What is the difference between mixed strategy and behavioral strategy games? 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
 A: 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.
A: Well the answer is rather simple, I think the video in coursera (referred in the question) made it unnecessarily complex. 
Suppose A and B are playing a game in which both have to randomly choose a card each from a pair 'W' and 'L'. 
Whoever gets a 'W' gets +1 and whoever gets 'L' gets -1.
A is allowed to play again, but under the condition that he has not seen whether he won or lost. 
Only the winner can choose whether to continue the play or not. 
If the game continues then A can decide whether to exchange cards with B or keep them as it is

S = stop, C= continue, K = keep, E = Exchange
A's strategies could be (S,E), (S,K), (C,E), (C,K)
B's strategy (S), (C)
In this context if A chooses to play the strategies  and  with probabilities say 0.5 and 0.5, then this is the mixed strategy.
If however, A assigns independent probabilities when he plays for the first time and the second time. 
That is S with say 0.4, C with 0.6 for the first time play and 
0.9 for E and 0.1 for K for the second time play
This independent assignment of strategy is called the behavioral strategy.
The mixed strategy for (S,E) and (C,K) is 0.36 and 0.06 
Reference: http://www.ma.huji.ac.il/hart/papers/ext-hgt.pdf
