[pymprog] Constraints and Iteration

[Nico G. <nic...@gm...>]

Hi everybody,

 

I'm working on a way to do inverse linear optimization for 2 player zero sum
games, but I'm encountering some problems concerning the constraints.

 

When doing the inverse optimization, I know the probabilities with which
each strategy is played in the nash equilibrium and want to calculate one of
the many combinations of payoffs, so that my desired probabilities are a
solution to this game.

 

So, regarding this example:
http://pymprog.sourceforge.net/tutorial.html#zero-sum-two-player-game, I
want to do it basically the other way around.

 

To make things easier, I'm only regarding symmetric two player zero sum
games like Rock-Paper-Scissors (RPS), which enables me to make further
assumptions:

 

1)      Both players have the same set of strategies available

2)      If both players utilize the same strategy, the payoff for both is
zero

3)      If strategy A versus strategy B leads to an outcome of X, then
strategy B versus strategy A will lead to an outcome of -X (If I win with
paper vs. rock and score one point, I will also lose one point if my
opponent pulls the same trick and uses his paper vs. my rock).

 

Now, there are several issues I have with the constraints.

I have created the matrix like in example
http://pymprog.sourceforge.net/advanced.html#re-optimize-the-assignment:

 

m = 3 # 3 strategies

M = range(m) # payoffs of player A

n = 3 # 3 strategies

N = range(n) # payoffs of player B

 

(.)

 

 

class Test:

            def __init__(self):

            beginModel('game')

      self.x = var(A, 'x')

 

 

So far, so good. But when I try to implement point 3, it doesn't work. The
idea was to ensure that:

 

payoff of self.x[i,j] = - payoff of self.x[j,i]

 

and it'd best be done with iterations. But when trying something like this:

 

        for i in M:      

            for j in N: 

                st((self.x[i,j]) == -(self.x[i,j]))

 

 

it leads to:

 

File "C:\Users\sano98\workspace\Balancer\src\Test.py", line 77, in calculate

    st((self.x[i,j]) == -(self.x[i,j]))

  File "C:\Python25\Lib\site-packages\pymprog.py", line 77, in st

    return prob.st(cons, name, inds)

  File "C:\Python25\Lib\site-packages\pymprog.py", line 267, in st

    cons = [t for t in cons] #copy

TypeError: 'bool' object is not iterable

 

 

Strangely, the constraint itself seems to work when called without
iteration:

 

self.constraint_01= st(self.x[0,1] == -(self.x[1,0]))

self.constraint_02= st(self.x[0,2] == -(self.x[2,0]))

self.constraint_03= st(self.x[2,1] == -(self.x[1,2]))

 

 

But when it comes to place assumption 2) in the form of a constraint, it
doesn't even work this way, since:

 

self.constraint_04= st(self.x[0,0] == 0)

 

also leads to

 

  File "C:\Users\sano98\workspace\Balancer\src\Test.py", line 98, in
calculate

    self.constraint_04= st(self.x[0,0] == 0)

  File "C:\Python25\Lib\site-packages\pymprog.py", line 77, in st

    return prob.st(cons, name, inds)

  File "C:\Python25\Lib\site-packages\pymprog.py", line 267, in st

    cons = [t for t in cons] #copy

TypeError: 'bool' object is not iterable

 

 

Now, does anyone have an idea what the problem is? I can't seem to find any
pattern why some of those things work and some don't.

Thanks for the time and effort and hopefully for a solution or hint. ^_-

 

Bye

Nico