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 cas-
cade will begin, pushing you further and further down.
Monopolyis 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 at-
tack 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 some-
times 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 ramifi-
cations. As an engineer in the 1990s, I spent a lot of
my time figuring out how to ensure that the sys-
tems 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 sail-
boat 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 engi-
neering 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 col-
lapse if nudged from the front or the rear. (Some engi-
neers 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 groundbreaking 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 cer-
tain systems gravitate toward either stability or insta-
bility. All you have to do is play board games.
Imagine, for instance, a game in which there was
a built-in stabilizing mechanism that actually penal-
ized 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 “set-
tlements” 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 win-
ning 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 me-
chanics are the opposite of those at work in Monopoly:
They are designed in a way that helps underdogs in-
stead of penalizing them.
Similarly, in the epic 1970s-era war game Civiliza-
tion—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 ad-
vantage, 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 los-
ing 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 Monopolycould be retro-
fitted 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 as-
sessed for street repairs: pay $40 per house and $1 15
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 win-
ning player does not get $200 every time he passes Go.
I could provide more examples, but you get the pic-
ture: These rules all serve to add a stabilizing dose of
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