Lecture10-new

Lecture10-new - 6.254 : Game Theory with Engineering...

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6.254 : Game Theory with Engineering Applications Lecture 10: Evolution and Learning in Games Asu Ozdaglar MIT March 9, 2010 1
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Game Theory: Lecture 10 Introduction Outline Myopic and Rule of Thumb Behavior Evolution Evolutionarily Stable Strategies Replicator Dynamics Learning in Games Fictitious Play Convergence of Fictitious Play Reading: Osborne, Chapter 13. Fudenberg and Levine, Chapters 1 and 2 2
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Game Theory: Lecture 10 Introduction Motivation Do people play Nash equilibrium? In class, in the context of the k -beauty game, we saw that even very smart MIT students do not play the unique Nash equilibrium (or the unique strategy profile surviving iterated elimination of strictly dominated strategies). Why? Either because in new situations, it is often quite complex to work out what is “best”. Or more likely, because, again in new situations, individuals are uncertain about how others will play the game. If we played the k -beauty game several more times, behavior would have approached or in fact reached the Nash equilibrium prediction. 3
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Game Theory: Lecture 10 Introduction Motivation (continued) This reasoning suggests the following: Perhaps people behave using simple rules of thumb ; these are somewhat “myopic,” in the sense that they do not involve full computation of optimal strategies for others and for oneself. But they are also “flexible” rules of thumb in the sense that they adapt and respond to situations, including to the (actual) behavior of other players. What are the implications of this type of adaptive behavior? Two different and complementary approaches: 1 Evolutionary game theory. 2 Learning in games. 4
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Game Theory: Lecture 10 Evolution Evolution and Game Theory The theory of evolution goes back to Darwin’s classic, The Origins of Species (and to Wallace). Darwin focused mostly on evolution and adaptation of an organism to the environment in which it was situated. But in The Descent of Man , in the context of sexual selection, he anticipated many of the ideas of evolutionary game theory. Evolutionary game theory was introduced by John Maynard Smith in Evolution and the Theory of Games , and in his seminal papers, Maynard Smith (1972) “Game Theory and the Evolution of Fighting” and Maynard Smith and Price (1973) “The Logic of Animal Conflict”. The theory was formulated for understanding the behavior of animals in game-theoretic situations (to a game theorist, all situations). But it can equally well be applied to modeling “myopic behavior” for more complex organisms—such as humans. 5
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Game Theory: Lecture 10 Evolution Evolution in Strategies In its simplest form the story goes like this: each organism is born programmed to play a particular strategy. The game is the game of life —with payoffs given as fitness (i.e., expected number of offsprings). If the organism is successful, it has greater fitness and more offspring, also programmed to play in the same way. If it is unsuccessful, it likely dies without offspring.
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Lecture10-new - 6.254 : Game Theory with Engineering...

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