An introduction to Game Theory
10. Jul 2011•0 gefällt mir•64,061 views
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This presentation is an attempt to introduce Game Theory in one session. It's suitable for undergraduates. In practice, it's best used as a taster since only a portion of the material can be covered in an hour - topics can be chosen according to the interests of the class. The main reference source used was 'Games, Theory and Applications' by L.C.Thomas. Further notes available at: http://bit.ly/nW6ULD
Paul TraffordFolgen
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An introduction to Game Theory
- 50. Assumes repeated play and is a result that is more reliable the more times played
- 51. In practice, it takes no account of the strategy of the opponent – even if they keep playing the same pure strategy, the expected return is no more, no less…
- 74. E2(x,y):=5xy-x-y+1 - think of this as the y-axis
- 75. Z:=0 – any value will be fine
Hinweis der Redaktion
- This presentation was originally delivered to 4th Year Management undergraduates at Gakushuin University, Tokyo.
- Idea of this game in slides 2 and 3 is to indicate the distinction between non-cooperative and co-operative games, and how the latter can radically improve the returns.
- A. Everyone can agree to writing down £1 and they would all share £1,000 … This is an example of a cartel. But it is unstable: if someone changes their mind at the last minute … ?Consider if this game were repeated in real life … issues of trust – short term gains, long term losses.
- Another definition is in terms of situations where there is conflict, but this emphasizes oppositional tendencies as it is derived from Latin, literally meaning “strike” or “hit” together, as in war, but actually competitions may not have such opposition (as we will discuss in topic on cooperation).
- (Philosophical) Assumptions:A certain predictability concerning human rationality…?A somewhat narrow definition of rationality?
- Strategy depends on the objective.
- Consider the traffic, the weather, … Comment: in practice, for complex games, it is not possible to determine a complete strategy.
- For repeated games, the level of cooperation may change and payoffs fall!
- Go, Bridge, Ludo, Draughts, Scissors-Paper-Stone (jan-ken), ChessMonopoly, Noughts and Crosses (Tic-tac-toe), Scrabble
- For each game, can ask class to choose which box.
- (zero-sim: the total wealth is a constant)
- “Nim-sum” (⊕) [this is the exclusive OR sum applied successively)Robtexhttp://www.robtex.com/frames.htm#http://www.robtex.com/robban/nim1.htmCount the matches left to right and click on the next one to remove that and all the rest to the right.
- Demonstration..
- As this is a zero-sum game, it means whenever there is a value > 0 for Player A, there is a negative value for Player B and conversely.
- It is the simplest form of equilibrium.
- Remember that the payoffs are given for player A and signs must be reversed when evaluated for Player B.
- notes: (i) right click col/row label deletes that col/row – to add rows, click on table icon next to avatar(ii) to resize columns and rows, drag towards right of cell
- In the file menu select: Tools -> Equilibrium and then (‘Computer all Nash equilibria’, ‘with Gambit’s recommended method).
- This is a famous problem that was originally formulated by A.W. Tucker
- <demo: prisoners2by2.gmb>
- Comments: It’s the difference between considering “what’s best for me, regardless” and “what’s best for everyone”.In practice, there may be a great difference in behaviour between playing this game once vs. many times.