Change representation of MixedBehaviorProfile and MixedStrategyProfile

[d-kad]

Reimplementing __repr__ method for classes MixedBehaviorProfile and MixedStrategyProfile in the style of the hierarchical index of pandas.Series

[edwardchalstrey1]

Hi @d-kad I have just taken a look at this, all looks good to me - I tested how the MixedBehaviorProfile and MixedStrategyProfile look with the changed __repr__ by combining this branch with my tutorials over on #556 and the changes look good to me, I would just need to update some of the print statements in those notebooks if we merge this first.

[tturocy]

This is something like what I had in mind, but I had two observations. The first is probably something we want to deal with straightaway, the second might be suitable for a follow-on issue.

The more immediate thing to look at is how this interacts with NashComputationReslut. For example, with the game g from contrib/games/e02.efg:

In[4]: gbt.nash.enummixed_solve(g)
Out[4]: 
NashComputationResult(method='enummixed', rational=True, use_strategic=True, equilibria=[Player 1 1* 1
         21 0
         22 0
Player 2 1  1
         2  0, Player 1 1* 1
         21 0
         22 0
Player 2 1  1/2
         2  1/2], parameters={})

Which is kind of ugly. We should probably change that to say something like
equilibria=[<list of N profiles>]? @rahulsavani suggestions for the terminology here?

The second thought is whether we want to have any column labels and/or provide other details. The command-line tool gambit-lcp offers "detailed" output for the profiles it finds. Again working with e02.efg here's what it generates for the strategic form:

Strategy profile for player 1:
Strategy   Prob          Value
--------   -----------   -----------
      1*             1             1
      21             0             0
      22             0             0
Strategy profile for player 2:
Strategy   Prob          Value
--------   -----------   -----------
       1             1             1
       2             0             1

And here's what it does for the extensive form (mixed behaviour profile):

Behavior profile for player 1:
Infoset    Action     Prob          Value
-------    -------    -----------   -----------
  (1,1)          R             1             1
  (1,1)          L             0           1/2
  (1,2)          r           1/2             0
  (1,2)          l           1/2             0

Infoset    Node       Belief        Prob
-------    -------    -----------   -----------
  (1,1)          1             1             1
  (1,2)          5             0             0

Behavior profile for player 2:
Infoset    Action     Prob          Value
-------    -------    -----------   -----------
  (2,1)          R           1/2             0
  (2,1)          L           1/2             0

Infoset    Node       Belief        Prob
-------    -------    -----------   -----------
  (2,1)          3             0             0

Probably showing beliefs ought to be separate (as we are not yet writing anything that produces a behaviour assessment!) - but showing payoffs as well might be nice.

To be clear in the above I wouldn't recommend the very verbose headers as done in the command-line output - I like having the players done a la pandas' hierarchical indexing as it is much more compact.