I usually avoid reading TechCrunch because its writers aren’t that great and the topics they cover rarely intersect the topics I find interesting. This morning, a tweet announced that TechCrunch had an article that seemed to say that the technology industry is a zero-sum environment. As a mathematician and a college teacher, this piqued my curiosity; I’m always looking for good examples of situations that admit game theoretic descriptions.

Ashkan Karbasfrooshan wrote this article to justify the claim that ldquo;tech is a zero-sum, winner takes all game. A reader called him on this, questioning his use of the term zero-sum. So Karbasfrooshan decided to take another run at the idea and show his readers how much he knows about game theory. Anybody can cut-and-paste the wikipedia definition of zero-sum game, but it takes someone willing to think carefully about a sophisticated idea (e.g., game theory, technology markets) to write anything insightful and of value.

The idea of zero-sum interactions refers to a game theoretic way to describe some competition between two or more individuals or teams. Game theory lingo started to be popularized in the media in the 1950s and 1960s in connection to the cold war, and its use has continued to grow as more people understand game theory’s applications to fields like biology, economics, evolution, business, and philosophy, to name only a few areas of application. It’s important to note that game theory is a very sophisticated sub-field of applied mathematics, and there are all sorts of nuances that can be layered on to situations (e.g., coalitions, iterations, bounded information). Because Karbasfrooshan kept it simple in his pieces, I’ll do the same.

Is technology a zero-sum game? (Forget the ‘winner takes all’ rider. I’m a mathematician, not an MBA.)

For Karbasfrooshan, the tech sector is zero-sum because a customer can only buy one company’s product. Framed in this way, the game he’s describing is being played by tech companies emand/em consumers. Dollars change hands, so game payoffs appear to be in dollars for Karbasfrooshan. This is reasonable, but this isn’t much of a game. Rational consumers have no motivation for playing it because money never flows from producers to consumers. So Karbasfrooshan is missing something in his analysis. He’s missing that game payoffs are in the more abstract form of utility. Consumers exchange dollars (which have general and explicity utility) for a product (which has specific and specialized utility for the consumer). If each transaction creates value for everyone, then this game isn’t zero sum.

But perhaps this isn’t the game that Karbasfrooshan is thinking about. He does talk about Jack Welsh, the famous and celebrated CEO of General Electric. Mr. Welsh seemed to espouse a certain Darwinian competitiveness in the markets, preaching of the importance of being #1 or #2 in a given market. Maybe Karbasfrooshan is thinking of the tech-sector game as being played by companies in competition with one another. What form does the payoff take in such a game? Karbasfrooshan suggests consumer dollars, but consumers aren’t even at the game table. Their dollars do, in a way, constitute a lsquo;bank’ from which payoffs can flow. But that is a hallmark of a non-zero-sum game. Maybe Karbasfrooshan thought of the companies as competing for market share. If a given tech market is static from quarter to quarter, then this could make sense; what one company gains in market share another company must lose. (Think of the market for smartphones; Apple and Android growth may be happening at the expense of RIM’s.)

If you want to be generous, you can assume that Karbasfrooshan was thinking about market share as the payoff companies are competing for. If you want to do this, stop reading now. Because nothing Karbasfrooshan wrote suggests this is what he was thinking. Instead, what he wrote suggests he didn’t think much when he was writing.

After having thought about Mr. Karbasfrooshan’s piece, I’ve come to the conclusion that he means well. But the road to hell is paved with good intentions. He wanted to throw around some important and sexy lingo to get page views. So instead of being a careful and thoughtful writer, he settled on being a bullshitter.

If he’s interested in understanding how game theory can describe markets, he should read some books. An easy, general start is William Poundstone’s The Prisoner’s Dilemma. A popular book on non-zero-sum games is Robert Wright’s Non-Zeror. More sophisticated mathematical treatments of the subject include Game Theory and Strategy by William Straffin, and The Mathematics of Games of Strategy by one of the founders of modern game theory, Melvin Dresher. If you want to really blow your mind, Mr. Karbasfrooshan, take a read through the short and deep treatise, The Evolution of Cooperation by Robert Axelrod.