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Game Theory, Competition and Cooperation Exacta, Vol 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 Available in: http://www.redalyc.org/articulo.oa?id=81009903 How to cite Complete issue Scientific Information System More information about this article Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Journal's homepage in redalyc.org Non-profit academic project, developed under the open access initiative Artigos 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 2 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 26 Exacta, São Paulo, v. 4, n. especial, p. 25-30, 25 nov. 2006 Artigos 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. 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 : 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.
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