Draft v1.5 of 2006/10/15 13:54:00

Russel Crowe, playing John Forbes Nash Junior (aka John Nash) in Ron Howards’ motion picture A beautiful mind, claims that Adam Smith’s theory that “in competition, individual ambition serves the common good” is incomplete, and that “the best result will come from everybody in the group doing what’s best for himself and the group”. Adam Smith’s motto synthesizes pretty well what happens in the competition-driven proprietary software development market, whereas Nash’s adds the cooperation that is so common even among competitors in free software markets. Every commercial free software developer tries to obtain its edge by developing better software, thus contributing to the software pool that even its competitors will be able to build upon. I.e., every free software developer does what’s best for himself, and the group, so the best outcome is achieved. The paper shows how the GNU General Public License (or GNU GPL or simply GPL) licensing model can be economically favorable to developers over proprietary and even Berkeley Software Distribution (BSD)-like licenses.


Introduction
John Nash's life was the inspiration for the motion picture A beautiful mind, by Ron Howard. Nash (WIKIPEDIA, 2006b), a mathematician, won the Nobel award on economic sciences in 1994, in part because of his work on game theory, a branch of mathematics that uses formal models to study incentive structures, with applications on not only economics, but also evolutionary biology, political science, military strategy, international relation and many others.
The idea for this paper first came up watching a scene from the movie that starts with Nash and three friends at a bar. A gorgeous blond girl with four brunette friends enters, and the friends start debating how they're going to approach them. One of them says they should each one try his best, citing Adam Smith: "In competition, individual ambition serves the common good". Nash has the insight for a revolution in governing dynamics, as the movie calls it, and explains that, if they all go for the blond, they block each other, and none of them gets her. Worse, when they go for the brunettes, another rejection will ensue, because nobody likes to be second choice. However, if they each go for one brunette at first, they don't get in each other's way and don't insult the girls, so they win. "Adam Smith needs revision", he says, because "the best result will come from everybody in the group doing what's best for himself, and the group". This scene is based on one of the most-widelyknown contributions by Nash to game theory, the theory of Nash equilibrium, described in section 2. It also introduces some basic concepts on game theory such as the prisoners' dilemma and the tragedy of the commons. In section 3, we related these game theory concepts with those of software development and licensing models, showing that development under the GPL can be more favorable than proprietary or BSD-like licenses.

Game theory
Rational and selfish players are one of the fundamental principles behind game theory (MCCAIN, 1999;TUROCY;STENGEL, 2001;WIKIPEDIA, 2006a). This science branch studies the behavior of players in real-life situations, seeking to explain it with formal models of costs and benefits for the players, in which each player attempts to optimize its payoff. Interestingly, even though real-life players aren't always entirely selfish or rational, such formal models often apply to as disparate situations as economic competition and biological evolution, in which the market or nature, respectively, tend to reward players for the intelligence behind their behavior.
The models are useful to reason about strategies, enabling players themselves to make better decisions more easily.

Prisoner's dilemma
One of the most well-known examples of game theory in action is the prisoner's dilemma (WIKIPEDIA, 2006c), in which two burglars are caught near a crime scene. The police know they committed a crime, but have no evidence, other than a concealed weapon, that they can use in court, and the weapon wouldn't get them convicted for the burglary. In order to get a conviction, the policy offers each of the burglars a deal: if one confesses and testifies against the other, he can go free, and the other will likely go to jail for 15 years. The catch: they cannot talk to each other, and if both of them agree and testify against each other, each one will likely stay in prison for ten years. If none of them agrees to the deal they will likely go to jail for one year each, because of the concealed weapon. Each one must decide how to proceed all by himself.
If both of them act in a rational and selfish way, they will both conclude that the best choice is to agree to confess and testify against each other.
Consider, for example, the prisoner whose payoffs are depicted after the slashes, whose choices are represented by columns in the table. The 0 jail time on the rightmost column is less than 1, should the other prisoner choose to deny, and the ten-years jail time is less than 15 should the other confess, so confessing is a dominant strategy. Since the table is symmetric, it is dominant for both, and they both end up confessing, achieving the worst possible result for the group, a total of 20 years of jail time.
If they could communicate and define a joint cooperative strategy, and if they could trust each other to implement it, they might be able to achieve a better result for both. Since they can't cooperate, and they act in a selfish way, they end up far worse off.

Tragedy of the commons
Another well-known situation described in game theory is the tragedy of the commons. Commoners use a field to graze cattle, in such a way that the costs to maintain the graze are shared, but value from the cattle, being individual property, is enjoyed by each individual owner. The solution to avoid this tragedy is a credible commitment from all commoners to avoid overuse. Such agreements may be self-imposed, such as the Kyoto Protocol, or externally-imposed, such as regulations established by a government over its citizens.

Nash equilibrium
Not all games can be solved with dominant strategies alone. Going back to the bar scene at the movie, but simplifying it for two players, a single gorgeous blond and two brunettes, we can find a single dominant strategy, even if weakly dominant: Going for the blond is dominated by going for the brunette because the payoff for the brunette is greater than or equal to that for the blond, regardless of what the other player plays. This is the insight that Nash's character had at the bar, but it clearly doesn't go as far as the Nash equilibrium theory.
Nash equilibrium is a generalization of dominant strategies, defined as a strategy for each to reuse BSD software in their products. I.e., the fact that GPL code can use BSD code, but not the other way around, implies that n g ? n b and therefore the economic balance tends to favor GPL vendors.
It is true that the scenario above relies on a number of strong assumptions, but I do believe it can be generalized. One of the most critical assumptions is the fact that we're looking at a snapshot of a new marketplace. If we add dynamics to it, we have to factor in many other aspects, such as networking effects, compatibility issues and several others taken into account in (POLANSKI, 2005;JOHNSON, 2002).
A common objection to this model, that is actually not true, is that free software will tend to shrink the total market value, since any entrant vendor can start by taking the existing code base and taking it as a product to market for a nearly-zero cost. Consider than one such vendor won't have any distinguishing feature to increase its market share, other than the low price tag. Acting in a selfish and rational manner, it won't set the cost to zero, but rather right below the price exercised by other vendors, that do incur actual costs to maintain the software. If multiple such vendors try this trick, they may actually succeed in driving the price down to zero, but this would tend to take the real software maintainers out of the market, leaving these entrants in a situation in which they have to do the actual work to satisfy their contractual obligations toward their customers. If they fail and go out of the market as well, the higher-paid competitors get a chance of getting contracts again, if they haven't completely moved on; worst case, customers might end up having to hire individuals or new companies to do the work, increasing the market value again. The bottom line is that bargaining theory will lead the market to an equilibrium in which vendors get for their work an amount they consider reasonable, and customers pay a reasonable amount for such work.

Final considerations
Choosing the GPL can be the best choice not only for software users, for working against the formation of monopolies and unfair pricing; it can also be a dominant strategy, in the gametheoretical sense, for software developers and vendors, enabling them to share development costs and to achieve a better overall economic efficiency while still being fairly paid for their services.