%pylab inline

# Helper functions

def other(x):
    return 1-x

def first(x):
    return x[0]

def second(x):
    return x[1]

# Print a 2x2 psayoff matrix
def print_mat(payoffs):
    for i in range(2):
        for j in range(2):
            print payoffs[i][j],
        print

# Find Nash equilibria (2x2 matrix)

def Nash(payoffs):
    for i in range(2):
        for j in range(2):
            if first(payoffs[i][j])>=first(payoffs[other(i)][j]) and second(payoffs[i][j])>=second(payoffs[i][other(j)]):
                    print moves[i],moves[j],' ===> resulting in:',payoffs[i][j]

# prisoners dillema

moves=['C','D']
payoffs=[[(-1,-1),(-3,0)],[(0,-3),(-2,-2)]]

print_mat(payoffs)
Nash(payoffs)

# Choosing sides

moves=['left','right']
payoffs=[[(10,10),(0,0)],[(0,0),(10,10)]]
print_mat(payoffs)
Nash(payoffs)

# Pure coordination game

moves=['Party','Home']
payoffs=[[(10,10),(0,0)],[(0,0),(5,5)]]
print_mat(payoffs)
Nash(payoffs)

# Battle of the sexes

moves=['Party','Home']
payoffs=[[(10,5),(0,0)],[(0,0),(5,10)]]
print_mat(payoffs)
Nash(payoffs)

# Stag hunt

moves=['Stag','Hare']
payoffs=[[(10,10),(0,8)],[(8,0),(7,7)]]
print_mat(payoffs)
Nash(payoffs)

def mixed(payoff):
    top,bottom=payoffs
    (A,a),(C,c)=top
    (B,b),(D,d)=bottom
    
    print "Player 1"
    p = float((d-b))/(a+d-b-c) 
    print p, "for ",moves[0]
    print 1-p, "for ",moves[1]
    
    print "Player 2"
    q = float((D-C))/(A+D-B-C)
    print q, "for ",moves[0]
    print 1-q, "for ",moves[1]

moves=['Party','Home']
payoffs=[[(10,5),(0,0)],[(0,0),(5,10)]]
print_mat(payoffs)
mixed(payoffs)

# Here is how you can get the computer to do the algebera for you.

from sympy import *
init_printing()

a,b,c,d,p = symbols("a b c d p")
A,B,C,D,q = symbols("A B C D q")

# to find p where LEFT=RIGHT we solve LEFT-RIGHT=0 for p.
print "p="
pretty_print(solve("p*a + (1-p)*b - p*c - (1-p)*d",p))

# to find q where UP=DOWN we solve UP-DOWN=0 for q.
print "q="
pretty_print(solve("q*A + (1-q)*C - q*B - (1-q)*D",q))

r,p,s = symbols("r p s")

solve(["-p+s-r+s",
       "r-s+r-p",
       "1-r-p-s"])