[Math] the difference between mixed strategy and behavioral strategy games

game theory

I a beginner in Game theory and reading the book "Non Cooperative Game Theory" by Tamer Basar. I am not able to comprehend the difference between behavioral strategy and mixed strategy.

I saw this video:https://class.coursera.org/gametheory-003/lecture/71 but could not understand it clearly.

Thanks in advance

Best Answer

To put it simply,

  • mixed strategies assign a probability distribution over pure strategies
  • behavioural strategies assign, independently for each information set, a probability distribution over actions

Here is an example in the Coursera Game Theory Course: 4-09 - Mixed and Behavioral Strategies - https://www.youtube.com/watch?v=tT0E7PaDVck

(extensive form image of the example)

They give this as a behavioural strategy A with probability 0.5 and and G with probability 0.3

Note:

  • each information set has an independent probability distribution over actions
  • when we use this strategy, we may play (A, G), (A, H), (B, G), or (B, H) depending on what happens randomly.

They give this as a mixed strategy which is not a behavioural strategy. (0.6 (A, G), 0.4 (B, H))

Note:

  • we assign a single probability distribution over the pure strategies (A, G) and (B, H)
  • we may only possibly play (A, G) or (B, H) (not (B, G) or (A, H))
  • both decisions depend on each other so it is not a behavioural strategy

In normal form games, these 2 concepts are equivalent since there is only 1 "information set". However, this is not necessarily the case in extensive form games.

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