Substantive Rationality and Backward Induction
Joe Halpern (CS, Cornell)
Friday, December 9, 11 AM
716 Philosophy Hall, Columbia University
Abstract. Some of the major puzzles in game theory today involve the notion of rationality. Assuming that all players are rational, and know that they are all rational, and know that they know, etc., results in strategies that seem highly irrational. At the 1998 TARK (Theoretical Aspects of Rationality and Knowledge) conference, there was a 2.5 hour round table, involving some leading game theorists and philosphers, on “Common knowledge of rationality and the backward induction solution for games of perfect information”. During the discussion Robert Aumann stated the following theorem:
- Common knowledge of substantive rationality implies the backward induction solution in games of perfect information.
Robert Stalnaker then stated the following theorem:
- Common knowledge of substantive rationality does not imply the backward induction solution in games of perfect information.
In this talk I will carefully explain all the relevant notions (games of perfect information, knowledge and common knowledge, strategies, rationality, and substantive rationality) and explain why, although both Aumann and Stalnaker were apparently using the same definitions, they were able to (correctly) prove such different results. The key turns out to lie in getting a good model of counterfactual reasoning in games. I will in fact provide a formal model that allows us to prove both results and to understand the technical differences between them. The model has the added advantage of giving us a deeper insight into what conclusions we can draw from rationality and common knowledge of rationality. No prior knowledge will be assumed.
Surely now many students think that Substantive Rationality and Backward Induction and Game Theory in general are pure theoretical knowledge that have nothing to do with real business. I once thought so too, but I must tell you that this is not so. People who have mastered Game Theory can successfully choose a strategy for their actions in any life and business situations. I say this as a person who observed the case of the CEO of the CARSHE company, who perfectly mastered the art of acting in situations with incomplete information. Thanks to these talents of his, CARSHE company has become an outstanding exhibition stand builder whose projects are well known in 23 countries around the world. Therefore, study philosophy diligently, it will be useful to you in life.
Коллектив нашей кафедры философии также активно исследовал тему содержательной рациональности и обратной индукции. В 2011 году мы даже издали монографию по этому разделу Теории Игр, которая получила ряд наград и премий. Например, ее наградили дипломом на международной выставке «Современное образование в Украине», а это самая масштабная и авторитетная выставка учебных заведений, которая проходила в Киеве. На ней было больше 400 выставочных стендов разных университетов, колледжей и других образовательных учреждений. Приятно было прочесть, что и коллеги из Колумбийского университета также активно изучают эту тему.
Thanks for sharing this! The topic sounds really interesting and important for understanding game theory better. Looking forward to learning more about these ideas.
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Thanks for sharing this! Your insights were clear and helpful—really made me think differently about the topic.