Teoria dos Jogos-Aneirson

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library(rgamer)
library(utf8)
game0<- normal_form(players = c("S","s"),
                    s1=c("A","B"),
                    s2=c("A","B"),
                    cells = list(c(3,3),
                                 c(0,1),
                                 c(1,1),
                                 c(2,3)),
                                 byrow = T)

s_game0<- solve_nfg(game0,show_table = T,mixed = TRUE)
s_game0$br_plot

game01<- normal_form(players = c("S","s"),
                    s1=c("A","B"),
                    s2=c("a","b"),
                    cells = list(c(3,2),
                                 c(5,5),
                                 c(0,0),
                                 c(7,4)),
                    byrow = T)

s_game01<- solve_nfg(game01,show_table = T)#mixed = TRUE)

Pure-strategy NE: [B, b]

		s
	strategy	a	b
S	A	3^, 2	5, 5^
	B	0, 0	7^, 4^

s_game01$br_plot

game02<- normal_form(players = c("j1","j2"),
                     s1=c("Alto","Baixo"),
                     s2=c("Esquerda","Direita"),
                     cells = list(c(4,2),
                                  c(-1,0),
                                  c(0,-1),
                                  c(1,3)),
                     byrow = T)

s_game02<- solve_nfg(game02,show_table = T,mixed = TRUE)

Pure-strategy NE: [Alto, Esquerda], [Baixo, Direita]

Mixed-strategy NE: [(2/3, 1/3), (1/3, 2/3)]

The obtained mixed-strategy NE might be only a part of the solutions.
Please examine br_plot (best response plot) carefully.

		j2
	strategy	Esquerda	Direita
j1	Alto	4^, 2^	-1, 0
	Baixo	0, -1	1^, 3^

s_game02$br_plot

game03<- normal_form(players = c("Mulher","Homem"),
                     s1=c("Jantar","Cinema"),
                     s2=c("Jantar","Cinema"),
                     cells = list(c(4,3),
                                  c(1,1),
                                  c(1,1),
                                  c(3,4)),
                     byrow = T)

s_game03<- solve_nfg(game03,show_table = T,mixed = TRUE)

Pure-strategy NE: [Jantar, Jantar], [Cinema, Cinema]

Mixed-strategy NE: [(3/5, 2/5), (2/5, 3/5)]

The obtained mixed-strategy NE might be only a part of the solutions.
Please examine br_plot (best response plot) carefully.

		Homem
	strategy	Jantar	Cinema
Mulher	Jantar	4^, 3^	1, 1
	Cinema	1, 1	3^, 4^

s_game03$br_plot

jogo4 <- normal_form(
  players = c("A", "B"),
  s1 = c("Producao_alta", "Producao_baixa"), 
  s2 = c("Producao_alta", "Producao_baixa"), 
  cells = list(c(8,8),
               c(12,6),
               c(6,12),
               c(10,10)),
  byrow = T)

 s_jogo4 <- solve_nfg(jogo4, 
                     mixed = TRUE, 
                     show_table = T)

Pure-strategy NE: [Producao_alta, Producao_alta]

The payoff matrix is degenerate; No full support mixed-strategy NE exist (or infinitely many exist).
Please examine br_plot (best response plot).

		B
	strategy	Producao_alta	Producao_baixa
A	Producao_alta	8^, 8^	12^, 6
	Producao_baixa	6, 12^	10, 10

  s_jogo4$br_plot

  
  
politica<- normal_form( 
  players = c("AB","CD"),
  s1=c("Moderado","Cinico","Agressivo"),
  s2=c("Moderado","Cinico","Agressivo"),
  payoffs1 = c(-0.7, 0.5, -0.4,0.5,-0.3,0,-0.3,0.2,0.7),
  payoffs2 = c(-0.7,0.5,-0.3,0.5,-0.3,0.2,-0.4,0,0.7))
  
s_politica <- solve_nfg(politica, show_table = TRUE,mixed = T)

Pure-strategy NE: [Cinico, Moderado], [Moderado, Cinico], [Agressivo, Agressivo]

Mixed-strategy NE: [(55/196, 15/28, 9/49), (55/196, 15/28, 9/49)]

The obtained mixed-strategy NE might be only a part of the solutions.

		CD
	strategy	Moderado	Cinico	Agressivo
AB	Moderado	-0.7, -0.7	0.5^, 0.5^	-0.3, -0.4
	Cinico	0.5^, 0.5^	-0.3, -0.3	0.2, 0
	Agressivo	-0.4, -0.3	0, 0.2	0.7^, 0.7^

s_politica

$psNE
[1] "[Cinico, Moderado]"     "[Moderado, Cinico]"    
[3] "[Agressivo, Agressivo]"

$msNE
$msNE$s1
[1] 0.2806122 0.5357143 0.1836735

$msNE$s2
[1] 0.2806122 0.5357143 0.1836735


$table

		CD
	strategy	Moderado	Cinico	Agressivo
AB	Moderado	-0.7, -0.7	0.5^, 0.5^	-0.3, -0.4
	Cinico	0.5^, 0.5^	-0.3, -0.3	0.2, 0
	Agressivo	-0.4, -0.3	0, 0.2	0.7^, 0.7^

$br_plot
NULL

$msNE_df

$msNE_prob
$msNE_prob$p
[1] 0.2806122 0.5357143 0.1836735

$msNE_prob$q
[1] 0.2806122 0.5357143 0.1836735

s_politica$br_plot

NULL

supermercado<- normal_form(players = c("ABC","XYZ"),
                     s1=c("Preco_alto","Preço_baixo"),
                     s2=c("Agressivo","Conservador"),
                     payoffs1 = c(80000,45000,45000,40000),
                     payoffs2 = c(70000,30000,60000,80000))
                     #cells = list(c(80000,70000),
                                 # c(45000,60000),
                                  #c(45000,30000),
                                 # c(40000,80000)),
                     #byrow = T)
s_super <- solve_nfg(supermercado, 
                     mixed = TRUE, 
                     show_table = T)

Pure-strategy NE: [Preco_alto, Agressivo]

The payoff matrix is degenerate; No full support mixed-strategy NE exist (or infinitely many exist).
Please examine br_plot (best response plot).

		XYZ
	strategy	Agressivo	Conservador
ABC	Preco_alto	80000^, 70000^	45000^, 60000
	Preço_baixo	45000, 30000	40000, 80000^

s_super$br_plot

s_super

$psNE
[1] "[Preco_alto, Agressivo]"

$msNE
NULL

$table

		XYZ
	strategy	Agressivo	Conservador
ABC	Preco_alto	80000^, 70000^	45000^, 60000
	Preço_baixo	45000, 30000	40000, 80000^

$br_plot

$msNE_df

$msNE_prob
$msNE_prob$p
[1] 0.8333333 0.1666667

$msNE_prob$q
[1] -0.1666667  1.1666667

game1<- normal_form(
  players = c("A","B"),
  s1=c("Confessar","calar"),
  s2=c("Confessar","calar"),
  cells = list(c(5,5),
               c(0,10),
               c(10,0),
               c(2,2)),
  byrow = T)

s_game1 <- solve_nfg(game1, show_table = T)

s_game1

jogo1 <- normal_form(
  players = c("Bonnie", "Clyde"),
  s1 = c("Confessar", "Não Confessar"), 
  s2 = c("Confessar", "Não Confessar"), 
  cells = list(c(-8, -8), 
               c(0, -15),
               c(-15, 0), 
               c(-1, -1)),
  byrow = T)
s_jogo1 <- solve_nfg(jogo1, show_table = T)


jogo2 <- normal_form(
  players = c("OilFlex", "EconoGas"),
  s1 = c("Manter Preço", "Reduzir Preço"), 
  s2 = c("Manter Preço", "Reduzir Preço"), 
  payoffs1 = c(50, 60, 30, 40), 
  payoffs2 = c(50, 30, 60, 40))

s_jogo2 <- solve_nfg(jogo2, show_table = TRUE)
s_jogo2

jogo4 <- normal_form(
  players = c("Governo", "Pobre"),
  s1 = c("Ajuda", "Não Ajuda"), 
  s2 = c("Trabalha", "Vadia"), 
  payoffs1 = c(3, -1, -1, 0), 
  payoffs2 = c(2, 1, 3, 0))

s_jogo4 <- solve_nfg(jogo4, 
                     mixed = TRUE, 
                     show_table = T)

s_jogo4$br_plot

jogo5 <- normal_form(
  players = c("cidade_A", "Cidade_B"),
  s1 = c("Apoia", "Rejeita"), 
  s2 = c("Apoia", "Rejeita"), 
  payoffs1 = c(8, -1, 9, 0), 
  payoffs2 = c(8, 9, -1, 0))

s_jogo5 <- solve_nfg(jogo5, 
                     mixed = TRUE, 
                     show_table = T)

s_jogo5$br_plot



jogo4 <- normal_form(
  players = c("A1", "A2"),
  s1 = c("Ajuda", "Não Ajuda"), 
  s2 = c("Ajuda", "Não Ajuda"), 
  payoffs1 = c(3, 4,5,1), 
  payoffs2 = c(3, 4,5,1))

s_jogo4 <- solve_nfg(jogo4, 
                     mixed = TRUE, 
                     show_table = T)

s_jogo4$br_plot

game4 <- normal_form(
  players = c("A1","A2"),
  s1 = c("Futebol", "Filmes","Auditorio"), 
  s2 = c("Futebol", "Filmes","Auditorio"), 
  payoffs1 = c(7,5,2,9,3,4,2,4,6), 
  payoffs2 = c(7,5,2,9,3,4,2,4,6))

s_game4 <- solve_nfg(game4, 
                     mixed = TRUE, 
                     show_table = T)

Pure-strategy NE: [Futebol, Filmes], [Auditorio, Auditorio]

Mixed-strategy NE: [(1/6, 1/2, 1/3), (7/18, 1/18, 5/9)]

The obtained mixed-strategy NE might be only a part of the solutions.

		A2
	strategy	Futebol	Filmes	Auditorio
A1	Futebol	7^, 7	9^, 9^	2, 2
	Filmes	5, 5^	3, 3	4, 4
	Auditorio	2, 2	4, 4	6^, 6^

s_game4

$psNE
[1] "[Futebol, Filmes]"      "[Auditorio, Auditorio]"

$msNE
$msNE$s1
[1] 0.1666667 0.5000000 0.3333333

$msNE$s2
[1] 0.38888889 0.05555556 0.55555556


$table

		A2
	strategy	Futebol	Filmes	Auditorio
A1	Futebol	7^, 7	9^, 9^	2, 2
	Filmes	5, 5^	3, 3	4, 4
	Auditorio	2, 2	4, 4	6^, 6^

$br_plot
NULL

$msNE_df

$msNE_prob
$msNE_prob$p
[1] 0.1666667 0.5000000 0.3333333

$msNE_prob$q
[1] 0.38888889 0.05555556 0.55555556

game5 <- normal_form(
  players = c("A1","A2"),
  s1 = c("Musica", "Filmes","series"), 
  s2 = c("Musica", "Filmes","series"), 
  payoffs1 = c(2,1,-1,-1,4,1,-2,-3,1), 
  payoffs2 = c(2,1,-1,-1,4,1,-2,-3,1))

s_game5 <- solve_nfg(game5, 
                     mixed = TRUE, 
                     show_table = T)

Pure-strategy NE: [Musica, Musica], [Filmes, Filmes], [series, series]

The payoff matrix is degenerate; No full support mixed-strategy NE exist (or infinitely many exist).
It might be useful to check 'msNE_df'.

		A2
	strategy	Musica	Filmes	series
A1	Musica	2^, 2^	-1, -1	-2, -2
	Filmes	1, 1	4^, 4^	-3, -3
	series	-1, -1	1, 1^	1^, 1^

s_game5$br_plot

NULL

s_game5

$psNE
[1] "[Musica, Musica]" "[Filmes, Filmes]" "[series, series]"

$msNE
NULL

$table

		A2
	strategy	Musica	Filmes	series
A1	Musica	2^, 2^	-1, -1	-2, -2
	Filmes	1, 1	4^, 4^	-3, -3
	series	-1, -1	1, 1^	1^, 1^

$br_plot
NULL

$msNE_df

$msNE_prob
$msNE_prob$p
[1]  0.38888889 -0.05555556  0.66666667

$msNE_prob$q
[1] 0.4722222 0.1666667 0.3611111

game5 <- normal_form(
  players = c("Tijolos","Chuva"),
  s1 = c("T1", "T2","T3"), 
  s2 = c("C1", "C2","C3"), 
  payoffs1 = c(80,60,80, 30,90,80,75,70,50), 
  payoffs2 = c(80,60,80, 30,90,80,75,70,50))

s_game5 <- solve_nfg(game5, 
                     mixed = TRUE, 
                     show_table = T)

Pure-strategy NE: [T1, C1], [T3, C1], [T2, C2]

Mixed-strategy NE: [(18/55, 6/11, 7/55), (5/11, 2/11, 4/11)]

The obtained mixed-strategy NE might be only a part of the solutions.

		Chuva
	strategy	C1	C2	C3
Tijolos	T1	80^, 80^	30, 30	75^, 75
	T2	60, 60	90^, 90^	70, 70
	T3	80^, 80^	80, 80^	50, 50

s_game5$br_plot

NULL

s_game5

$psNE
[1] "[T1, C1]" "[T3, C1]" "[T2, C2]"

$msNE
$msNE$s1
[1] 0.3272727 0.5454545 0.1272727

$msNE$s2
[1] 0.4545455 0.1818182 0.3636364


$table

		Chuva
	strategy	C1	C2	C3
Tijolos	T1	80^, 80^	30, 30	75^, 75
	T2	60, 60	90^, 90^	70, 70
	T3	80^, 80^	80, 80^	50, 50

$br_plot
NULL

$msNE_df

$msNE_prob
$msNE_prob$p
[1] 0.3272727 0.5454545 0.1272727

$msNE_prob$q
[1] 0.4545455 0.1818182 0.3636364

game1<- normal_form(
  players = c("Ladrao","Policia"),
  s1=c("Assaltos_noturnos","Assaltos_diurnos"),
  s2=c("Ronda_Noturna","Ronda_diurna"),
  payoffs1 = c(5,8,10,6), 
  payoffs2 = c(5,8,10,6))

s_game1 <- solve_nfg(game1, 
                     mixed = TRUE, 
                     show_table = T)

Pure-strategy NE: [Assaltos_diurnos, Ronda_Noturna], [Assaltos_noturnos, Ronda_diurna]

Mixed-strategy NE: [(2/7, 5/7), (4/7, 3/7)]

The obtained mixed-strategy NE might be only a part of the solutions.
Please examine br_plot (best response plot) carefully.

		Policia
	strategy	Ronda_Noturna	Ronda_diurna
Ladrao	Assaltos_noturnos	5, 5	10^, 10^
	Assaltos_diurnos	8^, 8^	6, 6

s_game1

$psNE
[1] "[Assaltos_diurnos, Ronda_Noturna]"
[2] "[Assaltos_noturnos, Ronda_diurna]"

$msNE
$msNE$s1
[1] 0.2857143 0.7142857

$msNE$s2
[1] 0.5714286 0.4285714


$table

		Policia
	strategy	Ronda_Noturna	Ronda_diurna
Ladrao	Assaltos_noturnos	5, 5	10^, 10^
	Assaltos_diurnos	8^, 8^	6, 6

$br_plot

$msNE_df

$msNE_prob
$msNE_prob$p
[1] 0.2857143 0.7142857

$msNE_prob$q
[1] 0.5714286 0.4285714

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