gamet

Stata help for gamet

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help for gamet
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Game Theory



    gamet , payoff(#U111,#U211, ... ,#U11_c,#U21_c ... ,#U11_C,#U21_C \ ... \
                   #U1_r1,#U2_r1, ... ,#U1_r_c,#U2_r_c ... ,#U1_r_C,#U2_r_C \ ... \
                   #U1_R1,#U2_R1, ... ,#U1_R_c,#U2_R_c ... ,#U1_R_C,#U2_R_C)



                 [ ls1(lab_s1) ls2(lab_s2)
                 player1(rlab1 ... rlab_r ... rlab_R)
                 player2(clab1 ... clab_c ... clab_C)



                 domist elids neps nefms maximin gtree



                 npath aspect(#) mlabpls(clockpos) mlabppm(clockpos) mlabpp1(clockpos) mlabpp2(clockpos)
                 savingpf(filename) textpp(textsizestyle) texts(textsizestyle) msizepp(relativesize)
                 msizes(relativesize)



                 scatter_options ]



Description



    gamet represents the extensive form (game tree) and the strategic form (payoff matrix) of a
          non-cooperative game and identifies the solution of a non-zero and zero-sum game through:
          dominant and dominated strategies, iterated elimination of strongly dominated strategies,
          Nash equilibrium in pure and fully mixed strategies. Further, gamet is able to identify the
          solution of a zero-sum game through maximin criterion and the solution of extensive form
          through backward induction.



Payoff matrix



    --------------------------------------------------------------------------------------
              |                                      lab_s2
       lab_s1 |      clab1         ...         clab_c         ...          clab_C
    ----------+---------------------------------------------------------------------------
        rlab1 | (#U111; #U211)     ...   (#U11_c; #U21_c)     ...    (#U11_C; #U21_C)
          ... |      ...           ...          ...           ...            ...
       rlab_r | (#U1_r1; #U2_r1)   ...   (#U1_r_c; #U2_r_c)   ...    (#U1_r_C; #U2_r_C)
          ... |      ...           ...          ...           ...            ...
       rlab_R | (#U1_R1; #U2_R1)   ...   (#U1_R_C; #U2_R_C)   ...    (#U1_R_C; #U2_R_C)
    --------------------------------------------------------------------------------------



    payoff(...) is not optional and provides a way to input, row after row, a general R by C payoff matrix
        (help matrix input), where



    #U1_r_c is the utility for lab_s1 if lab_s1 chooses strategy r and lab_s2 chooses strategy c
    #U2_r_c is the utility for lab_s2 if lab_s1 chooses strategy r and lab_s2 chooses strategy c



    with r = 1,2, ..., R and c = 1,2, ..., C



Remark



    gamet is an immediate command given that obtains data not from the data stored in memory but
          from numbers typed as arguments (help immed).



Options



    ls1(lab_s1) attaches a label to the set of strategies for player 1. The default is S1.



    ls2(lab_s2) attaches a label to the set of strategies for player 2. The default is S2.



    player1(rlab1 rlab2 ... rlab_r ... rlab_R) attaches a label for each strategy of player 1.  The default
        is A1, B2, C3 and so on.



    player2(clab1 clab2 ... clab_c ... clab_C) attaches a label for each strategy of player 2.  The default
        is a1, b2, c3 and so on.



    domist seeks strongly dominated and dominant strategies for each player.
    
    elids eliminates iteratively all strongly dominated strategies for each player.



    neps seeks Nash equilibrium in pure strategies.



    nefms seeks Nash equilibrium in fully mixed strategies (0<p<1 and 0<q<1).
        It works only if R and C are equal to 2.



    maximin seeks the saddle-point through the minimal column maximum for player 1 and maximal row minimum
        for player 2.  It works for zero-sum games. That is, #U1_r_c + #U2_r_c == 0.



    gtree seeks the equilibrium path through backward induction (player 1 moves first).  It produces a
        graphical representation of a sequential game, called game tree.



    savingpf(filename) saves the variables obtained by the conversion of the payoff matrix in a file. If the
        option elids is specified savingpf() saves one file(filename#) for each iteration.



    npath specifies no equilibrium path on the game tree.



    aspect(#) modifies the aspect ratio (height/widht) of the plot region. By default is set to 1 (equal
        height and width) so the plot region is a square. See  graph_display.



    mlabpls(clockpos) specifies the position for label lab_s1 and lab_s2 on the game tree. Use clockpos to
        make changes from the default (9).



    mlabppm(clockpos) specifies the position for #U1_r_c, #U2_r_c on the game tree. Use clockpos to make
        changes from the default (3).



    mlabpp1(clockpos) specifies the position for strategies' labels on the game tree for player 1. Use
        clockpos to make changes from the default (12).



    mlabpp2(clockpos) specifies the position for strategies' labels on the game tree for player 2. Use
        clockpos to make changes from the default (9).



    textpp(textsizestyle) specifies the text size style for lab_s1, lab_s2 and (#U1_r_c; #U2_r_c). Use
        textsizestyle to make changes from the default (medium).



    texts(textsizestyle) specifies the text size style for strategies' labels. Use textsizestyle to make
        changes from the default (small).



    msizepp(relativesize) choices for sizes for objects lab_s1, lab_s2 and (#U1_r_c; #U2_r_c).  Use
        relativesize to make changes from the default (2).



    msizes(relativesize) choices for sizes for strategies' labels. Use relativesize to make changes from the
        default (2).



    scatter_options are options of scatter.



Examples



     . gamet, payoff(2, 2, 0, 1 \ 3, 0 , 1, 1) player1(High Low) player2(Buy Not_buy) ///
                ls1(Provider) ls2(Customer) domist



     . gamet, pay(3, 0, 0 , 2 , 0, 3\2, 0 , 1, 1 , 2, 0 \ 0, 3 , 0 , 2, 3, 0 ) ///   
               ls1(C1) ls2(C2) player1(x1 y1 z1)  player2(x2 y2 z2) elids



     . gamet, payoff(0,0,12,8,18,9,36,0\ 8,12,16,16,20,15,32,0\9,18,15,20,18,18,27,0\0,36,0,32,0,27,0,0)///
               player1(H M L N) player2(h m l n) ls1(Firm_I) ls2(Firm_II) elids 



     . gamet, payoff(3, 1, 0, 0\0, 0, 1, 3) player1(Football Ballet) player2(Football Ballet) /// 
                ls1(Boy) ls2(Girl) neps



     . gamet, pay(0, 0, -10, 10 \ -1, 0, -6, -90) player1(Not_inspect Inspect) ///
                 player2(Comply Cheat) ls1(I) ls2(II) nems 



     . gamet, payoff(2, 2, 0, 1 \ 3, 0 , 1, 1) player1(High Low) ///  
                    player2(Buy Not_buy) ls1(I) ls2(II) gtree



     . gamet, payoff(0,0,12,8,18,9,36,0\ 8,12,16,16,20,15,32,0\9,18,15,20,18,18,27,0\0,36,0,32,0,27,0,0)///
               player1(H M L N) player2(h m l n) ls1(Firm_I) ls2(Firm_II) gtree



     . gamet, payoff(-5,5,3,-3,1,-1,20,-20\5,-5,5,-5,4,-4,6,-6\-4,4,6,-6,0,0,-5,5) /// 
                    player1(1 2 3) player2(1 2) maximin 



Authors



    Nicola Orsini, Institute of Environmental Medicine, Karolinska Institutet, Stockholm, Sweden.
    Debora Rizzuto, Department of Public Health, University of Siena, Italy.
    Nicola Nante, Department of Public Health, University of Siena, Italy.



Reference



    Myerson, R. B. 1991. Game Theory: Analysis of Conflict, Harvard University Press, Cambridge (MA).



Support



    http://nicolaorsini.altervista.org
    nicola.orsini@imm.ki.se



Also see



On-line:  help for matrix, _variables, tabdisp, macrolists

Worked examples for gamet

Click here to run or save the do-file

. capture net install http://nicolaorsini.altervista.org/stata/gamet

. 
. which gamet
.\gamet.ado
*! N.Orsini, D.Rizzuto, N.Nante
*! Version 1.0 - November 4, 2004
*! Version 1.1 - November 8, 2004
*! Version 1.2 - February 19, 2005

. 
. help gamet

. 
. * DOMINANT AND DOMINATED STRATEGIES
. 
. gamet , payoff(2, 2, 0, 1 \ 3, 0 , 1, 1) player1(High Low) player2(Buy Not_bu
> y) ls1(Provider) ls2(Customer) domist

----------------------------
          |     Customer    
 Provider |   Buy    Not_buy
----------+-----------------
     High |  (2; 2)   (0; 1)
      Low |  (3; 0)   (1; 1)
----------------------------

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for Provider is High
    No dominated strategy for Customer
    Dominant strategy for Provider is Low
    No dominant strategy for Customer

. 
. * ITERATED ELIMINATION OF STRONGLY DOMINATED STRATEGIES
. 
. gamet, payoff(0, 0, 12, 8, 18, 9, 36, 0\ 8, 12, 16, 16, 20, 15, 32, 0 \ 9, 18
> , 15, 20, 18, 18, 27, 0\0, 36, 0, 32, 0, 27, 0, 0) ///
>  player1(H M L N) player2(h m l n) ls1(Firm_I) ls2(Firm_II) elids

--------------------------------------------------
          |                Firm_II                
   Firm_I |     h         m         l         n   
----------+---------------------------------------
        H |  (0; 0)    (12; 8)   (18; 9)   (36; 0)
        M |  (8; 12)  (16; 16)  (20; 15)   (32; 0)
        L |  (9; 18)  (15; 20)  (18; 18)   (27; 0)
        N |  (0; 36)   (0; 32)   (0; 27)   (0; 0) 
--------------------------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for Firm_I is N
    Dominated strategy for Firm_II is n
    No dominant strategy for Firm_I
    No dominant strategy for Firm_II

----------------------------------------
          |           Firm_II           
   Firm_I |     h         m         l   
----------+-----------------------------
        H |  (0; 0)    (12; 8)   (18; 9)
        M |  (8; 12)  (16; 16)  (20; 15)
        L |  (9; 18)  (15; 20)  (18; 18)
----------------------------------------

Iteration 2

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for Firm_I is H
    Dominated strategy for Firm_II is h
    No dominant strategy for Firm_I
    No dominant strategy for Firm_II

------------------------------
          |      Firm_II      
   Firm_I |     m         l   
----------+-------------------
        M | (16; 16)  (20; 15)
        L | (15; 20)  (18; 18)
------------------------------

Iteration 3

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for Firm_I is L
    Dominated strategy for Firm_II is l
    Dominant strategy for Firm_I is M
    Dominant strategy for Firm_II is m

--------------------
          | Firm_II 
   Firm_I |     m   
----------+---------
        M | (16; 16)
--------------------

Iteration 4

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Firm_I
    No dominated strategy for Firm_II
    Dominant strategy for Firm_I is M
    Dominant strategy for Firm_II is m

. 
. * NASH EQUILIBRIM IN PURE STRATEGIES 
. 
. gamet , payoff(2, 2, 0, 1 \ 3, 0 , 1, 1) player1(High Low) player2(Buy Not_bu
> y) ls1(Provider) ls2(Customer) domist neps 

----------------------------
          |     Customer    
 Provider |   Buy    Not_buy
----------+-----------------
     High |  (2; 2)   (0; 1)
      Low |  (3; 0)   (1; 1)
----------------------------

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for Provider is High
    No dominated strategy for Customer
    Dominant strategy for Provider is Low
    No dominant strategy for Customer

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. Low Not_buy (1; 1)

. 
. * NASH EQUILIBRIM IN MIXED STRATEGIES 
.  
. gamet , payoff(2, 2, 0, 1 \ 3, 0 , 1, 1) player1(High Low) player2(Buy Not_bu
> y) ls1(Provider) ls2(Customer)  neps  

----------------------------
          |     Customer    
 Provider |   Buy    Not_buy
----------+-----------------
     High |  (2; 2)   (0; 1)
      Low |  (3; 0)   (1; 1)
----------------------------

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. Low Not_buy (1; 1)

. 
. gamet, pay(0, 0, -10, 10 \ -1, 0, -6, -90) player1(Not_inspect Inspect) playe
> r2(Comply Cheat) ls1(I) ls2(II) nefms

----------------------------------
            |          II         
          I |   Comply     Cheat  
------------+---------------------
Not_inspect |   (0; 0)   (-10; 10)
    Inspect |  (-1; 0)   (-6; -90)
----------------------------------

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.90
     q = 0.80

    (0.90*[Not_inspect]+0.10*[Inspect], 0.80*[Comply]+0.20*[Cheat])

    Expected equilibrium payoff for I
    0.80*0+(1-0.80)*-10 = -2
    0.80*-1+(1-0.80)*-6 = -2

    Expected equilibrium payoff for II
    0.90*0+(1-0.90)*0 = 0
    0.90*10+(1-0.90)*-90 = 0

. 
. * GAME TREE - BACKWARD INDUCTION
. 
. gamet , payoff(2, 2, 0, 1 \ 3, 0 , 1, 1) player1(High Low) player2(Buy Not_bu
> y) ls1(Provider) ls2(Customer) gtree 

----------------------------
          |     Customer    
 Provider |   Buy    Not_buy
----------+-----------------
     High |  (2; 2)   (0; 1)
      Low |  (3; 0)   (1; 1)
----------------------------

BACKWARD INDUCTION
    Equilibrium path: High Buy
    Payoffs pair: (2; 2)



. 
. gamet, payoff(2, 2, 0, 1 \ 3, 0 , 1, 1) player1(High Low)  player2(Buy Not_bu
> y) ls1(I) ls2(II) gtree ///
> plotregion(color(yellow)) graphregion(color(yellow))  note(Change layout as m
> uch as you like)  texts(large) ///
> msizes(*12) mlabpp1(9) title(Quality choice example) subtitle(I moves first) 

----------------------------
          |        II       
        I |   Buy    Not_buy
----------+-----------------
     High |  (2; 2)   (0; 1)
      Low |  (3; 0)   (1; 1)
----------------------------

BACKWARD INDUCTION
    Equilibrium path: High Buy
    Payoffs pair: (2; 2)



. 
. gamet, payoff(0, 0, 12, 8, 18, 9, 36, 0\ 8, 12, 16, 16, 20, 15, 32, 0 \ 9, 18
> , 15, 20, 18, 18, 27, 0\0, 36, 0, 32, 0, 27, 0, 0) ///
>  player1(H M L N) player2(h m l n) ls1(Firm_I) ls2(Firm_II) gtree title(Exten
> sive form) 

--------------------------------------------------
          |                Firm_II                
   Firm_I |     h         m         l         n   
----------+---------------------------------------
        H |  (0; 0)    (12; 8)   (18; 9)   (36; 0)
        M |  (8; 12)  (16; 16)  (20; 15)   (32; 0)
        L |  (9; 18)  (15; 20)  (18; 18)   (27; 0)
        N |  (0; 36)   (0; 32)   (0; 27)   (0; 0) 
--------------------------------------------------

BACKWARD INDUCTION
    Equilibrium path: H l
    Payoffs pair: (18; 9)


. 
. * MAXIMIN FOR ZERO-SUM GAME
. 
. gamet, payoff(-5, 5, 3, -3, 1, -1, 20, -20\5, -5, 5, -5, 4, -4, 6, -6\ -4, 4,
>  6, -6, 0, 0, -5, 5) ///
> player1(1 2 3) player2(1 2 3 4) maximin

------------------------------------------------------
          |                     S2                    
       S1 |     1          2          3          4    
----------+-------------------------------------------
        1 |  (-5; 5)    (3; -3)    (1; -1)   (20; -20)
        2 |  (5; -5)    (5; -5)    (4; -4)    (6; -6) 
        3 |  (-4; 4)    (6; -6)     (0; 0)    (-5; 5) 
------------------------------------------------------

ZERO-SUM GAME - MAXIMIN CRITERION
    Minimal Column Maximum of S1 = 4
    Maximal Row Minimum of -{S2} = -4
    Saddle-point = 2 3

. 
. * EXAMPLES 
. 
. * example from http://www.cdam.lse.ac.uk/Reports/Files/cdam-2001-09.pdf
. 
.  gamet, payoff(2, 2, 0, 1 \ 3, 0 , 1, 1) player1(High Low) player2(Buy Not_bu
> y) ls1(Provider) ls2(Customer) elids neps 

----------------------------
          |     Customer    
 Provider |   Buy    Not_buy
----------+-----------------
     High |  (2; 2)   (0; 1)
      Low |  (3; 0)   (1; 1)
----------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for Provider is High
    No dominated strategy for Customer
    Dominant strategy for Provider is Low
    No dominant strategy for Customer

--------------------------
          |    Customer   
 Provider |   Buy   Not_bu
----------+---------------
      Low | (3; 0)  (1; 1)
--------------------------

Iteration 2

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Provider
    Dominated strategy for Customer is Buy
    Dominant strategy for Provider is Low
    Dominant strategy for Customer is Not_buy

------------------
          |Custome
          |   r   
 Provider | Not_bu
----------+-------
      Low | (1; 1)
------------------

Iteration 3

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Provider
    No dominated strategy for Customer
    Dominant strategy for Provider is Low
    Dominant strategy for Customer is Not_buy

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. Low Not_buy (1; 1)

. 
.  gamet, payoff(2, 2, 0, 1 \ 1, 0 , 1, 1) player1(High Low) player2(Buy Not_bu
> y) ls1(Provider) ls2(Customer) elids  neps 

----------------------------
          |     Customer    
 Provider |   Buy    Not_buy
----------+-----------------
     High |  (2; 2)   (0; 1)
      Low |  (1; 0)   (1; 1)
----------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Provider
    No dominated strategy for Customer
    No dominant strategy for Provider
    No dominant strategy for Customer

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. High Buy (2; 2)
    2. Low Not_buy (1; 1)

. 
. gamet, pay(0, 0, -10, 10 \ -1, 0, -6, -90) player1(Not_inspect Inspect) playe
> r2(Comply Cheat) ls1(I) ls2(II) nefms

----------------------------------
            |          II         
          I |   Comply     Cheat  
------------+---------------------
Not_inspect |   (0; 0)   (-10; 10)
    Inspect |  (-1; 0)   (-6; -90)
----------------------------------

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.90
     q = 0.80

    (0.90*[Not_inspect]+0.10*[Inspect], 0.80*[Comply]+0.20*[Cheat])

    Expected equilibrium payoff for I
    0.80*0+(1-0.80)*-10 = -2
    0.80*-1+(1-0.80)*-6 = -2

    Expected equilibrium payoff for II
    0.90*0+(1-0.90)*0 = 0
    0.90*10+(1-0.90)*-90 = 0

.  
. gamet, payoff(-10,5, 8,-10\3, -1, 0,0) ls1(Iran) ls2(IAEA) player1(Make_nukes
>  No_nukes) player2(Inspect Not_inspect) nefms

-------------------------------------
           |           IAEA          
      Iran |   Inspect    Not_inspect
-----------+-------------------------
Make_nukes |   (-10; 5)     (8; -10) 
  No_nukes |   (3; -1)       (0; 0)  
-------------------------------------

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.06
     q = 0.38

    (0.06*[Make_nukes]+0.94*[No_nukes], 0.38*[Inspect]+0.62*[Not_inspect])

    Expected equilibrium payoff for Iran
    0.38*-10+(1-0.38)*8 = 1.1428571
    0.38*3+(1-0.38)*0 = 1.1428571

    Expected equilibrium payoff for IAEA
    0.06*5+(1-0.06)*-1 = -.625
    0.06*-10+(1-0.06)*0 = -.625

. 
. gamet, pay(50, 50, 80, 20 \ 90, 10, 20 , 80)  ls1(Serena) ls2(Venus) player1(
> DL CC) player2(DL CC) nefms

------------------------------
          |       Venus       
   Serena |    DL        CC   
----------+-------------------
       DL | (50; 50)  (80; 20)
       CC | (90; 10)  (20; 80)
------------------------------

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.70
     q = 0.60

    (0.70*[DL]+0.30*[CC], 0.60*[DL]+0.40*[CC])

    Expected equilibrium payoff for Serena
    0.60*50+(1-0.60)*80 = 62
    0.60*90+(1-0.60)*20 = 62

    Expected equilibrium payoff for Venus
    0.70*50+(1-0.70)*10 = 38
    0.70*20+(1-0.70)*80 = 38

. 
. gamet , pay(-1, -1, 3, 0 \ 0, 3, 0, 0) neps nefms elids 

------------------------------
          |         S2        
       S1 |    a1        b2   
----------+-------------------
       A1 | (-1; -1)   (3; 0) 
       B2 |  (0; 3)    (0; 0) 
------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for S1
    No dominated strategy for S2
    No dominant strategy for S1
    No dominant strategy for S2

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. A1 b2 (3; 0)
    2. B2 a1 (0; 3)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.75
     q = 0.75

    (0.75*[A1]+0.25*[B2], 0.75*[a1]+0.25*[b2])

    Expected equilibrium payoff for S1
    0.75*-1+(1-0.75)*3 = 0
    0.75*0+(1-0.75)*0 = 0

    Expected equilibrium payoff for S2
    0.75*-1+(1-0.75)*3 = 0
    0.75*0+(1-0.75)*0 = 0

. 
. gamet , pay(-1, -1, 4, 0 \ 0, 3, 0, 0) neps nefms ls1(MD) ls2(DK) player1(E D
> ) player2(E D) elids

------------------------------
          |         DK        
       MD |     E         D   
----------+-------------------
        E | (-1; -1)   (4; 0) 
        D |  (0; 3)    (0; 0) 
------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for MD
    No dominated strategy for DK
    No dominant strategy for MD
    No dominant strategy for DK

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. E D (4; 0)
    2. D E (0; 3)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.75
     q = 0.80

    (0.75*[E]+0.25*[D], 0.80*[E]+0.20*[D])

    Expected equilibrium payoff for MD
    0.80*-1+(1-0.80)*4 = 0
    0.80*0+(1-0.80)*0 = 0

    Expected equilibrium payoff for DK
    0.75*-1+(1-0.75)*3 = 0
    0.75*0+(1-0.75)*0 = 0

. 
. * examples from http://www.courses.fas.harvard.edu/~ec1052/lecture/lecture5.p
> df
. 
. gamet, pay(1, 1, 0, 4 \ 0, 2, 2 , 1) neps nefms ls1(player1) ls2(player2) pla
> yer1(U D) player2(L R) elids

--------------------------
          |    player2    
  player1 |    L       R  
----------+---------------
        U | (1; 1)  (0; 4)
        D | (0; 2)  (2; 1)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for player1
    No dominated strategy for player2
    No dominant strategy for player1
    No dominant strategy for player2

NASH EQUILIBRIUM IN PURE STRATEGIES
    None

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.25
     q = 0.67

    (0.25*[U]+0.75*[D], 0.67*[L]+0.33*[R])

    Expected equilibrium payoff for player1
    0.67*1+(1-0.67)*0 = .66666667
    0.67*0+(1-0.67)*2 = .66666667

    Expected equilibrium payoff for player2
    0.25*1+(1-0.25)*2 = 1.75
    0.25*4+(1-0.25)*1 = 1.75

. 
. gamet , pay(1, 1, 0, 2,0,4 \0,2,5,0,1,6 \0,2,1,1,2,1) player1(U M D) player2(
> L C R) elids 

----------------------------------
          |           S2          
       S1 |    L       C       R  
----------+-----------------------
        U | (1; 1)  (0; 2)  (0; 4)
        M | (0; 2)  (5; 0)  (1; 6)
        D | (0; 2)  (1; 1)  (2; 1)
----------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for S1
    Dominated strategy for S2 is C
    No dominant strategy for S1
    No dominant strategy for S2

--------------------------
          |       S2      
       S1 |    L       R  
----------+---------------
        U | (1; 1)  (0; 4)
        M | (0; 2)  (1; 6)
        D | (0; 2)  (2; 1)
--------------------------

Iteration 2

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for S1 is M
    No dominated strategy for S2
    No dominant strategy for S1
    No dominant strategy for S2

--------------------------
          |       S2      
       S1 |    L       R  
----------+---------------
        U | (1; 1)  (0; 4)
        D | (0; 2)  (2; 1)
--------------------------

Iteration 3

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for S1
    No dominated strategy for S2
    No dominant strategy for S1
    No dominant strategy for S2

. 
. gamet , pay(1, 1, 0, 2,0,4 \0,2,5,0,1,6 \0,2,1,1,2,1) player1(U M D) player2(
> L C R) elids

----------------------------------
          |           S2          
       S1 |    L       C       R  
----------+-----------------------
        U | (1; 1)  (0; 2)  (0; 4)
        M | (0; 2)  (5; 0)  (1; 6)
        D | (0; 2)  (1; 1)  (2; 1)
----------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for S1
    Dominated strategy for S2 is C
    No dominant strategy for S1
    No dominant strategy for S2

--------------------------
          |       S2      
       S1 |    L       R  
----------+---------------
        U | (1; 1)  (0; 4)
        M | (0; 2)  (1; 6)
        D | (0; 2)  (2; 1)
--------------------------

Iteration 2

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for S1 is M
    No dominated strategy for S2
    No dominant strategy for S1
    No dominant strategy for S2

--------------------------
          |       S2      
       S1 |    L       R  
----------+---------------
        U | (1; 1)  (0; 4)
        D | (0; 2)  (2; 1)
--------------------------

Iteration 3

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for S1
    No dominated strategy for S2
    No dominant strategy for S1
    No dominant strategy for S2

. 
. * examples from http://web.mit.edu/14.12/www/02F_lecture102.pdf
. 
. gamet, pay(-1, -1, 1, -10\ -10, 1, 2, 2) player1(C D) player2(C D) elids neps
>  nefms

------------------------------
          |         S2        
       S1 |     C         D   
----------+-------------------
        C | (-1; -1)  (1; -10)
        D | (-10; 1)   (2; 2) 
------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for S1
    No dominated strategy for S2
    No dominant strategy for S1
    No dominant strategy for S2

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. C C (-1; -1)
    2. D D (2; 2)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.10
     q = 0.10

    (0.10*[C]+0.90*[D], 0.10*[C]+0.90*[D])

    Expected equilibrium payoff for S1
    0.10*-1+(1-0.10)*1 = .8
    0.10*-10+(1-0.10)*2 = .8

    Expected equilibrium payoff for S2
    0.10*-1+(1-0.10)*1 = .8
    0.10*-10+(1-0.10)*2 = .8

. 
. * examples from http://web.mit.edu/14.12/www/02F_slides5_602.pdf (there is a 
> range)
. 
. * gamet, pay(2, 2, 4, 0 \0, 4, 5, 0) player1(Rabbit Stang) player2(Rabbit Sta
> ng) elids neps nefms
. 
. * examples from http://www.virtualperfection.com/gametheory/3.1.Nash%20Equili
> brium.1.0.pdf
. 
. gamet, payoff(9,9,0,8 \ 8,0,7,7) player1(U D) player2(l r) elids neps nefms

--------------------------
          |       S2      
       S1 |    l       r  
----------+---------------
        U | (9; 9)  (0; 8)
        D | (8; 0)  (7; 7)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for S1
    No dominated strategy for S2
    No dominant strategy for S1
    No dominant strategy for S2

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. U l (9; 9)
    2. D r (7; 7)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.88
     q = 0.88

    (0.88*[U]+0.13*[D], 0.88*[l]+0.13*[r])

    Expected equilibrium payoff for S1
    0.88*9+(1-0.88)*0 = 7.875
    0.88*8+(1-0.88)*7 = 7.875

    Expected equilibrium payoff for S2
    0.88*9+(1-0.88)*0 = 7.875
    0.88*8+(1-0.88)*7 = 7.875

. 
. gamet, payoff(2,1,0,0 \ 0,0,1,2) player1(U D) player2(l r) elids neps nefms

--------------------------
          |       S2      
       S1 |    l       r  
----------+---------------
        U | (2; 1)  (0; 0)
        D | (0; 0)  (1; 2)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for S1
    No dominated strategy for S2
    No dominant strategy for S1
    No dominant strategy for S2

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. U l (2; 1)
    2. D r (1; 2)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.67
     q = 0.33

    (0.67*[U]+0.33*[D], 0.33*[l]+0.67*[r])

    Expected equilibrium payoff for S1
    0.33*2+(1-0.33)*0 = .66666667
    0.33*0+(1-0.33)*1 = .66666667

    Expected equilibrium payoff for S2
    0.67*1+(1-0.67)*0 = .66666667
    0.67*0+(1-0.67)*2 = .66666667

. 
. * examples from http://www.virtualperfection.com/gametheory/3.2.NashEq2x2Norm
> alFormGames.1.0.pdf
. 
. gamet, payoff(1,-1,3,0 \ 4,2 ,0,-1) player1(U D) player2(l r) ls1(A) ls2(B) e
> lids neps nefms

----------------------------
          |        B        
        A |    l        r   
----------+-----------------
        U | (1; -1)   (3; 0)
        D |  (4; 2)  (0; -1)
----------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for A
    No dominated strategy for B
    No dominant strategy for A
    No dominant strategy for B

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. U r (3; 0)
    2. D l (4; 2)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.75
     q = 0.50

    (0.75*[U]+0.25*[D], 0.50*[l]+0.50*[r])

    Expected equilibrium payoff for A
    0.50*1+(1-0.50)*3 = 2
    0.50*4+(1-0.50)*0 = 2

    Expected equilibrium payoff for B
    0.75*-1+(1-0.75)*2 = -.25
    0.75*0+(1-0.75)*-1 = -.25

. 
. gamet, payoff(1,1.5,3,1 \ 4,2 ,3,3) player1(U D) player2(l r) ls1(A) ls2(B) e
> lids neps nefms

------------------------------
          |         B         
        A |     l         r   
----------+-------------------
        U | (1; 1.5)   (3; 1) 
        D |  (4; 2)    (3; 3) 
------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for A
    No dominated strategy for B
    No dominant strategy for A
    No dominant strategy for B

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. D r (3; 3)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.67
     q = 0.00

    (0.67*[U]+0.33*[D], 0.00*[l]+1.00*[r])

    Expected equilibrium payoff for A
    0.00*1+(1-0.00)*3 = 3
    0.00*4+(1-0.00)*3 = 3

    Expected equilibrium payoff for B
    0.67*1.5+(1-0.67)*2 = 1.6666667
    0.67*1+(1-0.67)*3 = 1.6666667

. 
. * examples from http://levine.sscnet.ucla.edu/econ201/game.pdf
. 
. gamet, payoff(1,1,0,0 \ 0,0,1,1) player1(U D) player2(l r) ls1(A) ls2(B) elid
> s neps nefms

--------------------------
          |       B       
        A |    l       r  
----------+---------------
        U | (1; 1)  (0; 0)
        D | (0; 0)  (1; 1)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for A
    No dominated strategy for B
    No dominant strategy for A
    No dominant strategy for B

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. U l (1; 1)
    2. D r (1; 1)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.50
     q = 0.50

    (0.50*[U]+0.50*[D], 0.50*[l]+0.50*[r])

    Expected equilibrium payoff for A
    0.50*1+(1-0.50)*0 = .5
    0.50*0+(1-0.50)*1 = .5

    Expected equilibrium payoff for B
    0.50*1+(1-0.50)*0 = .5
    0.50*0+(1-0.50)*1 = .5

. 
. gamet, payoff(2,2,-10,0 \ 0,-10,1,1) player1(U D) player2(l r) ls1(A) ls2(B) 
> elids neps nefms

------------------------------
          |         B         
        A |     l         r   
----------+-------------------
        U |  (2; 2)   (-10; 0)
        D | (0; -10)   (1; 1) 
------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for A
    No dominated strategy for B
    No dominant strategy for A
    No dominant strategy for B

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. U l (2; 2)
    2. D r (1; 1)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.85
     q = 0.85

    (0.85*[U]+0.15*[D], 0.85*[l]+0.15*[r])

    Expected equilibrium payoff for A
    0.85*2+(1-0.85)*-10 = .15384615
    0.85*0+(1-0.85)*1 = .15384615

    Expected equilibrium payoff for B
    0.85*2+(1-0.85)*-10 = .15384615
    0.85*0+(1-0.85)*1 = .15384615

. 
. gamet, payoff(6,6,2,7 \ 7,2,0,0) player1(U D) player2(l r) ls1(A) ls2(B) elid
> s neps nefms

--------------------------
          |       B       
        A |    l       r  
----------+---------------
        U | (6; 6)  (2; 7)
        D | (7; 2)  (0; 0)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for A
    No dominated strategy for B
    No dominant strategy for A
    No dominant strategy for B

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. U r (2; 7)
    2. D l (7; 2)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.67
     q = 0.67

    (0.67*[U]+0.33*[D], 0.67*[l]+0.33*[r])

    Expected equilibrium payoff for A
    0.67*6+(1-0.67)*2 = 4.6666667
    0.67*7+(1-0.67)*0 = 4.6666667

    Expected equilibrium payoff for B
    0.67*6+(1-0.67)*2 = 4.6666667
    0.67*7+(1-0.67)*0 = 4.6666667

. 
. * examples from http://www.polisci.ucsd.edu/~bslantch/courses/gt/problem-sets
> /w0403s.pdf
. 
. gamet, payoff(2,2,1,3\ 3,1,0,0) ls1(Player1) ls2(Player2) player1(D H) player
> 2(D H) elids neps nefms

--------------------------
          |    Player2    
  Player1 |    D       H  
----------+---------------
        D | (2; 2)  (1; 3)
        H | (3; 1)  (0; 0)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Player1
    No dominated strategy for Player2
    No dominant strategy for Player1
    No dominant strategy for Player2

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. D H (1; 3)
    2. H D (3; 1)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.50
     q = 0.50

    (0.50*[D]+0.50*[H], 0.50*[D]+0.50*[H])

    Expected equilibrium payoff for Player1
    0.50*2+(1-0.50)*1 = 1.5
    0.50*3+(1-0.50)*0 = 1.5

    Expected equilibrium payoff for Player2
    0.50*2+(1-0.50)*1 = 1.5
    0.50*3+(1-0.50)*0 = 1.5

. 
. gamet, payoff(1,1,0,0\ 0,0,1,1) ls1(Player1) ls2(Player2) player1(Bridge Barn
> ) player2(Bridge Barn) elids neps nefms

--------------------------
          |    Player2    
  Player1 | Bridge   Barn 
----------+---------------
   Bridge | (1; 1)  (0; 0)
     Barn | (0; 0)  (1; 1)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Player1
    No dominated strategy for Player2
    No dominant strategy for Player1
    No dominant strategy for Player2

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. Bridge Bridge (1; 1)
    2. Barn Barn (1; 1)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.50
     q = 0.50

    (0.50*[Bridge]+0.50*[Barn], 0.50*[Bridge]+0.50*[Barn])

    Expected equilibrium payoff for Player1
    0.50*1+(1-0.50)*0 = .5
    0.50*0+(1-0.50)*1 = .5

    Expected equilibrium payoff for Player2
    0.50*1+(1-0.50)*0 = .5
    0.50*0+(1-0.50)*1 = .5

. 
. gamet, payoff(1,1,0,0\ 0,0,2,2) ls1(Player1) ls2(Player2) player1(Bridge Barn
> ) player2(Bridge Barn) elids neps nefms

--------------------------
          |    Player2    
  Player1 | Bridge   Barn 
----------+---------------
   Bridge | (1; 1)  (0; 0)
     Barn | (0; 0)  (2; 2)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Player1
    No dominated strategy for Player2
    No dominant strategy for Player1
    No dominant strategy for Player2

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. Bridge Bridge (1; 1)
    2. Barn Barn (2; 2)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.67
     q = 0.67

    (0.67*[Bridge]+0.33*[Barn], 0.67*[Bridge]+0.33*[Barn])

    Expected equilibrium payoff for Player1
    0.67*1+(1-0.67)*0 = .66666667
    0.67*0+(1-0.67)*2 = .66666667

    Expected equilibrium payoff for Player2
    0.67*1+(1-0.67)*0 = .66666667
    0.67*0+(1-0.67)*2 = .66666667

. 
. gamet, payoff(0,1,1,0\ 1,0,0,1) ls1(Player1) ls2(Player2) player1(A B) player
> 2(A B) elids neps nefms

--------------------------
          |    Player2    
  Player1 |    A       B  
----------+---------------
        A | (0; 1)  (1; 0)
        B | (1; 0)  (0; 1)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Player1
    No dominated strategy for Player2
    No dominant strategy for Player1
    No dominant strategy for Player2

NASH EQUILIBRIUM IN PURE STRATEGIES
    None

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.50
     q = 0.50

    (0.50*[A]+0.50*[B], 0.50*[A]+0.50*[B])

    Expected equilibrium payoff for Player1
    0.50*0+(1-0.50)*1 = .5
    0.50*1+(1-0.50)*0 = .5

    Expected equilibrium payoff for Player2
    0.50*1+(1-0.50)*0 = .5
    0.50*0+(1-0.50)*1 = .5

. 
. gamet, payoff(1,-1,3,0\ 4,2,0,-1) ls1(Player1) ls2(Player2) player1(D H) play
> er2(D H) elids neps nefms

----------------------------
          |     Player2     
  Player1 |    D        H   
----------+-----------------
        D | (1; -1)   (3; 0)
        H |  (4; 2)  (0; -1)
----------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Player1
    No dominated strategy for Player2
    No dominant strategy for Player1
    No dominant strategy for Player2

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. D H (3; 0)
    2. H D (4; 2)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.75
     q = 0.50

    (0.75*[D]+0.25*[H], 0.50*[D]+0.50*[H])

    Expected equilibrium payoff for Player1
    0.50*1+(1-0.50)*3 = 2
    0.50*4+(1-0.50)*0 = 2

    Expected equilibrium payoff for Player2
    0.75*-1+(1-0.75)*2 = -.25
    0.75*0+(1-0.75)*-1 = -.25

. 
. gamet, payoff(0,0,1,0\ 0,1,3,3) ls1(Player1) ls2(Player2) player1(D H) player
> 2(D H) elids neps nefms

--------------------------
          |    Player2    
  Player1 |    D       H  
----------+---------------
        D | (0; 0)  (1; 0)
        H | (0; 1)  (3; 3)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Player1
    No dominated strategy for Player2
    No dominant strategy for Player1
    No dominant strategy for Player2

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. D D (0; 0)
    2. H H (3; 3)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 1.00
     q = 1.00

    (1.00*[D]+0.00*[H], 1.00*[D]+0.00*[H])

    Expected equilibrium payoff for Player1
    1.00*0+(1-1.00)*1 = 0
    1.00*0+(1-1.00)*3 = 0

    Expected equilibrium payoff for Player2
    1.00*0+(1-1.00)*1 = 0
    1.00*0+(1-1.00)*3 = 0

. 
. * examples from  http://www.andrew.cmu.edu/user/xinming/gametheory/
. 
. * gamet, pay(-1,-1, -9,0 \ 0, -9, -6,-6) ls1(Prisoner1) ls2(Prisoner2) player
> 1(mum confess) player2(mum confess) elids neps nefms
. 
. gamet, pay(-1,1,1,-1\1,-1,-1,1) player1(Head Tail) player2(Head Tail) elids n
> eps nefms

----------------------------
          |        S2       
       S1 |   Head     Tail 
----------+-----------------
     Head | (-1; 1)  (1; -1)
     Tail | (1; -1)  (-1; 1)
----------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for S1
    No dominated strategy for S2
    No dominant strategy for S1
    No dominant strategy for S2

NASH EQUILIBRIUM IN PURE STRATEGIES
    None

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.50
     q = 0.50

    (0.50*[Head]+0.50*[Tail], 0.50*[Head]+0.50*[Tail])

    Expected equilibrium payoff for S1
    0.50*-1+(1-0.50)*1 = 0
    0.50*1+(1-0.50)*-1 = 0

    Expected equilibrium payoff for S2
    0.50*1+(1-0.50)*-1 = 0
    0.50*-1+(1-0.50)*1 = 0

. 
. gamet, pay(2, 1, 0, 0 \ 0,0, 1, 2) ls1(Chris) ls2(Pat) player1(Opera Prize_Fi
> ght) player2(Opera Prize_Fight) elids neps nefms

--------------------------------------
            |           Pat           
      Chris |    Opera     Prize_Fight
------------+-------------------------
      Opera |    (2; 1)       (0; 0)  
Prize_Fight |    (0; 0)       (1; 2)  
--------------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Chris
    No dominated strategy for Pat
    No dominant strategy for Chris
    No dominant strategy for Pat

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. Opera Opera (2; 1)
    2. Prize_Fight Prize_Fight (1; 2)

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.67
     q = 0.33

    (0.67*[Opera]+0.33*[Prize_Fight], 0.33*[Opera]+0.67*[Prize_Fight])

    Expected equilibrium payoff for Chris
    0.33*2+(1-0.33)*0 = .66666667
    0.33*0+(1-0.33)*1 = .66666667

    Expected equilibrium payoff for Pat
    0.67*1+(1-0.67)*0 = .66666667
    0.67*0+(1-0.67)*2 = .66666667

. 
. gamet, pay(50, 90, 50, 100 \0, -10, 100, -100) ls1(Employee) ls2(Manager) pla
> yer1(Work Shirk) player2(Monitor Not_monitor) elids neps nefms

------------------------------------
          |         Manager         
 Employee |   Monitor    Not_monitor
----------+-------------------------
     Work |   (50; 90)    (50; 100) 
    Shirk |   (0; -10)   (100; -100)
------------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Employee
    No dominated strategy for Manager
    No dominant strategy for Employee
    No dominant strategy for Manager

NASH EQUILIBRIUM IN PURE STRATEGIES
    None

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.90
     q = 0.50

    (0.90*[Work]+0.10*[Shirk], 0.50*[Monitor]+0.50*[Not_monitor])

    Expected equilibrium payoff for Employee
    0.50*50+(1-0.50)*50 = 50
    0.50*0+(1-0.50)*100 = 50

    Expected equilibrium payoff for Manager
    0.90*90+(1-0.90)*-10 = 80
    0.90*100+(1-0.90)*-100 = 80

. 
. gamet, pay(6,4,2,6 \3,3,6,1) ls1(Player1) ls2(Player2) player1(T B) player2(L
>  R) elids neps nefms

--------------------------
          |    Player2    
  Player1 |    L       R  
----------+---------------
        T | (6; 4)  (2; 6)
        B | (3; 3)  (6; 1)
--------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Player1
    No dominated strategy for Player2
    No dominant strategy for Player1
    No dominant strategy for Player2

NASH EQUILIBRIUM IN PURE STRATEGIES
    None

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.50
     q = 0.57

    (0.50*[T]+0.50*[B], 0.57*[L]+0.43*[R])

    Expected equilibrium payoff for Player1
    0.57*6+(1-0.57)*2 = 4.2857143
    0.57*3+(1-0.57)*6 = 4.2857143

    Expected equilibrium payoff for Player2
    0.50*4+(1-0.50)*3 = 3.5
    0.50*6+(1-0.50)*1 = 3.5

. 
. * Prisoner's dilemma
. 
. gamet , payoff(-5, -5, 0 , -6 \ -6, 0 , -1, -1) player1(Confess Not_confess) 
> player2(Confess Not_confess)  domist neps

--------------------------------------
            |            S2           
         S1 |   Confess    Not_confess
------------+-------------------------
    Confess |   (-5; -5)     (0; -6)  
Not_confess |   (-6; 0)      (-1; -1) 
--------------------------------------

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for S1 is Not_confess
    Dominated strategy for S2 is Not_confess
    Dominant strategy for S1 is Confess
    Dominant strategy for S2 is Confess

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. Confess Confess (-5; -5)

.  
. gamet, payoff(3, 3, 0, 5  \ 5, 0 , 1, 1) player1(C D) player2(C D) ls1(Provid
> er) ls2(Customer) domist neps

--------------------------
          |    Customer   
 Provider |    C       D  
----------+---------------
        C | (3; 3)  (0; 5)
        D | (5; 0)  (1; 1)
--------------------------

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for Provider is C
    Dominated strategy for Customer is C
    Dominant strategy for Provider is D
    Dominant strategy for Customer is D

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. D D (1; 1)

. 
. gamet, payoff(-3, -3, 0, -5  \ -5, 0 , -1, -1)  player1(C D) player2(C D) dom
> ist neps

------------------------------
          |         S2        
       S1 |     C         D   
----------+-------------------
        C | (-3; -3)   (0; -5)
        D |  (-5; 0)  (-1; -1)
------------------------------

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for S1 is D
    Dominated strategy for S2 is D
    Dominant strategy for S1 is C
    Dominant strategy for S2 is C

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. C C (-3; -3)

. 
. gamet, payoff(-10,5, 8,-10\3, -1, 0,0) ls1(Player_1) ls2(Player_2) player1(Up
>  Down) player2(Left Right) elids neps  nefms

------------------------------
          |      Player_2     
 Player_1 |   Left      Right 
----------+-------------------
       Up | (-10; 5)  (8; -10)
     Down |  (3; -1)   (0; 0) 
------------------------------

Iteration 1

DOMINATED AND DOMINANT STRATEGIES
    No dominated strategy for Player_1
    No dominated strategy for Player_2
    No dominant strategy for Player_1
    No dominant strategy for Player_2

NASH EQUILIBRIUM IN PURE STRATEGIES
    None

NASH EQUILIBRIUM IN FULLY MIXED STRATEGIES
     p = 0.06
     q = 0.38

    (0.06*[Up]+0.94*[Down], 0.38*[Left]+0.62*[Right])

    Expected equilibrium payoff for Player_1
    0.38*-10+(1-0.38)*8 = 1.1428571
    0.38*3+(1-0.38)*0 = 1.1428571

    Expected equilibrium payoff for Player_2
    0.06*5+(1-0.06)*-1 = -.625
    0.06*-10+(1-0.06)*0 = -.625

. 
. gamet , payoff(5, 5, 0 , 6 \ 6, 0 , 1, 1) player1(Confess Not_confess) player
> 2(Confess Not_confess) domist neps 

--------------------------------------
            |            S2           
         S1 |   Confess    Not_confess
------------+-------------------------
    Confess |    (5; 5)       (0; 6)  
Not_confess |    (6; 0)       (1; 1)  
--------------------------------------

DOMINATED AND DOMINANT STRATEGIES
    Dominated strategy for S1 is Confess
    Dominated strategy for S2 is Confess
    Dominant strategy for S1 is Not_confess
    Dominant strategy for S2 is Not_confess

NASH EQUILIBRIUM IN PURE STRATEGIES
    1. Not_confess Not_confess (1; 1)

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