#OK to post homework
#George Spahn, 1-30-2022, Assignment 2
# 4

IsNash:= proc(G,a1,a2)
	a1 in BR1v(G)[a2] and a2 in BR2v(G)[a1]:
end:

# 5

PureNashEqui:= proc(G)
local r,c,nash:
	nash := {}:
	for r from 1 to nops(G) do
		for c from 1 to nops(G[1]) do 
			if IsNash(G, r, c) then
				nash := nash union {[r,c]}:
			fi:
		od:
	od:
	nash:
end:



# [[[83, 1], [39, 40], [108, 8], [88, 117], [36, 12], [17, 46], [20, 45], [62, 95], [34, 42], [23, 29], [5, 5], [7, 44]], [[103, 30], [15, 103], [80, 53], [97, 17], [40, 14], [2, 111], [102, 18], [117, 56], [112, 66], [27, 24], [55, 58], [84, 65]], [[3, 108], [100, 33], [70, 104], [16, 71], [19, 22], [93, 120], [75, 112], [14, 59], [85, 4], [72, 114], [94, 23], [76, 55]], [[56, 94], [28, 28], [90, 69], [98, 36], [41, 92], [47, 89], [9, 11], [60, 110], [81, 72], [37, 83], [111, 80], [50, 47]], [[68, 97], [87, 62], [13, 60], [59, 37], [31, 90], [96, 13], [11, 61], [86, 113], [110, 9], [51, 19], [29, 25], [101, 51]], [[66, 118], [6, 49], [104, 67], [73, 68], [78, 20], [35, 107], [24, 76], [74, 15], [33, 50], [69, 100], [79, 54], [49, 105]], [[109, 84], [54, 102], [77, 91], [119, 73], [4, 57], [46, 27], [92, 38], [105, 31], [118, 99], [120, 7], [65, 64], [18, 48]], [[107, 88], [1, 34], [99, 35], [82, 75], [91, 106], [63, 101], [113, 32], [10, 116], [57, 98], [8, 77], [21, 85], [115, 43]], [[32, 2], [116, 115], [30, 63], [12, 82], [22, 79], [53, 93], [64, 74], [25, 10], [52, 26], [44, 21], [106, 39], [114, 86]], [[67, 78], [71, 52], [43, 41], [89, 70], [61, 96], [26, 3], [38, 16], [48, 87], [58, 119], [42, 109], [95, 6], [45, 81]]]
# this game has exactly 1 pure nash equilibrium: [9,2]

# [[[25, 7], [83, 117], [38, 80], [43, 35], [119, 62], [60, 67], [69, 79], [90, 97], [103, 92], [101, 12], [7, 14], [6, 38]], [[76, 60], [61, 96], [117, 108], [33, 84], [104, 112], [67, 6], [49, 22], [53, 9], [62, 66], [20, 44], [35, 58], [2, 77]], [[22, 69], [114, 41], [84, 88], [82, 111], [36, 18], [112, 55], [52, 31], [21, 27], [47, 116], [57, 81], [50, 32], [44, 64]], [[16, 21], [99, 36], [23, 83], [118, 30], [27, 11], [42, 99], [10, 54], [46, 71], [107, 28], [24, 47], [73, 17], [89, 103]], [[48, 1], [12, 29], [100, 120], [65, 61], [28, 63], [81, 74], [98, 65], [56, 93], [26, 118], [88, 34], [31, 40], [94, 98]], [[96, 37], [51, 5], [75, 95], [78, 70], [45, 110], [86, 101], [11, 49], [19, 106], [17, 8], [87, 50], [32, 68], [79, 13]], [[97, 102], [4, 25], [68, 109], [58, 107], [30, 114], [64, 100], [55, 75], [70, 2], [54, 57], [85, 90], [13, 46], [110, 10]], [[105, 48], [9, 76], [63, 73], [93, 59], [34, 39], [40, 87], [39, 33], [109, 115], [115, 52], [108, 85], [113, 16], [106, 86]], [[74, 94], [116, 91], [59, 56], [66, 45], [120, 53], [14, 104], [102, 19], [8, 113], [41, 82], [80, 89], [37, 72], [77, 24]], [[29, 23], [71, 51], [15, 3], [92, 43], [95, 4], [91, 15], [18, 26], [3, 78], [1, 42], [72, 105], [5, 20], [111, 119]]]
# this game has 2 pure nash equilibria: [8,8] and [10,12]

# [[[108, 8], [20, 28], [25, 7], [89, 58], [53, 64], [51, 6], [114, 40], [115, 84], [33, 95], [62, 66], [5, 4], [23, 105]], [[32, 60], [41, 68], [74, 15], [90, 32], [86, 26], [31, 31], [98, 97], [55, 44], [1, 85], [68, 103], [52, 86], [71, 78]], [[17, 98], [95, 45], [2, 74], [101, 18], [34, 99], [94, 72], [106, 1], [59, 115], [103, 107], [60, 23], [57, 101], [45, 42]], [[22, 65], [61, 30], [97, 17], [102, 48], [112, 111], [104, 89], [36, 87], [110, 2], [64, 27], [107, 39], [69, 13], [77, 36]], [[109, 90], [99, 10], [4, 63], [30, 52], [79, 43], [81, 54], [100, 57], [42, 120], [88, 25], [118, 16], [40, 71], [26, 50]], [[82, 96], [12, 80], [93, 55], [87, 109], [15, 81], [48, 37], [6, 100], [43, 47], [3, 19], [120, 33], [8, 77], [96, 59]], [[39, 3], [85, 11], [76, 75], [21, 70], [35, 38], [56, 106], [75, 62], [58, 118], [70, 12], [83, 49], [24, 14], [116, 102]], [[78, 119], [38, 76], [19, 114], [73, 94], [49, 110], [54, 46], [7, 61], [66, 69], [92, 41], [119, 9], [11, 116], [50, 20]], [[47, 82], [113, 21], [91, 92], [29, 91], [117, 22], [84, 35], [13, 93], [9, 67], [27, 24], [65, 34], [28, 79], [37, 83]], [[80, 108], [16, 29], [44, 73], [63, 5], [10, 51], [18, 117], [105, 112], [67, 104], [72, 113], [14, 56], [111, 53], [46, 88]]]
# this game does not have any pure nash equilibria 

#[[[15, 54], [94, 21], [82, 78], [56, 117], [74, 25], [57, 118], [23, 5], [52, 119], [64, 26], [72, 59], [81, 35], [14, 79]], [[18, 106], [17, 73], [10, 88], [29, 100], [12, 89], [84, 9], [38, 98], [73, 72], [106, 19], [33, 16], [77, 92], [9, 70]], [[79, 36], [42, 46], [21, 14], [13, 55], [32, 56], [107, 27], [76, 67], [4, 85], [101, 109], [102, 8], [6, 49], [49, 104]], [[90, 50], [5, 48], [37, 91], [97, 71], [115, 80], [53, 114], [41, 99], [78, 77], [8, 3], [99, 93], [7, 6], [69, 95]], [[60, 84], [65, 64], [19, 65], [95, 43], [71, 101], [116, 87], [44, 20], [68, 86], [51, 33], [63, 60], [30, 38], [2, 40]], [[83, 47], [35, 2], [89, 90], [27, 97], [86, 39], [50, 75], [109, 37], [48, 115], [31, 29], [54, 81], [112, 94], [88, 41]], [[3, 12], [92, 45], [113, 62], [36, 10], [87, 24], [39, 76], [103, 82], [24, 34], [119, 23], [110, 57], [40, 42], [47, 83]], [[16, 7], [55, 74], [93, 30], [80, 13], [70, 63], [22, 111], [58, 52], [11, 96], [26, 31], [62, 68], [59, 53], [96, 22]], [[20, 110], [66, 113], [114, 116], [118, 28], [117, 18], [34, 17], [91, 32], [104, 44], [108, 51], [111, 107], [61, 58], [105, 66]], [[45, 1], [25, 15], [43, 102], [100, 69], [1, 103], [120, 108], [75, 11], [67, 105], [28, 120], [98, 4], [46, 61], [85, 112]]]
# this game has exactly 1 pure nash equilibrium: [9,3]

# [[[94, 112], [93, 1], [86, 18], [53, 106], [84, 60], [15, 64], [75, 47], [118, 90], [4, 46], [25, 76], [111, 29], [34, 77]], [[76, 35], [58, 3], [33, 8], [36, 30], [23, 109], [60, 15], [6, 91], [1, 101], [92, 86], [5, 26], [98, 98], [90, 119]], [[107, 108], [41, 120], [57, 28], [8, 19], [67, 40], [30, 80], [110, 96], [16, 102], [105, 118], [26, 82], [50, 70], [74, 36]], [[106, 114], [39, 21], [73, 41], [12, 27], [21, 23], [89, 94], [72, 75], [56, 72], [69, 104], [71, 73], [2, 10], [3, 66]], [[13, 83], [120, 38], [11, 37], [103, 58], [87, 87], [96, 51], [108, 105], [55, 74], [95, 84], [37, 113], [91, 59], [66, 33]], [[51, 97], [81, 57], [114, 69], [18, 89], [46, 111], [22, 62], [20, 25], [115, 107], [65, 2], [80, 93], [48, 61], [85, 67]], [[24, 56], [64, 116], [79, 79], [83, 45], [54, 92], [101, 55], [112, 32], [49, 95], [104, 50], [61, 31], [88, 110], [14, 16]], [[102, 22], [35, 103], [63, 52], [44, 7], [19, 39], [70, 11], [119, 4], [27, 12], [32, 17], [68, 5], [78, 99], [116, 81]], [[42, 100], [62, 20], [113, 24], [40, 13], [77, 54], [47, 43], [43, 78], [52, 6], [7, 9], [9, 42], [59, 71], [100, 53]], [[99, 34], [45, 88], [109, 68], [29, 63], [17, 14], [117, 48], [10, 44], [82, 65], [97, 49], [28, 115], [38, 117], [31, 85]]]
# this game does not have any pure nash equilibria