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Thursday, December 21, 2017

Modelling Wholesale Inequality And Video Games

Steve Roth (publisher of Evonomics) asked an interesting question on Twitter: is inequality an inevitable result of capitalism? I split the sources of inequality into two factors, which I flippantly label retail inequality (inequality due to wage differentials), and wholesale inequality (inequality due to ownership of large, successful businesses). I am going to avoid the issue of retail inequality, and just discuss how we would model wholesale inequality. I think a lesson can be drawn from the decades of experience of designing strategy video games: the tendency towards inequality largely depends upon the rules of the game.

My comments here could possibly be viewed as commentaries on agent-based modelling. I have only read a few papers in that area, and I am going to pretend that I know nothing about the subject. I will let readers attempt to see whether my comments are useful for that area or not.

Wholesale versus Retail

Based on a cursory analysis of inequality data, the top 0.01% of the income distribution has been doing very well. Furthermore, the people with the big bucks tend to be owner of dominant corporations. If there is a tendency for large corporations to become even more successful, then we should see increasing inequality in that cohort versus everyone else.

For the rest of the distribution, the big divide is between C-suite salaries and the rest of the hierarchy. However, since a lot of the highest paid CEO's are also in charge of the largest corporations, the question of increasing corporate inequality is perhaps relevant. However, it is possible for wage scales to become more equal while the owners become more unequal, and vice versa.

Therefore, I am looking at the question of corporate dominance, and let that stand in for inequality.

(Some readers might wonder about passive investors -- the rentier class that so animates European politics. I would argue that this is just following a particular "corporate" strategy, being the passive ownership of bonds, land, and minority shareholdings. In order to model this, we would have to have a good simulation of those asset markets, which is harder than a real economy simulation.)

This is Frivolous!

The more serious readers might be shocked at my bringing up video games. However, we actually need to do so, for very good theoretical reasons.

Firstly, an aggregated model is utterly useless for modelling the diverging fortunes of individual components of the aggregate. At the minimum, we need to split out the large corporations as individual model entities -- agents. (We could leave other components of the model aggregated.)

We therefore must have an agent-based model of some sort, with corporations as the agents. These agents are competing to get bigger, following various algorithms describing their behaviour. This is a (serious) simulation.

What happens if a human takes over the decision-making of one of the corporations? You have a single-player strategy game, which fits into the genre of simulation-style games. (These games bear little resemblance to abstract strategy games like Go or Chess.) This genre came into its own in the early 1990s, following the success of Sid Meier's Civilization. (There were fore-runners to Civilization, but CPU limitations resulted in more primitive simulations.)

What is the first lesson we learn when humans take over the decision-making of one agent? We learn that human players rip the faces off AI (artificial intelligence) players. They will find any weaknesses in the rules of the game, and exploit them to tear ahead of AI players. In a loose sense, they optimise. Also, one should note that when I write "rules of the game," it is not just the question of what is legal. It also includes the "laws of nature" within the simulation, such as production functions.

This observation might cause some distress to heterodox economists, as it hints that DSGE modellers have a point about optimising behaviour. However, they were only half right. We cannot turn the complex decision-making in these situations into an optimal control problem (an area that I covered in my doctorate, so yeah, I know what I am writing about). Instead, humans find heuristics that act in "as optimal a fashion as possible" (whatever that means).

In any event, this explains why I am interested in building a financial/economic simulator that could either work as a serious simulator -- or an economic engine for a video game. The gamer tendency to explore exploits would keep the serious simulation types honest.

Do the Big Get Bigger?

What is the lesson to be learned from strategy video games? Well, if we look at successful commercial video games, we see that the end games are almost always defined by a single player racing ahead and smashing the competition. The advantages of a dominant position translate into greater future advantages -- what people (other than pedantic control theorists) call a positive feedback loop.

Is this an iron law of economics? No, it's the iron law of commercial success. Nobody wants to play a game where they know that they are in the winning position after five hours, but it takes another twenty to finish off the game. The designer embeds rules that reinforces a dominant position, allowing for a more rapid game termination.

However, the rest of the game generally features the opposite mechanic: mechanisms for catching up ("negative feedback" for dominance). People do not want to play a game where some AI player gets a small early lead, and just runs away with it in an unstoppable fashion. (Since the games I am discussing here featured one human versus multiple AI players, just luck from the randomised starting positions might be enough to lock in an early lead for one AI player in most games.)

In other words, the returns to dominance is entirely under the control of the game designer, and represents the bulk of design work. Even small tweaks to the rules can have a huge effect in observed human strategies.

For example, the first release of Civilization allowed for aggressive starting strategies. This was addressed in later releases by a few changes to the simulation to block this. One of the changes was  parameter tweaks to one unit (the chariot). The change removed the core unit behind those aggressive starts. The equivalent in a business simulation would be a change to a production function. If one wanted to sound mathematical, one would say that the optimal strategy is not a continuous function of simulation parameters. This principle means that unless we replicate all of the rules of a simulation exactly, we should not be surprised by wildly different optimal behaviour. This makes it extremely difficult to generalise across models.

OK, What About Economics?

There were not a whole lot of successful strategy games based on corporate behaviour. The problem is that realistic depictions are boring. There are "positive feedback" effects, but they are generally fairly small. "Your corporation had an annual growth rate of 8%, versus 6.5% of your main competitor!" Yay. Generally speaking, in order to make the game interesting, designers needed to inject unrealistic components to make it work (such as extremely high rates of return, etc.).

There are a lot of reasons to expect "positive feedback" in a realistic simulation.
  • Economies of scale. In the real world, there are generally positive economies to scale. This can be viewed as a "law of economic nature" (if my assertion is true; it's based on post-Keynesian empirical work).
  • Research. Larger corporations can lock down proprietary technologies, which can augment the returns to scale.
  • First Mover Advantage. An obvious issue for tech firms in the real world, but probably hard to model.
  • Balance sheet abuse. I am considering adding a futures market to my simulation. The first thing I considered was: Is it possible to set the rules of the exchange so that trading does not turn into a continuous squeeze-the-shorts party? Corporations with big balance sheets can corner the market, and crush weaker competitors. This is the difference between AI algorithms and humans: AI's play fair; humans generally play to win. 
Going the other way, there are less factors that I can think of.
  • Specialisation. The last time conglomerates were popular was in the 1960s (with a few notable exceptions, built around CEO personality cults). There are management costs associated with running too many business lines. (I think this is the problem with the big banks, where I believe researchers have found dis-economies to scale.) That is, there might be an advantage to being the biggest firm in an industry, but costs to spreading across industries.
  • New technologies. A small firm with a new technology can wipe out the existing business lines of a large firm. The difficulty with simulating this is that we normally allow agents (and players) to know the parameters of industries. We we would need to insert some uncertainty into the simulation to make it possible for firms to misjudge the effects of new technologies.
  • Incompetence (an idea that I took from the writings of the management guru Scott Adams). Very simply, given a large enough supply of MBA's, one can run practically any organisation into the ground within a decade or two. Once the clear-minded greedy founders are out of the picture, large corporations fall into a boiling mass of incompetence and office politics. Unfortunately, it is very hard to model incompetence in a simulation.
As can be seen, it is easy to come up with simulations where dominance snowballs, but it would not be that much harder to come up with catch-up mechanisms. Furthermore, rules set by (simulated) regulators would tend to level the playing field.

However, it seems clear that a strategy of wiping out your competitors is going to be a dominant one. In order to keep market shares stable in a simulation, the simulation rules (and/or algorithmic behaviour) probably has to be stacked in a way to prevent firms from knocking out weaker competitors.

Can things like taxes make a difference? If you are busy driving your competitors out of business, it is unclear to me how tweaking corporate tax rates will make a difference. The generic strategy of losing money in short term by engaging in predatory pricing (to allow future super-normal profits) is going to work in a lot of different simulation structures. Wealth taxes might go after the corporate founders, breaking the link between corporate success and individual wealth. Another angle of attack is anti-trust law; I do not know enough about anti-trust law to know how to implement it within a simulation. (My excuse is that such laws have not been enforced since I was a little kid.)

Concluding Remarks

Saying that wholesale inequality depends upon the rules of the game is probably not going to satisfy anyone. That said, any attempts to simulate the dynamics of wholesale inequality will be extremely sensitive to the parameters of the simulation, and the only way to test this is to experiment with the model. Anyone who is just stuck with a research paper is not going to be able to do such experiments.

Appendix: Multi-Player

Single player strategy games are no longer of much commercial interest. However, we can draw less conclusions from multiplayer games.

There is not a whole lot of difference between a 1-player and 2-player game; both players are trying to beat each other and the AI players.

For 3-8 players, the dynamics of human politics dominates the play balance decisions of the designer. People will tend to gang up on the leader, since they lose even if they are in second place. This is not typical behaviour in real-world corporations.

One might hope that there are lessons from games with massive numbers of players. However, the economic systems in those games are extremely fine-tuned for play balance. The designers need to reward the more enthusiastic players, but they cannot be allowed to be too dominant. As a result, they feature interactions that are far more egalitarian than the real world. Nobody wants to log in and have to follow the orders of a pointy-haired boss; they do that all day in the real world.

(c) Brian Romanchuk 2017

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