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Unformatted text preview: Lecture VIII: Learning Markus M. M¨obius March 10, 2004 Learning and evolution are the second set of topics which are not discussed in the two main texts. I tried to make the lecture notes self-contained. • Fudenberg and Levine (1998), The Theory of Learning in Games, Chap- ter 1 and 2 1 Introduction What are the problems with Nash equilibrium? It has been argued that Nash equilibrium are a reasonable minimum requirement for how people should play games (although this is debatable as some of our experiments have shown). It has been suggested that players should be able to figure out Nash equilibria starting from the assumption that the rules of the game, the players’ rationality and the payoff functions are all common knowledge. 1 As Fudenberg and Levine (1998) have pointed out, there are some important conceptual and empirical problems associated with this line of reasoning: 1. If there are multiple equilibria it is not clear how agents can coordinate their beliefs about each other’s play by pure introspection. 2. Common knowledge of rationality and about the game itself can be difficult to establish. 1 We haven’t discussed the connection between knowledge and Nash equilibrium. As- sume that there is a Nash equilibrium σ * in a two player game and that each player’s best-response is unique. In this case player 1 knows that player 2 will play σ * 2 in response to σ * 1 , player 2 knows that player 1 knows this etc. Common knowledge is important for the same reason that it matters in the coordinated attack game we discussed earlier. Each player might be unwilling to play her prescribed strategy if she is not absolutely certain that the other play will do the same. 1 3. Equilibrium theory does a poor job explaining play in early rounds of most experiments, although it does much better in later rounds. This shift from non-equilibrium to equilibrium play is difficult to reconcile with a purely introspective theory. 1.1 Learning or Evolution? There are two main ways to model the processes according to which players change their strategies they are using to play a game. A learning model is any model that specifies the learning rules used by individual players and examines their interaction when the game (or games) is played repeatedly. These types of models will be the subject of today’s lecture. Learning models quickly become very complex when there are many play- ers involved. Evolutionary models do not specifically model the learning process at the individual level. The basic assumption there is that some un- specified process at the individual level leads the population as a whole to adopt strategies that yield improved payoffs. These type of models will the subject of the next few lectures....
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This note was uploaded on 05/19/2010 for the course 412 002 taught by Professor Dingli during the Spring '10 term at École Normale Supérieure.
- Spring '10