#Ok to post homework
#Lucy Martinez, 02-17-22, Assignment 8
read `C7.txt`:
#----------------------Problem 3-----------------------#
# Prove that in the version of the Snwodrift game in section 1.4, 
# with T>R>S>P, (Refuse,Pay) and (Pay,Refuse) are two pure Nash equilibria
# Either by hand, or using Maple, prove that in addition there is 
# a mixed Nash equilibrium. Find an explicit expression for that additional 
# Nash equilibrium, in terms of the parameters T,R,S,P, and check it 
# for random numerical values using MNE(G)

G:=Matrix([[[4,4],[3,5]],[[5,3],[1,1]]]):

# Since the Mixed Nash Equilibrium for this problem is expected to be ((P-S)/(R-S-T+P),(P-S)/(R-S-T+P))
# in which this case G gives us that T=5,R=4,S=3,P=1 where T>R>S>P. 
# Here, given those values from G, we should get that the mixed nash equilibrium 
# is (2/3,2/3) after some calculation.

MNE22(G);
# { [0, 1], [1, 0], [2/3,2/3] }