On Sugar Mountain

Oh, to live on Sugar Mountain

With the barkers and the colored balloons,

You can't be twenty on Sugar Mountain

Though you're thinking that

You're leaving there too soon 

--Sugar Mountain, Neil Young

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Below is a mathematical model by researchers Joshua Epstein and Robert Axtell which suggests that a trend toward increasing economic inequality in any economic system is likely, and maybe even an emergent property of economic systems (fr. Eric Beinhocker's The Origin of Wealth (Harvard Business Review Press, 2007).

A recent National Geographic special on lions brought the message home (more comments to follow.) Want to share any thoughts on the idea?

"Where do economies come from? ... How do the behaviors, relationships, institutions, and ideas that underpin an economy form, and how do they evolve over time? ... Joshua Epstein and Robert Axtell are researchers at the Brookings Institution, one of the leading public-policy think tanks in Washington, D.C. In 1995, they decided to conduct an experiment to see if they could grow an economy from scratch ... in the simulated world of a computer. ...

"They wanted to go back to the very beginning, to a state of nature, and have a model that included nothing more than people with a few basic abilities, and an environment with some natural resources. They wanted to find out the minimum conditions required to set off a chain reaction of economic activity. What would it take to get the system to start climbing the ladder of increasing economic order?

"To picture Epstein and Axtell's model, imagine a group of people shipwrecked on a desert island, except that both the island and the castaways are simulations inside a computer. The computer island is a perfect square with a fifty-by-fifty grid overlaid on top of it, like a giant chessboard. The virtual island has only one resource -- sugar -- and each square in the grid has different amounts of sugar piled on it. The heights of the sugar piles range from four sugar units high (the maximum) to zero (no sugar). The sugar piles are arranged such that there are two sugar mountains, one mountain at the northeast corner and one at the southwest corner, each with sugar piled three and four units high. Between the two mountains is a 'badlands' area with little or no sugar. Epstein and Axtell called their imaginary sugar island Sugarscape. ...

"Each agent [or 'person'] on Sugarscape can only do three things: look for sugar, move, and eat sugar. That's it. In order to find food, each agent has vision that enables it to look around for sugar, and then has the ability to move toward this source of energy. Each agent also has a metabolism for digesting sugar.

"Epstein and Axtell wanted to see if simple agents in a simple landscape could create something like an economy. Thus, each agent had a basic set of rules that it followed during each turn of the game. The agent looks ahead as far as its vision will allow in each of four directions on the grid: north, south, east, and west. The agent determines which unoccupied square within its field of vision has the most sugar. The agent moves to that square and eats the sugar. The agent is credited by the amount of sugar eaten and debited by the amount of sugar burned by its metabolism. If the agent eats more sugar than it burns, it will accumulate sugar in its sugar savings account (you can think of this savings as body fat) and carry this savings through to the next turn. If it eats less, it will use up its savings (depleting fat). If the amount of sugar stored in an agent's savings account drops below zero, then the agent is said to have starved to death and is removed from the game. Otherwise, the agent lives until it reaches a predetermined maximum age.

"In order to carry out these tasks, each agent has a 'genetic endowment' for its vision and metabolism. In other words, associated with each agent is a bit of computer code, a computer DNA, that describes how many squares ahead that agent can see and how much sugar it burns each round. An agent with very good vision can see sugar six squares ahead, while an agent with very poor vision can only see one square ahead. Likewise, an agent with a slow (good) metabolism needs only one unit of sugar per turn of the game to survive, versus an agent with a fast (bad) metabolism, which requires four. Vision and metabolism endowments are randomly distributed in the population; thus, the population of agents is heterogeneous (meaning that not all agents are alike). ... Each agent also has a randomly assigned maximum lifetime, after which a computer Grim Reaper comes and removes it from the game. Finally, as sugar is eaten, it grows back on the landscape like a crop, at the rate of one unit per time period. So if a sugar pile of height four is eaten, it will take four periods to grow back to its original level.

"The game begins with 250 agents randomly dropped on the Sugarscape. Some agents happen to land on the rich sugar mountains and thus are born into sugar wealth, while others have bad luck and are born in the poor areas of the badlands. ...

"At the beginning of the simulation, Sugarscape is a fairly egalitarian society and the distribution of wealth is a smooth, bell-shaped curve with only a few very rich agents, a few very poor, and a broad middle class. In addition, the distance between the richest and the poorest agents is relatively small. As time passes, however, this distribution changes dramatically. Average wealth rose as the agents convened on the two sugar mountains but the distribution of wealth became very skewed, with a few emerging superrich agents, a long tail of upper-class yuppie agents, a shrinking middle class, and then a big, growing underclass of poor agents. ...

"An agent's place of birth, like its genetic endowment, is perfectly random, so if that were the cause of an agent's ultimate economic class, the distribution would also be evenly distributed. How, then, from these random initial conditions do we get a skewed wealth distribution?

"The answer is, in essence, 'everything.' The skewed distribution is an emergent property of the system. It is a macro behavior that emerges out of the collective micro behavior of the population of agents. The combination of the shape of the physical landscape, the genetic endowments of the agents, where they were born, the rules that they follow, the dynamics of their interactions with each other and with their environment, and, above all, luck all conspire to give the emergent result of a skewed wealth distribution."