# 040152 UK Learning in Games (2012S)

Continuous assessment of course work

## Labels

## Registration/Deregistration

**Note:**The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

- Registration is open from
**Th 09.02.2012 09:00**to**Mo 20.02.2012 17:00** - Registration is open from
**Mo 27.02.2012 09:00**to**Tu 28.02.2012 17:00** - Deregistration possible until
**We 14.03.2012 23:59**

## Details

max. 50 participants

Language: English

### Lecturers

### Classes (iCal) - next class is marked with N

- Thursday 01.03. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 08.03. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 15.03. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Friday 23.03. 10:45 - 12:15 (ehem. Hörsaal 23 Hauptgebäude, 1.Stock, Stiege 5)
- Thursday 29.03. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 19.04. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 26.04. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 03.05. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 10.05. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 24.05. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 31.05. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 14.06. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 21.06. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)
- Thursday 28.06. 12:00 - 13:30 (ehem. Seminarraum 10 Hauptgebäude, Tiefparterre Stiege 5 Hof 3)

## Information

### Aims, contents and method of the course

### Assessment and permitted materials

### Minimum requirements and assessment criteria

The objective is to receive an overview of the literature and to understand, under which

circumstances we can trust classic game theory and when not.

circumstances we can trust classic game theory and when not.

### Examination topics

### Reading list

References:

- Weibull (1995), Evolutionary Game Theory, MIT Press

Imitation:

This is a simplified cultural learning story in which individuals observe what others do and imitate those that are more successful. The specific type of imitation matters so we first need to investigate which type of imitation or learning rule has good properties. Then we can move on to make predictions. It turns out that the underlying dynamics is the replicator dynamics encountered above.References:

- K.H. Schlag, Why Imitate, and if so, How? A Boundedly Rational Approach to Multi-Armed

Bandits, Journal of Economic Theory 78(1) (1998), 130-156.- Alos-Ferrer, C. and K.H. Schlag (2007), Imitation and Learning, Handbook of Rational and Social Choice, Chapter 11, http://www.uni-konstanz.de/micro/team/alosferrer/

papers/Imitation.pdfReenforcement Learning:

In this model, players experiment between the different strategies, choosing those that performed well more likely.Reference:

- Börgers, T. and R. Sarin (1997) Learning Through Reinforcement and Replicator Dynamics, Journal of Economic Theory 77, 1-14Best Response Learning:

Next we consider more sophisticated players who know which game they are playing and who have information about what others did in the last round. A variant is fictitious play where players look at the entire history of play by others. They do not anticipate what others will do.Reference:

- Fudenberg and Levine (1998), The theory of learning in games, MIT Press.

Anticipatory Learning:

Finally we briefly consider learning when players anticipate that others will also change their strategy.Reference:

- R. Selten, Anticipatory learning in 2-person games, in R. Selten (Ed.), Game Equilibrium

Models. vol. I, Springer-Verlag, Berlin (1991), pp. 98-254

- Weibull (1995), Evolutionary Game Theory, MIT Press

Imitation:

This is a simplified cultural learning story in which individuals observe what others do and imitate those that are more successful. The specific type of imitation matters so we first need to investigate which type of imitation or learning rule has good properties. Then we can move on to make predictions. It turns out that the underlying dynamics is the replicator dynamics encountered above.References:

- K.H. Schlag, Why Imitate, and if so, How? A Boundedly Rational Approach to Multi-Armed

Bandits, Journal of Economic Theory 78(1) (1998), 130-156.- Alos-Ferrer, C. and K.H. Schlag (2007), Imitation and Learning, Handbook of Rational and Social Choice, Chapter 11, http://www.uni-konstanz.de/micro/team/alosferrer/

papers/Imitation.pdfReenforcement Learning:

In this model, players experiment between the different strategies, choosing those that performed well more likely.Reference:

- Börgers, T. and R. Sarin (1997) Learning Through Reinforcement and Replicator Dynamics, Journal of Economic Theory 77, 1-14Best Response Learning:

Next we consider more sophisticated players who know which game they are playing and who have information about what others did in the last round. A variant is fictitious play where players look at the entire history of play by others. They do not anticipate what others will do.Reference:

- Fudenberg and Levine (1998), The theory of learning in games, MIT Press.

Anticipatory Learning:

Finally we briefly consider learning when players anticipate that others will also change their strategy.Reference:

- R. Selten, Anticipatory learning in 2-person games, in R. Selten (Ed.), Game Equilibrium

Models. vol. I, Springer-Verlag, Berlin (1991), pp. 98-254

## Association in the course directory

*Last modified: Tu 01.10.2024 00:08*

The classical approach is to assume rationality. Players correctly anticipate what others are doing and in equilibrium none of the players has an incentive to deviate when assuming that none of the others deviate.

But do we really believe that players have the same beliefs and follow this equilibrium concept? In this lecture we relax these assumptions, do not make heroic assumptions about players think about each other. We assume instead that they learn over time. We investigate what happens in the long run. What will they learn? Will they all do the same thing? Will they learn to play an equilibrium as defined above? Will they sometimes never learn anything as they constantly change their actions?

This is the topic of this course.

In very simple games we will investigate what players learn to play. This will of course depend on how they learn. The models of learning highlighted below will be considered.Methodology:

There is some mathematics involved as one has to understand how play in the population changes over time. However, emphasis will be on understanding intuition in simple settings, and analysis of examples, not proving theorems nor proving general results. Notes are supplied as often the original papers too mathematical.Specific Models

Evolutionary Learning:

This is a simplified biological story in which there are only two types of players, incumbants and mutants. Those that are more successful reproduce. Search is for an evolutionarily stable strategy. In an extended version there are many types and one considers change of play according to the replicator dynamics.