#OK to post homework
#George Spahn, 1-30-2022, Assignment 3

with(combinat):

# 3

# a
# output of RandDisGame(4,4) 
# [[[13, 8], [14, 6], [11, 4], [6, 5]], [[9, 10], [1, 11], [16, 3], [7, 9]],
#  [[3, 2], [2, 7], [12, 15], [5, 1]], [[4, 13], [10, 16], [8, 12], [15, 14]]]

# i
# row 1:  [13,8]
# row 2:  [1,11]
# row 3:  [12,15]
# row 4:  [10,16]
# Therefore row 1 is the row players best move, and the outcome is [13,8]

# ii 
# col 1: [13,8]
# col 2: [14, 6]
# col 3: [16, 3]
# col 4: [15, 14]
# Therefore col 4 is the col players best move, and the outcome is [15,14]

# iii
# set of Nash equilibria {[row 1, col 1]}
# There is a single Nash equilibrium

#b
# output of RandDisGame(5,7) 
# [[[30, 28], [16, 13], [15, 21], [11, 2], [17, 23], [29, 15], [28, 33]], 
#  [[32, 27], [1, 35], [26, 17], [31, 16], [12, 11], [9, 19], [22, 1]], 
#  [[18, 6], [13, 9], [24, 29], [8, 26], [25, 32], [33, 34], [10, 10]], 
#  [[34, 30], [27, 25], [2, 12], [23, 20], [20, 22], [4, 8], [14, 24]], 
#  [[21, 3], [6, 5], [3, 4], [19, 31], [5, 7], [7, 14], [35, 18]]]

# i
# row 1:  [28, 33]
# row 2:  [1, 35]
# row 3:  [33, 34]
# row 4:  [34, 30]
# row 5:  [19, 31]
# Therefore row 4 is the row players best move, and the outcome is [34, 30]

# ii 
# col 1: [34, 30]
# col 2: [27, 25]
# col 3: [26, 17]
# col 4: [31, 16]
# col 5: [25, 32]
# col 6: [33, 34]
# col 7: [35, 18]
# Therefore col 6 is the col players best move, and the outcome is [33, 34]

# iii
# set of Nash equilibria {[row 3, col 6], [row 4, col 1]}
# There are two Nash equilibrium



# 4
# AllGames(a,b)
# inputs positive integers a and b and outputs the st of (a*b)!^2 games where
# each player's payoffs are distinct and drawn from {1, ..., a*b}

AllGames:=proc(a,b)
local p1:
	p1 := permute(a*b):
	
	{seq(seq( 
	
	#the below line of code was copied from RandDisGame in C3.txt
	[seq([seq([pi1[b*i1+j1],pi2[b*i1+j1]],j1=1..b)],i1=0..a-1)] ,
	
	pi2 in p1), pi1 in p1)}:
end:


# 5

FullStat:=proc(a,b)
local g,toRet,n,rc,cr:
	toRet := [0,0,0,0,0,0]:
	for g in AllGames(a,b) do
		n := nops(PureNashEqui(g)):
		if n = 0 then
			toRet[1] := toRet[1]+1:
		elif n = 1 then
			toRet[2] := toRet[2]+1:
		elif n = 2 then 
			toRet[3] := toRet[3]+1:
		fi:
		rc := DynRC(g)[2]:
		cr := DynCR(g)[2]:
		if rc[1] < cr[1] then 
			toRet[4] := toRet[4]+1:
		fi:
		if rc[2] > cr[2] then 
			toRet[5] := toRet[5]+1:
		fi:
		if rc = cr then
			toRet[6] := toRet[6]+1:
		fi:
		
	od:
	toRet:
end:


# 6

SampleStat:=proc(a,b,K)
local i,toRet,g,n,rc,cr: 
	toRet := [0,0,0,0,0,0]:
	for i from 1 to K do
		g:= RandDisGame(a,b):
		n := nops(PureNashEqui(g)):
		if n = 0 then
			toRet[1] := toRet[1]+1:
		elif n = 1 then
			toRet[2] := toRet[2]+1:
		elif n = 2 then 
			toRet[3] := toRet[3]+1:
		fi:
		rc := DynRC(g)[2]:
		cr := DynCR(g)[2]:
		if rc[1] < cr[1] then 
			toRet[4] := toRet[4]+1:
		fi:
		if rc[2] > cr[2] then 
			toRet[5] := toRet[5]+1:
		fi:
		if rc = cr then
			toRet[6] := toRet[6]+1:
		fi:
	od:

	[seq(evalf(k/K), k in toRet)]:
end: