The Skeptics Society & Skeptic magazine

Imagine that you are in the late stages of a game of Monopoly, battling it out against a lone remaining opponent. You each control a bunch of expensive properties, all loaded with hotels. Both of you also are cash-poor, with no spare properties left to mortgage. Every roll of the dice carries high stakes. If your opponent lands on one of your hotels, the only way he can pay the rent will be to sell off his own hotels at a 50-percent discount (because that is how the rules of Monopoly work), and vice versa. Which means that the first player who lands on an opponent’s hotel will not just lose a lot of money: He will also lose the assets he needs to earn that money back. In real life, the analogy would be the poor worker in Victorian Britain who, unable to pay a small debt, goes to debtor’s prison, which further compromises his ability to earn a livelihood, and so pushes his family deeper into complete destitution.

“Well, that’s capitalism,” you might say. Perhaps. We will get to that later. For now, I want to emphasize that this aspect of Monopoly — the poor get poorer, while the rich get richer — is not only typical of laissez-faire economics. It is also characteristic of a certain dynamic observed in nature, engineering and human relationships, one that mathematicians sometimes describe as unstable equilibrium.

Take a simple physical metaphor: a marble resting at the bottom of a salad bowl is going to exhibit a stable equilibrium — because small movements in any direction will push the marble up against the walls of the bowl, and the marble will roll back toward its start position, also known as its equilibrium point.

If the salad bowl is turned upside down, however, and the marble is placed at the top of it, the marble will exhibit an unstable equilibrium: Even if the marble is balanced perfectly on top of the bowl, and so remains temporarily motionless, a nudge in any direction will lead to a feedback loop whereby the marble rolls off the bowl, moving slowly at first and then accelerating downward. In general, a stable equilibrium tends to correct itself, restoring the balance of offsetting forces that held it in check to begin with; while an unstable equilibrium tends to destabilize in one direction or another, until the system in some way collapses or reaches a different stable equilibrium.

Now let us return to Monopoly. You and your imaginary opponent are moving your tokens around the board, seeking to avoid one another’s hotels. In a way, you each inhabit an economic state analogous to the marble sitting on top of that salad bowl. All you need is a single initial nudge toward poverty and a cascade will begin, pushing you further and further down.

Monopoly is not the only game in which this kind of phenomenon plays out. The same thing happens in chess: If your opponent blunders away a bishop or a rook, she not only has one fewer pieces available to attack your king, she also has one fewer pieces available to defend her remaining pieces. It becomes more likely that one of those other pieces will also be lost, and then another, and another, until her side collapses completely. This is why expert chess players sometimes will resign a game after losing just a single pawn — because they know that top-flight opponents will exploit any tiny advantage so as to create larger and larger advantages, until the game ends in a rout. This is why chess is such a tense game.

Stability theory has enormous real-world ramifications. As an engineer in the 1990s, I spent a lot of my time figuring out how to ensure that the systems I designed, whether software or hardware, would not go haywire if they were nudged in one direction or another. In some cases, solutions can be obvious and low-tech. Remember those old toys called Weebles? The reason “Weebles wobble but they don’t fall down” is that the toy’s weight is bottom-loaded. Similarly, a sailboat in a windstorm also can exhibit a stable equilibrium: The more the wind pushes the sailboat to one side, the less sail height is presented to the wind, meaning that less rotational force is applied to the boat — a true self-correcting system (within certain environmental limits).

But in other cases, ensuring stability in an engineering system requires high-tech methods. Think of a Segway scooter, a system that, like a marble sitting atop an inverted bowl, very much looks like it should collapse if nudged from the front or the rear. (Some engineers call it the “inverted pendulum” problem.) The system achieves stability only through the ingenious use of hidden electric motors, gyroscopes and tilt sensors.

I went through a period of life when I was fixated on the nature of dynamical systems — including the chaotic dynamical systems represented by certain forms of fractal geometry, which I discovered through James Gleick’s ground-breaking 1987 book, Chaos: Making a New Science. It is a rich area of mathematical modeling that I am giving only the most superficial treatment in this text. But you do not have to be a mathematician or engineer to appreciate the way certain systems gravitate toward either stability or instability. All you have to do is play board games.

Imagine, for instance, a game in which there was a built-in stabilizing mechanic that actually penalized a player for being in the lead? Well, guess what: I just described the “robber” in Catan (formerly known as Settlers of Catan), a popular game in which players compete to create networks of resource-gathering “settlements” on a modular hexagonal map-board. Of course, there is no rule that says the robber has to be placed in a way that targets the winning player. But that is what usually happens (except when the winning player herself is repositioning the robber), since everyone has a built-in incentive to take down the player closest to victory. In this way, the game mechanics are the opposite of those at work in Monopoly: They are designed in a way that helps underdogs instead of penalizing them.

Similarly, in the epic 1970s-era war game Civilization — in which ancient armies seek the domination of Eurasia — the losing player gets the benefit of moving her troops last in any game turn (a huge strategic advantage, since you can see what everyone else is doing before you commit to your own strategy). And in the popular German game Power Grid, in which players compete to build power-generation networks, the losing player gets to bid first on available fuel sources, when they are cheapest. Think of these elements as the gameplay equivalent of the sensor-driven motors in a Segway that push back against gravity and keep the thing from falling over.

It is not hard to see how Monopoly could be retrofitted in the same stability-encouraging way. Indeed, the game already has a few stabilizing elements such as the Community Chest card that reads “You are assessed for street repairs: pay $40 per house and $115 per hotel you own.” There is another version of this card in the Chance deck that assesses costs for houses and hotels at $25 and $100 respectively. Both of these cards greatly penalize players with lots of houses and hotels, but do little to harm the interests of a player with few assets.

If you wanted to make a more “stable” version of Monopoly, all you would have to do is add a lot more cards like this to the decks, and perhaps increase the assessed amounts. You could also stipulate that the person who draws this card does not pay the assessed fees to the bank, but instead pays it to the player with the fewest houses and hotels. Or you could make it progressively more expensive for players to buy houses and hotels depending on how many houses and hotels they already own. Or you could stipulate that the winning player does not get $200 every time he passes go. I could provide more examples, but you get the picture: These rules all serve to add a stabilizing dose of the-rich-get-soaked or the-poor-get-a-helping-hand to the game’s naturally unstable rich-get-richer dynamic.

Of course, what I am describing here is not just a way to fix Monopoly. It is a way to fix one of the basic problems with capitalism as we now experience it in the era of globalized winner-take-all commerce. A hundred years ago, a successful store owner could put other store owners in his neighborhood out of business. In 2020, Amazon and Alibaba are pushing whole bricks-and-mortar retail sectors into bankruptcy on a global level. Meanwhile, Google and Facebook are vacuuming up the lion’s share of web advertising. As The New Republic reported in late 2018, monopolies now penetrate almost every economic sector: “Two companies make 64 percent of American diapers; one company builds 52 percent of America’s mobile homes; two companies produce 78 percent of its corn seeds; and one company assembles 61 percent of syringes.”

As many economists have noted, the resultant income inequality is not just a threat to egalitarian ideals. It is a threat to capitalism itself, since the health of the free market always will depend on a viable middle class that supplies both demand and labor to a mass-retail economy. (Poor people do not have enough money to buy much. And the super-rich spend a very small percentage of their income on goods and services.)

A game of Monopoly ends when one player has all the money and everyone else is bankrupt. But a human society is not something that you fold up and put back in the box. It is not supposed to end. So you need a way to stabilize the economic dynamic, to make sure the rider doesn’t fall off the Segway, to keep the marble on top of the upside-down salad bowl. Otherwise, you get depressions, financial crises and even revolutions.

Critics of capitalism often decry the “greed” that animates successful entrepreneurs. The real problem, however, is not the amount of money made by people at the top; it is the systematic suppression of people at the bottom. The real-life equivalent of the Monopoly player who has to mortgage all his money-making assets to pay his debts is the hand-to-mouth day laborer who, unable to pay his car insurance, loses his car and, unable to drive to his job, is unable to pay his rent. The villain here is not necessarily the avarice of the banker who loaned this poor fellow his money in the first place. It is the unstable dynamic of a system that mercilessly drives some people down to the bottom through a succession of cascading misfortunes.

To experience the board game version of this kind of misery vortex in Monopoly is to appreciate the advantages of the welfare state, which, when it is functioning properly, doesn’t just redistribute money from rich people to poor people. It also softens the iterative feedback dynamics within the system so as to ensure that minor nudges — a lost job, a criminal conviction, a divorce, a medical setback — do not create feedback effects that ultimately produce a full-blown personal catastrophe. Job training, public health care, a humane criminal justice system, community housing and support for single mothers are examples of programs that can achieve that effect.

It has been almost thirty years since I devoted myself to the academic examination of stability theory and dynamical systems. Regardless, it is the sort of subject that, once studied, can never be forgotten. And this kind of analysis continues to color every aspect of my outlook on life — including the way I think of the future of our species.

Consider climate change, perhaps the most important issue facing the planet. One of the reasons why climate modeling is so complicated is that our climate is, on at least one level of analysis, an unstable dynamical system that, if pushed hard in one direction (say, by massive surges in atmospheric carbon-dioxide concentrations) can cause a cascade of feedback effects that compound the initial perturbation, and send the whole atmosphere into a radically different equilibrium state.

Understanding the nature of these “feedback effects” is critical if we are to understand the threat. To take one example, a warming earth causes glaciers to melt, thereby decreasing the amount of surface snow and ice that reflect solar radiation back into the atmosphere. Thanks to this sort of positive feedback mechanism, a warmer earth keeps getting warmer, melting more ice, absorbing more solar radiation and so on, until Miami Beach is chest-deep in water.

Or consider war, that ancient scourge of human civilization. “Firepower and heavy defensive armament — not merely the ability but also the desire to deliver fatal blows and then steadfastly to endure, without retreat, any counter-response — have always been the trademark of Western armies,” wrote Victor Davis Hanson in his 1989 classic, The Western Way of War: Infantry Battle in Classical Greece. The reason why these ancient battles typically were so decisive — “a single, magnificent collision of infantry,” as Hanson described the archetype — is that the brand of warfare waged by Greek phalanxes (and, later, Roman maniples) often exhibited the same fundamentally unstable equilibrium you see in chess, even when the adversaries were, at the dawn of battle, evenly matched.

When soldiers lost their nerve because an aspect of the battle initially went poorly, or because they were surrounded by a flanking maneuver, they sometimes would turn and flee, progressively throwing the soldiers around them into greater states of confusion and terror, and exposing everybody to complete slaughter. This domino effect was on bloody display at Adrianople, for instance, in 378 AD, when Gothic cavalry surrounded and hacked to death a larger force of Roman troops, thereby accelerating the fall of the Western half of the empire. Something similar happened six centuries earlier, at Cannae, where 50,000 Carthaginian troops commanded by Hannibal massacred a force of 86,000 Romans almost to the last man. In the first two years of World War II, the German army performed roughly analogous feats of arms by using columns of blitzkrieging tanks to encircle and defeat Polish, French and Russian defenders.

This helps explain why these conflicts are such popular themes for war games. Unstable battle dynamics tend to produce exciting, dramatic results. World War II, with its highly kinetic battles, has inspired more war games than any other war. Indeed, the 1942 Battle of Stalingrad alone (which ended with the encirclement and massacre of the German Sixth Army) has been the subject of at least 70 published board game titles.

Compare this with World War I, which is a relatively rare subject for board-game designers. The reason is obvious: The hyper-stable trench-warfare dynamic that governed the conflict makes gameplay predictable and boring. In World War II, the availability of massed tanks and air power meant that an attacker could apply enormous striking power in a way that could easily overwhelm an enemy’s localized defenses. In World War I, on the other hand, the reliance on trenches and machine guns created the opposite dynamic: Many attacks resulted in hideous casualties for the attacker and few for the defender. Any perturbation to the battlefield dynamic would usually end with a reversion to the status quo.

Does this suggest some sort of simple, linear relationship between battlefield dynamical instability and gaming fun? No, because at some point, a military dynamic becomes so unstable that it does not really lend itself to any satisfying form of recreational simulation. It is notable, for instance, that hyper-modern forms of warfare, especially those involving standoff missile systems or nuclear payloads, are not particularly popular themes among war-gamers. If you can annihilate whole countries with the push of a button, the game becomes a simple race to see who can push the button first. There have been some good games produced on the Cold War theme (such as Twilight Struggle), yet these tend to avoid the apocalyptic military aspect and instead focus on espionage, geopolitics, diplomacy, trade and technology.

In gaming, as in some parts of life, there is always going to be a sweet spot between perfectly stable and perfectly unstable system dynamics. The rich-get-richer aspect of Monopoly may produce bitterness and social friction. But on the other hand, no one would want to play a perfectly socialistic version of the game, in which all income is distributed equitably, no one ever goes bankrupt, and the game never ends. Likewise, a real-life economy in which there are no winners and no losers would not work because, as 20th-century experiments with communism showed us, an economy in which hard work yields no personal benefits is an economy in which no one does hard work.

Board games take inspiration from real life. That does not mean they always reflect the values and preferences we exercise in our real-life capacities as workers, family members, friends and political actors. Some of us may be drawn to the cutthroat dynamical instability of Monopoly because it makes for exciting game play, while also recognizing the fact that real life has to follow different rules because humans have more complex and urgent needs than game tokens.

Even so, the dynamics that govern Monopoly can help us understand how much of the character of our societies is embedded in — and dictated by — the dynamical feedback processes encoded in our economy and laws. If you want to improve the moral character of a society, you do not necessarily have to change the way people think and feel. Sometimes, all you have to do is fiddle with the rules that govern what happens every time they pass Go.