

The losers of the male intrasexual competition, which are most nowadays most commonly known as incels – seem to be extremely miserable, even though most of them are better off in most facets of life (health and material goods) compared to the average person in earlier times. It makes sense that a failure in something as crucial (in the evolutionary sense) as reproduction will cause suffering – just like hunger, thirst or physical pain.

In the case of status, it seems that there is at least some research that shows that social status influences well being, but most of the weight of the importance of status lies in revealed preferences, And while there is a lot of plausible deniability involved I think the work of both Hanson and Veblen is very convincing in demonstrating just how much people really care about status.

Now if we accept the idea that winning zero-sum games is very important for human thriving and happiness the logical implications are quite unsettling.

First, it seems that conflict theorists were mostly right all along. If one’s chance at happiness and thriving depend on zero-sum competition and position-based results then there is a very fundamental conflict of interests between people, and it’s quite rational to do things that might hurt everyone but will help you and your ingroup to beat the competition. It might be better to be the chief of a bush tribe than a low-status incel in modern Switzerland.

It also means playing by the rules is a bad strategy if you’re at the bottom of the totem pole – and you might be better with the riskier “get rich or die tryin’ ” approach. If you got dealt a bad hand playing by the rules means you’re probably going to lose and if these zero-sum games are crucial for your happiness and reproduction it makes sense to do anything that it takes to win, hence: “All is fair in love and war.”

But the propagation of these truths might be bad both for society, and for the ruling elite that benefits from the fact that people play positive-sum games, As they both get to keep their positional advantage and enjoy the economical growth that is the result of people creating value. That’s why the millionaire Naval Ravikant tells the clueless masses to avoid zero-sum games while aiming for status himself.

[1] – A more accurate term would be low-positive-sum games. Situations where the utility of the expected Pareto improvements is very low compared to non-Pareto improvements.


21 comments, sorted by Highlighting new comments since Today at 6:20 PM
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This piece seems to fundamentally misunderstand what zero-sum games are and why they matter.

There is no substantive difference between negative-sum and positive-sum games; the only difference is between zero-sum vs nonzero. If there's a possibility for both sides to be worse off, then there's a possibility for both sides to be better off (by avoiding the both-sides-worse-off outcome).

Even the "zero-sum subgames" are radically altered by the presence of nonzero-sum possibilities. This is the classic work of Schelling on negotiations (including things like salary negotiations, chores between a couple, or elections). The presence of negative-sum alternatives allows parties to use threats (i.e. threaten to make the negative-sum alternative happen if they don't get their way in the negotiation), which would not work at all in a true zero-sum game. In zero-sum, making the other party worse off is always better for me, so there's no reason to threaten - I just make them worse off whenever the opportunity arises.

The large majority of the examples in the post are nonzero sum, and even the exceptions are debatable - most real-world games allow some way for the parties to throw away resources.

This is a fair criticism of the game theory aspects - I concede it seems wrong. Do you also believe this mistake undermines the main point of the post - that positional results are important to happiness which makes it that not everyone can be happy?

I think that, after correcting the game theoretic aspects, the post provided very little argument for that conclusion. That's not to say that the rarity of true zero-sum games makes the conclusion implausible, it's just that it requires a different/additional argument.

even if you work together to increase the size of the pie, the question of how the pie will be divided always stays pressing and relevant.

Yes, the choice between "greater part of a pie" and "part of a greater pie" is somewhat a false dilemma; some people obviously have both. And when precisely those people tell you "please focus on making the pie grow, and forget about how it is distributed; don't worry, everything will turn out okay at the end", yeah, it sounds quite self-serving. It is obvious how they would benefit both from you making the pie grow and you not caring how the pie is distributed.

Funny thing is, if you take the opposite perspective... if you honestly believe that people who ignore the distribution of the pie and focus on making it grow, will somehow magically end up with a large part of the pie... then, the observed facts [people having the largest parts of the growing pie telling everyone that their mindset is focusing on making the pie grow] seem to match your belief, too.

And of course, yet another explanation is survivor bias: Some people focus on making the pie grow. Some of them succeed. Some of those also accidentally succeed at capturing a large part of the value they created... and those are the ones whose opinions get amplified because they are now the important people. Yes they are sincere, but no they do not describe a realistic picture. Anecdote is filtered data.

Or perhaps this is a case of the law of equal and opposite advice: Maybe some people are naturally focused on getting the greater part of the pie... and it may be very useful for them to realize that helping the pie grow (and grabbing the part they helped grow) is a viable strategy. Meanwhile, some other people are naturally focused on helping the pie grow, and those would benefit from advice how not to let all that added value slip away from their fingers.

It seems to me that the nice-but-not-naive approach is to take care of growing the pie while also taking care that you get a certain share of it. -- Yes, this approach deserves to be called nice. A nasty one would focus exclusively on taking the larger part of the pie, assuming that most likely there are enough nice and naive people who will focus on making it grow, especially if you ask them nicely and appeal to their sense of hope, or if there are not enough such people then everything is doomed regardless of what you do.

For example, in the context of employment, clearly understand the difference between co-owners and employees. If you are an employee, your salary is the only part of the pie you will ever get. When your boss tells you "hey, if we get this project right, the company will be a fantastic success", remember that he is talking about his part of the pie, not yours. Yes, he may become a millionaire, and he is probably a nice and hard-working guy who deserves it. None of that is going to pay your bills or feed your children, though. (Well, maybe unless you plan to marry him. But even then I'd strongly suggest to marry him before he becomes a millionaire.)

A possible solution is to make a deal about splitting the pie first, and then you can fully focus on growing it. Even that is not 100% reliable -- people can have multiple projects at the same time, so after making the deal about fair share, your partner can leave most work to you, and focus on his other projects that seem to promise greater rewards per unit of effort (remember this if you happen to talk to a venture capitalist) -- but it is already a better deal than you would get in most situations. Perhaps cooperatives should be a more popular form of ownership, but coordination is hard.

I would trust Silicon Valley billionaires more if they promoted things like UBI. But looking at their anti-salary-growth cartels, I guess even the idea of paying their employees fair market wage is too futuristic for them.

Even if the status game is zero-sum, that alone doesn't necessarily imply how much the people at bottom will suffer. There is some necessary part, like, of course, anyone would resent being at the bottom. But there are all kinds of unnecessary suffering that higher-status people are free to inflict on the lower-status, simply because it is enjoyable for the higher-status, and if you care about it too much, you signal that you are not sufficiently high-status yourself. There is an option to treat the poor with dignity; we just collectively decided not to take it, because it is more fun to poke them and laugh. (We especially like to laugh at people who happen to be both at the bottom of the social ladder, and on the opposite side of whatever political divide we perceive.)

Mostly agree with this post, but honestly, I think it's still a bit too optimistic. Growing the pie vs. Making sure you have a larger piece of the pie aren't equally important.

In general, making sure you have a larger piece of the pie is more important in most cases because it deals with existing value vs. future value (which entails risk and might fail). If you make sure you get a larger piece of the pie, you will increase your slice even if the pie doesn't grow while focusing on increasing the size of the pie might fail, or the pie might grow not enough to compensate you for share % drop. Increasing your slice of the pie is a more prudent strategy and can also increase your relative position in your society if we are talking about a society-wide pie (e.g., taxes)

I don't think status is a zero-sum game.  Some people may play it as such, unfortunately.  But some ways to increase your social standing also confer benefits to others without anyone losing out. By being being kind and considerate (as well as knowledgeable, competent, etc.) you can notice people's good qualities and confer status to others, flattening the status hierarchy and making it more multi-dimensional (making sure different types of talents get noticed).

It also depends what kind of status you're after. If you care more about the approval of people with depth and good character, that's easier to achieve in ways that build others up than if you care primarily about the most shallow metrics of status.

More specifically, interpersonal interaction has both a dominance dimension ("of status, dominance, power, ambitiousness, assertiveness, or control") and a warmth dimension ("of agreeableness, compassion, nurturant, solidarity, friendliness, warmth, affiliation or love"). Dominance is zero-sum, but warmth is not.

Cultures also vary in how much they emphasize the dominance and warmth dimensions. In more "status-flat" cultures (such as the Nordic countries), social conventions tend to de-emphasize status differences, making relative status less important and letting the warmth dimension matter more.

It seems interesting to me that I feel like I mostly encounter arguments such as "status is zero-sum so we can't ever make everyone happy" expressed by people from non-Nordic countries. The notion always seemed unintuitive to me, and I don't think that the reason is just "Kaj personally pays less attention to dominance status" since I do feel pretty sensitive to it. Rather, it feels like a significant part of it is Finnish culture just not caring about dominance status that much, relative to warmth, making it hard for me to see why the zero-sumness of status should necessarily be a significant problem.

Agreed. Status becomes zero sum when the dimensionality of competition gets reduced to 1 (otherwise known as a hierarchy). In an environment with specialization you wind up with a multi dimensional deference network where people are deferred to in their areas of expertise and everyone benefits from the efficiency of this. A status lattice, otherwise known as prestige.

That's a good point, but a "global status" definitely exists. For example - Elon musk has a higher status than Joona Sotala (Which most people here never heard of) even though they are both pretty much at the top of the games they are playing. 99.999% of the people in the world will be more excited to meet Musk than Sotala.

different status games and specializations still have relative importance, which is zero-sum, a mathematical intuition could be described as:
Importance of game (zero-sum) X position in-game (zero-sum)= total status
The product is still a zero-sum positional game, but it creates a more equal distribution than one-dimensional hierarchy.

if the things that status are getting you are satisficing and not maximizing this doesn't matter much. E.g. if Sotala is getting his needs met from the communities he is a part of Musk is not relevant.

That's true only if everyone could reach this theoretical threshold of status that will make them happy, but it's not clear that this is the case. 

e.g. if you're the best accordion player in your village it might not be enough if no one really cares about accordion skills - global status is important.

From a strict game theory perspective, zero sum games have a technical definition, ie being zero sum, that is rarely met in practice. A zero sum game is one where the opponents are perfectly opposed to each other. So it does not contain any outcomes that all players consider bad. In a zero some game, for one player to win, another must loose. For one player to loose, another must win. (Game theory usually only talks about 2 player zero sum games, because these have a nice mathematical structure. )

If we take a perfectly zero sum game, and give one player the opportunity to headbutt a wall (which gives them -1 util and doesn't effect the rest of the game) then the game is no longer zero sum. If you take 2 zero sum games and play one after the other, the result is not in general zero sum. 

To see this consider Alice and Bob, two expected money maximisers playing a game that always has exactly one winner. They each get a (possibly different) prize for winning. (and can't transfer money between each other) A game where Alice can win £10, or Bob can win £1 is zero sum (up to Linear transformation of utility function). But follow that with a game where Alice can win £1, and Bob can win £10, and the result is no longer zero sum.

The set of games I think you are really talking about are the games where there is a big difference between the Nash equilibria society often lands in, and the Parito optimal.

Can you provide an example of how you can get a significant Pareto improvement in the mentioned games? 

In a war, a parito improvement would involve neither side making any weapons, and working together to divide up resources in proportion to how they would be divided if they did have a war.

In status games, a parito improvement might be neither side buying expensive status symbols, instead buying something they will actually enjoy. 

These are not Pareto Improvements as they will lower the utility of the winning side...

It depends on the utilities. And what the other option is.  Take a war between Aland and Bland. Look at the results. Does Aland take all Blands territory? The parito improvement is to just do that without shooting at each other first. 

In status games, what exactly do you mean by status. Is it possible for everyone to just decide to hand bob high status. If so, a parito improvement is just to hand status out in the same way.

Here is a toy model of war. Each country has a utility of 100 for winning (say winning control over a disputed stretch of land), and a utility of -1 for buying tanks, whichever side has more tanks wins. Both sides buy lots of tanks, and one side wins. A parito improvement would be for that neither side buys any tanks, and the side that would win the war gets the land.

The war Pareto improvement is not realistic from a game-theory perspective if both of the players act rationally. Obviously, one can always imagine some deus-ex-machina-Pareto-improvement (A silly example would be to imagine that one of the sides creates a god that changes the game completely and prevents the war, and brings both sides to a post-scarcity utopia). Still, I think it misses the point as the idea is to play within the realistic versions of the games. Your toy model solution requires a level of cooperation/ability to predict the future that doesn't exist.

Status is hierarchical and always relative; by increasing the status of bob, you effectively lower the status of all the other players. If you increased the status of everyone by 10% (whatever that means...), reality wouldn't change at all.

A pareto improvement is a change that harms no one and helps at least one person. The options I've outlined don't always happen. (Although countries often don't go to war, it isn't clear if this is cooperating in a prisoners dilemma, or that they expect going to war to be worse for them.) The point of a Pareto improvement is that it is something within the combined action space. Ie something they would do if they somehow gained magical coordination ability. It doesn't realy on any kind of magical capabilities, just different decisions. If both agents are causal decision theorists, and the war resembles a prisoners dilemma situation, "cooperate - cooperate" might be unrealistic, but its still a pareto improvement. 

Consider also that when a zero-sum game is embedded in a positive-sum one, often the most effective way to negotiate is to threaten to walk away from the positive-sum game if you don't get a bigger share of the spoils (e.g. threaten to leave the job if you don't get a rise). The simplified version is the ultimatum game: 

This also means that holding a positive-sum trade sacred has the side effect of freezing the zero-sum part of it to the status quo.

I wrote an article on this subject (i.e. why do we play zero-sum games while praising positive-sum games?)

Is this sentence correct, or is a verb missing after 'employee'? 'every extra dollar the employee is a dollar that the employer could have and vice versa'

I also think one of the are's is extra: 'Two questions that are worth asking: How important are the results of these games are to our well-being?'