Exacta ISSN: 1678-5428 [email protected] Universidade Nove de Julho Brasil
Oliva, Alexandre A beautiful mind meets free software: game theory, competition and cooperation Exacta, vol. 4, núm. Esp, novembro-special, 2006, pp. 25-30 Universidade Nove de Julho São Paulo, Brasil
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A beautiful mind meets free software: game theory, competition and cooperation
Alexandre Oliva Unicamp, Instituto de Computação, Laboratório de Sistemas Distribuídos. Campinas – SP [Brasil] [email protected]
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, in- dividual 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 mar- ket, 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. Key words: Adam Smith. Competition. Cooperation. Game theory.
Exacta, São Paulo, v. 4, n. especial, p. 25-30, 25 nov. 2006 25 1 Introduction 2 Game theory
John Nash’s life was the inspiration for the Rational and selfish players are one of the motion picture A beautiful mind, by Ron Howard. fundamental principles behind game theory Nash (WIKIPEDIA, 2006b), a mathematician, (MCCAIN, 1999; TUROCY; STENGEL, 2001; won the Nobel award on economic sciences in WIKIPEDIA, 2006a). This science branch stud- 1994, in part because of his work on game theory, ies the behavior of players in real-life situations, a branch of mathematics that uses formal models seeking to explain it with formal models of costs to study incentive structures, with applications on and benefits for the players, in which each play- not only economics, but also evolutionary biology, er attempts to optimize its payoff. Interestingly, political science, military strategy, international even though real-life players aren’t always en- relation and many others. tirely selfish or rational, such formal models of- The idea for this paper first came up watching ten apply to as disparate situations as economic a scene from the movie that starts with Nash and competition and biological evolution, in which three friends at a bar. A gorgeous blond girl with the market or nature, respectively, tend to reward four brunette friends enters, and the friends start players for the intelligence behind their behavior. debating how they’re going to approach them. One The models are useful to reason about strategies, of them says they should each one try his best, cit- enabling players themselves to make better deci- ing Adam Smith: “In competition, individual am- sions more easily. bition serves the common good”. Nash has the in- sight for a revolution in governing dynamics, as the 2.1 Prisoner’s dilemma movie calls it, and explains that, if they all go for One of the most well-known examples of the blond, they block each other, and none of them game theory in action is the prisoner’s dilemma gets her. Worse, when they go for the brunettes, (WIKIPEDIA, 2006c), in which two burglars are another rejection will ensue, because nobody likes caught near a crime scene. The police know they to be second choice. However, if they each go for committed a crime, but have no evidence, other one brunette at first, they don’t get in each other’s than a concealed weapon, that they can use in way and don’t insult the girls, so they win. “Adam court, and the weapon wouldn’t get them con- Smith needs revision”, he says, because “the best victed for the burglary. In order to get a convic- result will come from everybody in the group do- tion, the policy offers each of the burglars a deal: ing what’s best for himself, and the group”. if one confesses and testifies against the other, This scene is based on one of the most-widely- he can go free, and the other will likely go to known contributions by Nash to game theory, the jail for 15 years. The catch: they cannot talk to theory of Nash equilibrium, described in section each other, and if both of them agree and testify 2. It also introduces some basic concepts on game against each other, each one will likely stay in theory such as the prisoners’ dilemma and the prison for ten years. If none of them agrees to the tragedy of the commons. In section 3, we related deal they will likely go to jail for one year each, these game theory concepts with those of software because of the concealed weapon. Each one must development and licensing models, showing that decide how to proceed all by himself. development under the GPL can be more favorable If both of them act in a rational and selfish than proprietary or BSD-like licenses. way, they will both conclude that the best choice is
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Bob * Cattle Value-cost * Jail time confess deny n n Al confess 10\10 0\15 k cN k p n N * deny 15\0 1\1 -
Board 1: Prisoner’s dilemma n 1 n 1 k c Source: The author. k n 1 N 1 p - N 1
Board 2: Tragedy of the commons to agree to confess and testify against each other. Source: The author. Consider, for example, the prisoner whose payoffs are depicted after the slashes, whose choices are moners will tend to follow, thus overusing the represented by columns in the table. The 0 jail time common resource to the point of depleting it. on the rightmost column is less than 1, should the The solution to avoid this tragedy is a credible other prisoner choose to deny, and the ten-years commitment from all commoners to avoid over- jail time is less than 15 should the other confess, use. Such agreements may be self-imposed, such as so confessing is a dominant strategy. Since the the Kyoto Protocol, or externally-imposed, such table is symmetric, it is dominant for both, and as regulations established by a government over they both end up confessing, achieving the worst its citizens. possible result for the group, a total of 20 years of jail time. 2.3 Nash equilibrium If they could communicate and define a Not all games can be solved with dominant joint cooperative strategy, and if they could trust strategies alone. Going back to the bar scene at each other to implement it, they might be able to the movie, but simplifying it for two players, a achieve a better result for both. Since they can’t single gorgeous blond and two brunettes, we can cooperate, and they act in a selfish way, they end find a single dominant strategy, even if weakly up far worse off. dominant:
2.2 Tragedy of the commons Male 1 * Gets a girl Brunette 1 Blond Another well-known situation described in Male 2 Brunette 2 1\1 1\1 game theory is the tragedy of the commons. Com- * Blond 1\1 0\0 moners use a field to graze cattle, in such a way Board 3: Nash equilibrium that the costs to maintain the graze are shared, Source: The author. but value from the cattle, being individual prop- erty, is enjoyed by each individual owner. Going for the blond is dominated by going Since costs are shared by all commoners, for the brunette because the payoff for the bru- they effectively divide the costs of maintaining nette is greater than or equal to that for the blond, the graze; since per-cattle value is obtained by its regardless of what the other player plays. This is owner alone, the payoff model is such that there’s the insight that Nash’s character had at the bar, an incentive to increase the number of cattle each but it clearly doesn’t go as far as the Nash equilib- commoner owns. Since this increases value for the rium theory. individual while sharing the cost with all other Nash equilibrium is a generalization of do commoners, it’s a dominant strategy that all com- minant strategies, defined as a strategy for each
Exacta, São Paulo, v. 4, n. especial, p. 25-30, 25 nov. 2006 27 player such that no single player can increase its panied computers they sold. A software industry payoff by changing only its own strategy. It does was then formed around the idea of selling licenses indeed cover the solution for the game that the to programs that didn’t permit them to be studied, character proposes, but it leaves out the two other modified, inspected, improved or distributed. In Nash equilibriums present in this game, namely, fact, such licenses would even impose restrictions one of them goes for the blond and the others go on the execution of the programs. The free soft- for brunettes. ware movement started as a reaction against the Oddly enough, a more accurate modeling of ongoing trend of licensing more and more soft- the situation, in which getting the gorgeous blond ware under proprietary terms. yields a higher payoff than getting one of the bru- Proprietary software vendors seek a competi- nettes, leads to two Nash equilibriums that do not tive edge by denying users the freedoms to run, match the solution proposed in the movie: study, distribute and improve the licensed software or works derived from it, most often also denying Male 1 them access to the source code needed to exercise Gets a girl, weighted Brunette 1 Blond several of these freedoms. Since they consider the Male 2 Brunette 2 1\1 1\2 Blond 2\1 0\0 source code a trade secret, it is very difficult for
Board 4: Nash equilibrium with maximin them to cooperate. In fact, this very alleged need problem-solving strategy for secrecy of the source code is their attempt to Source: The author. minimize losses to competitors, requiring any en- trants in the market to duplicate all of the effort The direct use of the maximin problem- other competitors have already gone through to solving strategy that consists in choosing the move get their product to market. But while such secre- that maximizes the lowest possible outcome for cy may have been originally regarded as a means the move, leads to the solution in which everybody to minimize losses to competitors, thus increasing goes for a brunette, but if the players could coop- their potential payoff, is it really the case that it erate by agreeing on only one of them going for the maximizes the payoffs? Setting back a competi- blond, they could reach a Pareto optimum. This tor does not necessarily lead to an increase in a depends on the players’ willingness to trust each player’s payoff. Nevertheless, proprietary soft- other to remain faithful to the agreement. With- ware vendors appear to work under Adam Smith’s out cooperation or credible commitment, each one motto, “Individual ambition serves the common would reason that they’re better off going for the good”, a non-cooperative behavior that leads the brunette to avoid the worst-case result. prisoners to jail for the longest time in the prison- ers’ dilemma. BSD-like licenses (those based on or similar 3 Software development to the modified BSD license, without the adver- tising clause) impose attribution as the single re- Software used to be distributed along with quirement: sharing the code is considered good, computers in the early days of the computer in- cooperation is welcome, and reusing the code even dustry. Years later, vendors began to believe they in proprietary software is acceptable, as long as could obtain an edge by not distributing the source the authors of the original software are acknow code along with the binary programs that accom- ledged. Although there is economic incentive to
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contribute code back instead of maintaining forks place snapshot, they all offer products, developed with proprietary improvements, the reasoning that from scratch, that are functionally equivalent, led to keeping additions proprietary may remain, but are offered under different licensing terms. turning such potential contributors into free rid- Further assume that some of them choose to use ers, with a potential outcome similar to the deple- proprietary licensing terms, some use a BSD-like tion scenario in the tragedy of the commons: the license, and some use the GPL. more free riders there are, the fewer contributors We can reason that, since the software pro there are to improve the common code base. ducts are essentially equivalent, the cost to de- A credible commitment to steer people away velop them should have been essentially the same, from the free-riding temptation is the GPL, that and the market will not concentrate around any grants the four freedoms to anyone who receives single vendor; rather, each vendor should get an the software, enabling people to distribute modi- essentially identical fraction of the market. Since fied copies of the software only if they use the same the market is divided equally, income from this license, thus extending the freedoms to users of the product is the same for all vendors, so those with improved software. By forbidding any third party lower costs will get the highest payoffs. from turning the software proprietary, the license prevents the creation of proprietary forks. Fur- License Proprietary BSD-like GPL Costs thermore, even if a potential contributor chooses k k k to not contribute her changes to the maintainer of 1 nb ng the original project, any third party that obtains * the modified software may choose to merge the Board 5: Cost to develop them should have been changes upstream. Therefore, most competitors essentially the same tend to choose to short-circuit this process and Source: The author. contribute the changes themselves, such that they get the credit and goodwill from it. It’s still a very Proprietary vendors tend to not cooperate, competitive marketplace, but competition is en- and thus incur the entire development costs K by riched with a significant amount of cooperation. themselves. free software vendors can cooperate, As developers contribute their changes to the com- thus dividing their costs among the several ven- mon code base, all of them get better grounds to dors nb and ng, thus reducing the amount each one build upon, reducing waste of resources, increas- has to fork over to get the product ready, even in ing economic efficiency and enabling each vendor the presence of redundant efforts. The more con- to differentiate from others to better serve their tributors there are, the better off free software chosen market niche starting from a better code vendors end up, since the lower their individual base. As Nash’s character put it, “The best result costs tend to be. will come from everybody in the group doing So far, BSD-like and GPL appear to be equal- what’s best for himself, and the group”. ly advantageous, the balance pending to whatever I believe the GPL is the credible commitment community is bigger. However, since software li- that leads to cooperation and to the best outcome, censed under BSD-like terms can be relicensed un- so let me try to show why. Consider a number of der any other license, the BSD vendors may actu- vendors competing for a market niche of a given ally help reduce the costs incurred by proprietary size, at a given time. Assume that, in this market- and GPL vendors, since both categories can choose
Exacta, São Paulo, v. 4, n. especial, p. 25-30, 25 nov. 2006 29 to reuse BSD software in their products. I.e., the Final considerations fact that GPL code can use BSD code, but not the
other way around, implies that ng ? nb and therefore Choosing the GPL can be the best choice the economic balance tends to favor GPL vendors. not only for software users, for working against It is true that the scenario above relies on a the formation of monopolies and unfair pricing; number of strong assumptions, but I do believe it it can also be a dominant strategy, in the game- can be generalized. One of the most critical as- theoretical sense, for software developers and ven- sumptions is the fact that we’re looking at a snap- dors, enabling them to share development costs shot of a new marketplace. If we add dynamics to and to achieve a better overall economic efficiency it, we have to factor in many other aspects, such while still being fairly paid for their services. as networking effects, compatibility issues and several others taken into account in (POLANSKI, 2005; JOHNSON, 2002). References A common objection to this model, that is actually not true, is that free software will tend JOHNSON, J. P. Economics of open source software. May 2002. Disponível em:
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