| Is God in Game Theory? |
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| Written by Meira Levinson | |||||
| Tuesday, 13 December 2005 | |||||
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Nobel Prize Laureate Applies Mathematic to Religion, Ethics When I first heard about 2005 Nobel Prize Laureate for Economic Science, Robert Aumann, my reaction might have been classified as polite disinterest. Economics, game theory, mathematical equations – these terms all spur images of failed tests, mind-numbing tutorials, and indecipherable formulae. “I’m an English major,” I generally respond when people ask me about my math knowledge. But reading about Robert/Israel Aumann made me realize what a unique figure he is and how much his work can impact not only economics, but religious thought, as well. Aumann’s background is in both Talmudic studies and math, in which he earned his PhD at MIT. It was at his post-doc appointment at Princeton that he became involved in game theory work. He now works at the Center for Study of Rationality at the Hebrew University of Jerusalem. Although Aumann’s specializations are in the economic and mathematical aspects of game theory – specifically, in the realms of repeated games and non-cooperative game theory – he has also applied this knowledge to his other main area of interest: Talmud. For example, he used game theory to explain a difficult case – the “division problem,” a dilemma of dividing up property among a dead husband’s wives – that had long puzzled scholars. The application of game theory to religion, however, goes deeper than specific case-by-case scenarios. In an interview with Aumann, his colleague Sergiu Hart asked him, “A world populated by rational players [i.e. the criteria for game theory] – is it consistent with the religious view?...Isn’t there, in a sense, an extra player, which would be G-d or something that you cannot understand by rational means, an extra non-rationally driven player?” “There is a passage in the Torah reading of yesterday that relates to this,” Aumann answered. ‘This commandment that I command you today is not far away from you. It is not in Heaven so that one would have to say, ‘Who will go up to heaven and will take it from there and tell us about it?’ (Deuteronomy 30,: 11-12). The Talmud interpreted [it] as signifying a duty on part of human beings to interpret the whole of Scripture in each generation. So the Torah must be given practical meaning by human beings.” In other words, as Aumann further explained, game theory fits perfectly with religion. It clarifies exactly those areas of life that Torah and Rabbinic Judaism left blank. While Judaism tells us that we must give charity, it does not tell us how much. Game theory principles can. While Judaism tells us we must not cheat our neighbors when bargaining, it does not tell us how to bargain. Game theory does. Game theory also explains the underlying concepts behind Jewish law, or, as Aumann put it, “…one needs game theory to explain the ethical and moral rules themselves. Why not steal software? Why have accurate weights and measures? Why love one’s neighbor as oneself? How did it come about, what function does it serve, what keeps it together? All these are game-theoretic questions.” The ramifications of Aumann’s arguments are by no means insignificant. To sort through the tangled world of ethics, morality, and halachic law with mathematics is controversial. It assumes that many dilemmas generally considered relativistic are actually quantifiable and definitive. Aumann’s claim here is subtle, yet striking. In essence, he purports that game theory not only explains and predicts interactions between people in a military, economic, or otherwise “secular” venue, but that it can be used to understand divine imperative. It seems that God, who may not have dictated game theory to Moses at Mt. Sinai, was certainly a fan of it.
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