Game Theory: The Force that Binds Us
When two rights make a wrong.
I. Lame Theory
I used to think Game Theory was a little overrated. I’d often heard it discussed but I associated it with a small subset of niche problems. Like how knowing the atomic number of neodymium is a fact that’s useful in very specific contexts, but probably not useful generally.
Recently however, I had an epiphany and now I see it everywhere. If anything, it's not discussed nearly enough. I imagine this is how Newton must have felt when he realized that the force that governs falling apples is the same force that governs the celestial bodies. But first, lets walk through a few intuitions that led me to this point.
II. A Primer on Game Theory
The game that receives the most attention is the Prisoner's Dilemma. Briefly, The Prisoner's Dilemma has 2 players. The players have two available choices: either Cooperate or Defect. The payoff each player receives depends on both players' choices. A Nash-Equilibrium is a solution where each player cannot improve their own payoff whilst the other players' choices are held constant. A Pareto Optimum is a solution where each player cannot change their strategy without making the other players' payoffs worse.
cooperate defect player_b cooperate [2, 2], [0, 3] defect [3, 0], [1, 1] player_a
Due to the way the payoff matrix is structured in the Prisoner's Dilemma, both players are incentivized to defect. And a (Defect, Defect) solution leaves both players with a worse payoff than if they'd both cooperated. It's counter-intuitive at first glance, but it's helpful to understand many unfortunate phenomena, such as the existence of warfare. The key to understanding why bad outcomes dominate is to realize that:
A) each player has less control over their destiny than that of others;
B) each player's destiny is perversely related to the destiny of others. Choosing the strategy which slightly increases your own payoff happens to completely sabotage the payoff of others. And if we assume players are rational actors who are completely indifferent to the suffering of others, the dominant strategy is to Defect.
The Prisoner's Dilemma is not the only game in town. There's other interesting 2-player games with different optima and different equilibria. And there's other games that vary the rules in other ways. However, I don’t think we need to extend the analysis that far for our purposes.
III. The Unreasonable Ineffectiveness of Circular Reasoning
Circular Reasoning is fallacious. Fallacies are invalid. Therefore, Circular Reasoning is invalid. Right? Well, sort of.
When an argument is rhetorically invalid, it's usually because it's deductively invalid. Circular Reasoning is an exception though. The reason it's considered a bad argument isn't because the conclusion fails to deductively flow from the premises. (A => A) is tautologically true, after all. Rather, the reason it's considered a bad argument is because the conclusion lacks novel information. But what if it were possible to salvage Circular Reasoning as being a useful construct?
More generally, circular motion signifies stability and periodicity. I.e. that some object often ends where it started. E.g. the Water Cycle uses a circular metaphor to convey the idea that the total amount of water in the environment doesn't change. Recycling is meant to take manufacturing waste, which at some point consisted of raw materials, and turn them back into raw materials. The Otto Cycle is a process used to describe combustion engines, which perform work continuously and reliably. Yet when it comes to logic and rhetoric, circles are bad. Is there no place for circles in this context?
Consider the JK flip-flop. They're circuits that typically constitute the RAM in computers. I.e. they're memory circuits. These circuits are useful because they store information over time. If a latch's truth-value is set to (0) at t=0, its truth-value 1will continue to stay (0) for t=1, t=2, t=3. I.e. it's periodic and self-reinforcing and stable.
“Wait what? Don't memory-cells also have the ability to store both 0's and 1's? How does it flip? Is it really a circle?” Well I suppose it's more like a figure-eight, since latches also have the ability to be “toggled”, in addition to the ability to be “set to 1” or “set to 0”. In any case, the broader point is that circularity, when applied to the domain of logic, often looks like a self-fulfilling prophecy. Which is a characteristic the concept has in common with Network Effects. Perhaps we can use this to identify analogous phenomena.
IV. Network Effects
Network effects are something I typically associate with telephone companies and social media. Under normal circumstances, the utility a user derives from some product or service is constant w.r.t the number of other users. E.g. when I buy a sneakers, the usefulness of those sneakers is independent of how many others bought that type of sneaker. But when Network Effects are in play, each user's utility increases with the number of users who already use the same product/service (and therefore part of a "network"). E.g. the usefulness I derive from Facebook is dependent on how many others also use Facebook. If all my friends and family are already part of Facebook, Facebook suddenly looks attractive to me. But if nobody uses Facebook, Facebook has little use to me.
I used to believe that this was all there was to know about Network Effects. I would be wrong. E.g. Gwern posits that Network Effects drive flamewars, such as those fought over politics, religion, programming languages, etc. And Antonio Garcia of The Pull Request (it's hard for me to find a point where he lays out this view explicitly) posits that the Network Effects of language, as amplified by the Gutenberg Printing Press, is what historically led to Nationalism. And Moldbug, posits “The Cache Theory of Cash”. TLDR money is money because it's the commodity with the highest rate of appreciation, which causes its functionality as a currency to be self-fulfilling. I.e. it's a bubble that cannibalizes other bubbles.
So by now, the concept of Network Effects seems to have a lot of explanatory power. I started to question whether there was something I was missing. If the isomorphic nature of all these phenomena had previously flown under my radar, maybe I didn't understand the concept of Network Effects on a deep level.
V. The Key that will Pierce the Hash-Tables
The key to this puzzle also came from Moldbug. In a different post, Moldbug explains his solution for breaking up Facebook's monopoly. In his opinion, a tech-savvy government would require media-giants to publish their communication-protocols. E.g. Facebook would continue operating normally, but indie devs would be able to write customized clients which tap into Facebook's extant social-network through an API. In theory, this would break the monopoly-esque network-effects of Facebook, without the U.S. Government needing to artificially split Facebook into different companies via anti-trust law.
While this is certainly an interesting alternative to anti-trust law, the more valuable insight for me was that "Protocols = Networks". When I think of networks, I think of a web of dots. When I think of protocols, I think of a behavior or methodology. They don't seem to bear any relationship, prima facie. But really, they go hand in hand. Because in order for a node in a network to associate with another node (e.g. finding friends on Facebook), the two nodes often need a standard way of interfacing (e.g. via an API). And anyway, isn't "a protocol" just another way of saying "a standard"? And isn't "a standard" just another way of saying "social norm"? And isn't "social norm" just another way of saying "culture?"
VI. We Live in a Society
I think we now have enough context to understand what I like to refer to in my headcanon as:
The Fundamental Theorem of Asabiyyah:
Society is Game Theory all the way down.
"Asabiyyah" is an Arabic term which means "social trust" or "social cohesion". It's associated with Ibn Khaldun, a 14th century Islamic Scholar often remembered for his cyclical theory of civilization. The theory goes: a cohesive brotherhood takes control of the state; society flourishes; brotherhood gets lazy and complacent; infighting and decay; coup d'etat by upstarts; cycle repeats.
The other part of the name is just a silly likeness to the Fundamental Theorem of Algebra.
When I first encountered Game Theory, it was described as a punnet-square between 2-players. My mind tended to stick with that 2-player assumption. When there's only 2 forces, the equilibrium isn't hard to perturb. But when I tried to generalize the idea of an equilibrium beyond 2-player games, I realized that coordinating a switch from one equilibrium to another becomes increasingly difficult. Piling more players onto an equilibrium amplifies the self-fulfilling positive-feedback loop. I.e. they're subject to network effects. I think the most apt metaphor is that of a gravity-well. And I believe this mental model neatly unifies a variety of multi-polar social phenomena.
VII. Wait, it's all Game Theory?
Always has been. Below is a list of some of the examples I understand. Economists have a longer list. Though I feel like economists are biased toward discussing things that are more legible.
VIII. Glass Canons
Consider fiction. Starwars fans are upset at Disney. XKCD pretends The Matrix 2 and The Matrix 3 don't exist. Nintendo is highly protective of its intellectual property. Why? Because the canon is an equilibrium. I think these equilibria can be fragile relative to the other examples, since fiction is spread across a countless number of IP's.
When Disney released their Starwars sequels, they polluted the Starwars brand. The IP may have been owned by Disney de jure. But it also belongs to the public de facto. The idea takes on a life of its own in the public consciousness. If a non-canon interpretation gains popularity and conflicts with the actual canon, the public can become confused about which version they're referring to when discussing the IP. The fans and/or the original author might not appreciate this fracturing of the canon.
IX. Flip-Flops
One example is Reflective Equilibrium. I brought up flip-flops earlier, because I wanted to associate circularity with memory and logic. This might seem odd, since a latch is just a single memory-cell, and Game Theory is usually analyzed in the context of a game between 2 or more players. But we can imagine the latch itself as setting up a game between electrons.
Similarly, it’s often said that "one man's Modus Ponens is another man's Modus Tollens". For those unfamiliar with formal logic, let's unpack what this means. Modus Ponens is a form of logical implication that most people understand at least implicitly. E.g. "if it's raining, the sky is cloudy; it's raining; therefore the sky is cloudy". Modus Tollens is a related form of logical implication that asserts also asserts "if it's raining, the sky is cloudy" but then flips the position and truth-value of the other two propositions. E.g. "if it's raining, the sky is cloudy; the sky isn't cloudy; therefore it's not raining".
Modus Ponens Modus Tollens
P -> Q P -> Q
P ~Q
=> Q => ~POften times, two parties with opposing viewpoints will agree on P -> Q, but one will apply Modus Ponens while the other party will apply Modus Tollens. E.g. a conservative might posit "if you have a right to guns, everyone has a right to guns; you have a right to guns; therefore everyone has a right to guns". But a progressive might say "If you have a right to guns, everyone has a right to guns; everyone does not have a right to guns; therefore you do not have a right to guns". Both pundits have internally consistent views, yet arrive at opposite conclusions. A bundle of consist propositions is often called a reflective equilibrium, because it's a system of beliefs that's resistant to perturbation upon internal reflection. When you scale this across individuals in a society, I think it's often the case that you ends up with certain ideological positions that occupy certain game-theoretic equilibria, where the "game" is proving the ideological opposition wrong by finding inconsistencies in their belief-system.
X. Race Conditions
Another example is racism. The term "racism" is a shorthand for "racial discrimination". And if we're to believe in the West's current Zeitgeist, it's the root of all evil. Though I have a somewhat different perspective.
Although he did not invent the idea, Wikipedia informs me that the term "reflective equilibrium" was popularized by John Rawls while advocating for his personal theory of justice, in which the terms of the social contract are collectively selected from behind a "veil of ignorance". I.e. each person would be ignorant of his specific circumstances in life such as gender, ethnicity, socio-economic status, etc. Additionally, each person would be ignorant of others' opinions on what constitutes a good life.
Theoretically, reflective equilibrium is being used here as a tool to incentivize each person to choose the terms of the social contract impartially and equitably. Ironically, his objective of optimizing the social contract for impartiality and equitability is itself part of a reflective equilibrium. Meanwhile, the political right seems to advocate for a contrary position in which self-interest takes precedence.
Suppose you're a scientist exploring the arctic and you encounter a polar bear. Do you try to befriend it? or do you run in the opposite direction. One one hand, to assume that it's dangerous would be unfairly prejudiced against to that particular bear. You've only just met it. It could be the friendliest polar bear in the world. On the other hand, it could also eat you. If you don't run away, it probably will eat you. Do you want to take that chance? The homunculus on your shoulder that advises you to stereotype the polar bear is the same homunculus that advises you to stereotype your fellow man. And this stereotyping appears to be what Rawls's egalitarian thought-experiment was trying to avoid.
Acting on stereotypes is often a rational, self-interested response to a situation where an agent's information is imperfect/incomplete. To throw this information away in the name of fairness is to sacrifice your own self-interest for a chance of achieving the Pareto-Optimal solution. In a 2-player game, coordinating a Pareto-Optimal solution is relatively easy. In a society of millions, the opportunity-cost of any one person choosing to cooperate gets multiplied a million fold and coordination becomes harder.
Now, being non-racist is all fine and dandy. (No sane person enjoys defection in the abstract, except maybe psychopaths.) But it might be useful, even for progressives, for us to recognize that non-racism is not a forgone conclusion, and that contrary opinions are not necessarily driven by irrational hatred.
XI. Confidence Games
The Diamond-Dybvig Model was developed to describe bank runs. A bank run is a situation where the bank runs out of money. To understand how it arises, it's helpful to first understand how a bank works normally.
When you deposit money in a bank, that deposit doesn't just sit in a vault, it gets lent to someone else. Maybe it's a business loan, or a mortgage, etc. And even though the bank gives the depositor a small amount of interest, the bank still makes a profit in the long-term by charging a higher interest-rate on money given to the borrower.
The money the bank loans out is "illiquid", whereas the money the bank receives from the debtor is "liquid". A liquid asset is an asset someone can buy or sell quickly and easily. Whereas an illiquid asset is "semi-frozen" in the sense that it's hard to move it through the market without selling at a large discount or buying at a premium. The deposit is liquid, because the depositor expects to take out the money at any time. But the loan the bank gives out is usually "tied up" in some project, and therefore will only be repaid back to the bank over time.
Here's the catch. Normally, a bank keeps a fraction of the money in a vault, so it can satisfy small withdrawals. But if the depositor asks to withdraw a lot of money at once, the bank may not have enough money in its vault to cover the withdrawal. When you scale this to thousands of depositors, some of the depositors become afraid that the bank *might* go bankrupt before they can withdraw their own money. Which results in everyone trying to withdraw their money simultaneously, which means the bank does go bankrupt. Which is how a bank-run happens.
Diamond-Dybvig is a Stag Hunt. Cooperate/Cooperate and Defect/Defect are both stable strategies. Though simultaneously, Cooperate/Cooperate is Pareto-optimal. So long as each individual depositor is confident that the other depositors will cooperate, each individual depositor will also choose to cooperate. But if each depositor is distrustful, each depositor will defect.
This dynamic not only applies to bank runs, but also to other commodities. For example, when everyone was losing their mind over toilet-paper during the COVID pandemic, that was the same dynamic. This dynamic also plays out in bubbles in the stock market. This is why economists are always speaking about "consumer confidence".
XII. Riot Games
Several years ago, I remember reading a article which proposed a theory about how riots form. I think it was this one, though my memory is hazy. The theory goes:
The layman's account of riots is they're caused by the voices of the oppressed and unheard. This theory, however, is unable to account for riots undertaken by the fans of a victorious sports team. A better hypothesis is that riots represent a tragedy of the commons. Each member of a crowd may want to participate in an extant riot, but no member wants to initiate a riot for fear of being singled-out by police. This then represents a coordination game. Occasionally, something or other lowers the cost of initiation. Maybe the size and chaos of the crowd can insulate a potential initiator, or maybe the police become distracted, etc. Then someone breaks a window or alights a car, and this forms a Schelling Point around which other members join. And suddenly, a riot.
XIII. Just One More Turn
In machine learning, there's an idea called The Multi-Armed Bandit Problem. Suppose there's a row of slot machines. You know nothing about their pay-off structure. How do you maximize your earnings?
One strategy might be to try a bunch slots until you find one that seems profitable, and then you ignore the rest. Another strategy would be to experiment with each slot-machine extensively, in order to learn about their payoff structure in detail. This strategy has a higher chance of finding the best slot-machine, but you spend a lot of your bankroll getting there. Another reasonable strategy is to hold onto your money, since there's no guarantee that the slot-machines offer any payout at all. Sometimes the only winning move is not to play.
Information has a cost. This results in a trade-off between exploring vs exploiting. No single strategy dominates in all scenarios. I.e. no matter what strategy you choose, there's always a chance that you'll either pay too much money experimenting with unprofitable machines, or you'll pay too little money because you didn't experiment with a particular machine enough to realize it had an infinitesimally unlikely jackpot. In either case, a different strategy might have done better. But since there's no way to incorporate that information into your analysis a priori, the question of the "best" strategy is simply a wild guess.
Observe, however, that the over-exploration strategy is optimistic about the existence of a jackpot, whereas under-exploration is pessimistic about the existence of a jackpot. Huh, this almost sounds like the difference between those who are politically progressive, and those who are politically conservative.
XIV. Risk of Rain
Why are cities predominantly comprised of progressives, while the countryside is predominantly comprised of conservatives? Because cities lower the barrier of cooperation, and the benefits of cooperation shield them from the demands of nature. Or as economists like to say, cities benefit from positive-externalities of agglomeration. However, it makes their residents more dependent on each other. Conservatives, on the other hand, are more self-reliant. They are more directly exposed to the harsh demands imposed by nature. As such, they often take a more pessimistic view by planning for the worst. As such, defection has greater appeal.
This is sufficient, I think, to explain why e.g. a Texan who lives 40 miles from his nearest neighbor might have a different relationship with guns than someone who lives in NYC. The Texan cannot rely on police to defend himself from crime or wild animals, since the police would be too far away. Gun ownership is quite attractive in this scenario. Meanwhile the city-dweller lives in close proximity to his or her neighbors. Some of whom have guns. Maybe… too many?
XV. The Logic of Logistics
Consider David Ricardo's notion of Comparative-Advantage. If two nations trade with each other, and if each specializes in the production of their comparative advantage, they can both achieve a higher standard of living than if they hadn't. It's practically a free lunch! At least until trade is disrupted. Whether by war, tariffs, natural disaster, pandemic, etc. Then the trade stops and each country has an imbalance of the material goods they need.
Incidentally, I remember hearing once (I forget where) that the U.S. and Russia are the only modern economies that have a little bit of everything, and this economic independence is one of the main reasons why they were able to become superpowers. I don't know enough about economics to vindicate this, but it sounds convincing to me. Historically I've been unimpressed with the U.S.'s adventures in foreign policy. But seeing geopolitics through this lens has softened my attitude.
XVI. Why are other people so dumb?
Now that I’ve associated the concept of Game Theory with Equilibria and Network Effects, I can’t help but look at any given social or economic phenomenon and not immediately wonder about the equilibria. It’s useful to frame this explicitly because many social phenomena we take for granted as being mono-polar, turn out to be multi-polar on closer inspection.
This solves a class of interesting questions about why other people often seem so obviously wrong. Often, people use what I like to call in my headcanon “linear inference”. which looks like
A, B, C, therefore D
But since the conclusion D feels “solved” and “uniquely true”, there’s never any curiosity to venture beyond what has already been decided as true. Consequently, they miss other conclusions which may turn out to be equally valid. To me, this reinforces this heuristic I often use where I remind myself to explore the other regions of state space of a given question before drawing any conclusions.