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A Beautiful Mind Meets Free Software:
Game Theory, Competition and Cooperation
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Russel Crowe, playing 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 competitiondriven proprietary software development market, whereas John 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 GPL licensing model can be economically favorable to developers over proprietary and even BSDlike licenses.
1 Introduction John Forbes Nash, Jr.’s life was the inspiration for the motion picture “A Beautiful Mind”, by Ron Howard. John Nash [WPJN], 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 John Nash and 3 friends at a bar. A gorgeous blond girl with 4 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”. John 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 mostwidelyknown contributions by John 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 GNU GPL can be more favorable than proprietary or BSDlike licenses.
2 Game Theory Rational and selfish players are one of the fundamental principles behind game theory [McC, TS, WPGT]. This science branch studies the behavior of players in reallife 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 reallife 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 wellknown examples of game theory in action is the prisoner’s dilemma [WPPD], 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 10 years. If none of them agrees to the deal, they will likely go to jail for 1 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 10years 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 wellknown 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.
Since costs are shared by all commoners, they effectively divide the costs of maintaining the graze; since percattle value is obtained by its owner alone, the payoff model is such that there’s an incentive to increase the number of cattle each commoner owns. Since this increases value for the individual while sharing the cost with all other commoners, it’s a dominant strategy that all commoners will tend to follow, thus overusing the common resource to the point of depleting it.
The solution to avoid this tragedy is a credible commitment from all commoners to avoid overuse. Such agreements may be selfimposed, such as the Kyoto Protocol, or externallyimposed, 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 John 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 player such that no single player can increase its payoff by changing only its own strategy. It does indeed cover the solution for the game that the character proposes, but it leaves out the two other Nash Equilibriums present in this game, namely, one of them goes for the blond and the others go for brunettes.
Oddly enough, a more accurate modeling of the situation, in which getting the gorgeous blond yields a higher payoff than getting one of the brunettes, leads to two Nash
The direct use of the Maximin problemsolving strategy, that consists in choosing the move that maximizes the lowest possible outcome for the move, leads to the solution in which everybody goes for a brunette, but if the players could cooperate by agreeing on only one of them going for the blond, they could reach a Pareto optimum. This depends on the players’ willingness to trust each other to remain faithful to the agreement. Without cooperation or credible commitment, each one would reason that they’re better off going for the brunette to avoid the worstcase result.
3 Software Development Software used to be distributed along with computers in the early days of the computer industry. Years later, vendors began to believe they could obtain an edge by not
they sold. A software industry was then formed around the idea of selling licenses to programs that didn’t permit them to be studied, modified, inspected, improved or distributed. In fact, such licenses would even impose restrictions on the execution of the programs. The Free Software movement started as a reaction against the ongoing trend of licensing more and more software under proprietary terms.
Proprietary software vendors seek a competitive edge by denying users the freedoms to run, study, distribute and improve the licensed software or works derived from it, most often also denying them access to the source code needed to exercise several of these freedoms. Since they consider the source code a trade secret, it is very difficult for them to cooperate. In fact, this very alleged need for secrecy of the source code is
duplicate all of the effort other competitors have already gone through to get their product to market. But while such secrecy may have been originally regarded as a means to minimize losses to competitors, thus increasing their potential payoff, is it really the case
increase in a player’s payoff. Nevertheless, proprietary software vendors appear to work under Adam Smith’s motto, “Individual ambition serves the common good”, a non cooperative behavior that leads the prisoners to jail for the longest time in the prisoners’ dilemma.