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from pymprog import *



#####Solve this 2-player 0-sum game:

##

##     Gain for player 1 

##    (Loss for player 2)

##   

##            ||  Player  2

##   Player 1 ||  B1     B2

##      A1    ||  5      9

##      A2    ||  8      6

##

##############################



begin('game')

# the gain of player 1

v = var('game_value', 

      bounds=(None,None)) #free

# mixed strategy of player 2

p = var('prob', [1,2]) 

# player 2 wants to minimize v

minimize(v) 

# probability sums to 1

st(p[1]+p[2] == 1)

# player 1 plays the best strat.

r1=st(v >= 5*p[1] + 9*p[2])

r2=st(v >= 8*p[1] + 6*p[2])

solve()

print(v)

print("Player 1's mixed Strategy:" )

print("A1: %r; A2: %r"%(r1.dual, r2.dual))

print("Player 2's mixed strategy:" )

print("B1: %r; B2: %r"%(p[1].primal, p[2].primal))

end()