notebook.community

Edit and run 





In [1]:



    


import pandas as pd
import numpy as np
import os.path as ospath



    











In [2]:



    


excelfile = ospath.join('..','Serious games','Games','БД4_Лёгкая.xlsm')

Alldata = pd.read_excel(excelfile,sheet_name='Данные')
Games = pd.read_excel(excelfile,sheet_name='Игры')
print(Alldata.columns)
Games.columns



    


















    






Index(['Game', 'Time', 'Subject', 'Group', 'GrSubject', 'Type', 'Gain',
       'Penalty', 'x', 's1', 's2', 's3', 'AcceptAdvice', 'CalcCount',
       'CalcAdviceCount', 'UseHelp'],
      dtype='object')










    
Out[2]:








Index(['Session', 'Game', 'Date', 'Place', 'GamersCount', 'R',
       'Parametr1_alfa', 'Parametr2_beta', 'Mechname', 'GameMech',
       'Cooperation', 'talks', 'Name', 'Datafile', 'Sbjfile', 'стимул',
       'Group', 'Курс балла'],
      dtype='object')

















In [3]:



    


YHGames=Games[(Games.Mechname=='yh') & (Games.GameMech=='agree')]
YHExpGames=Games[(Games.Mechname=='yh') & (Games.GameMech=='exp')]

YHData=Alldata[Alldata.Game.isin(YHGames.Game)]
YHEData=Alldata[Alldata.Game.isin(YHExpGames.Game)]



    











In [4]:



    


print(YHData.shape,YHEData.shape)



    


















    






(1035, 16) (75, 16)

















In [85]:



    


GLGames=Games[(Games.Mechname=='gl') & (Games.GameMech=='agree')]
GLData=Alldata[Alldata.Game.isin(GLGames.Game)]

GLEGames=Games[(Games.Mechname=='gl') & (Games.GameMech=='exp')]
GLEData=Alldata[Alldata.Game.isin(GLEGames.Game)]



    











In [86]:



    


GLData.shape



    


















    
Out[86]:








(2847, 16)

Нэш-торги





In [5]:



    


YHg=YHData.groupby(['Game','Time'])



    











In [53]:



    


YHg.sum();

Функции расчёта выигрышей в игре





In [6]:



    


class Game:
    import numpy as np
    def __init__(self,R,s0,types):
        self.R = R
        self.s0 = np.array(s0)
        self.n = len(s0)
        self.types = np.array(types)
    def u(self,x):
        return self.np.sqrt(self.types+x)
game = Game( 115,(115/3,115/3,115/3), (1,9,25))

class Mechanism:
    def __init__(self,game,params,xfunc,tfunc):
        self.game = game
        for k,v in params.items():
            setattr(self,k,v)
        self.xfunc = xfunc
        self.tfunc = tfunc
        
    def x(self,s):
        return self.xfunc(s,self.game)
    def t(self,s):
        return self.tfunc(s,self.game,self)
    def f(self,s):
        return game.u(self.x(s))-self.t(s)

YHMechanism = Mechanism(game,
                        {'beta':0.0005}, 
                        lambda s,g: s*g.R/s.sum(),
                        lambda s,g,m: m.beta*s*(np.repeat(s.sum(),3)-s))

class GLClass:
    from scipy.spatial import distance
    def __init__(self):
        self.glx = lambda s,g: s.sum(axis=0) / g.n
    def glt(self,s,g,m):
        p = m.beta * self.distance.cdist([self.glx(s,g)],s,'sqeuclidean')
        pmean = m.alfa * p.mean()
        return p - pmean
GL = GLClass()
    
GLMechanism = Mechanism(game,{'beta':0.0005,'alfa':1},
                        GL.glx,
                        GL.glt
                        )
def Unash(f,f0):
    df = f-f0
    return (np.fabs(df)).prod() * np.min(np.sign(df))



    











In [7]:



    


print(YHMechanism.beta)
s = np.array([1.2,40,80])
print(YHMechanism.t(s))
YHMechanism.f(s)



    


















    






0.0005
[0.072 1.624 1.648]










    
Out[7]:








array([1.39040003, 5.22828395, 8.39727704])

















In [8]:



    


print(YHMechanism.game.s0)

f0 = YHMechanism.game.u([0,0,0])
print(f0)

Unash(f0,s)



    


















    






[38.33333333 38.33333333 38.33333333]
[1. 3. 5.]










    
Out[8]:








-1056.000000000001

Цикл получения исходных данных для Нэш-торгов





In [9]:



    


import itertools
res = []
for name,group in YHg:
    group = group.sort_values(by='GrSubject')
    if name[1] == 1 :
        curname = name[0]
        prevg = group
        continue
    
    fprev = prevg['Gain'].values
    sprev = prevg['s2'].values
    s = group['s2'].values
    s1, s2, s3 = sprev.copy(), sprev.copy(), sprev.copy()
    s1[0] = s[0]
    s2[1] = s[1]
    s3[2] = s[2]
    f1 = YHMechanism.f(s1)
    f2 = YHMechanism.f(s2)
    f3 = YHMechanism.f(s3)
    U = Unash(fprev,f0)
    U1 = Unash(f1,f0)
    U2 = Unash(f2,f0)
    U3 = Unash(f3,f0)
    Unew = Unash(YHMechanism.f(s),f0)
    res.append( [a for a in itertools.chain(name,[U1>U,U2>U,U3>U,Unew>U,U,U1,U2,U3,Unew],s)] )
    prevg = group
    #print(name,prev['Gain'])



    











In [10]:



    


a = np.vstack(res)
data_a = pd.DataFrame(a)
data_a.columns = ['Game','Step','U1>U','U2>U','U3>U','Unew>U','U','U1','U2','U3','Unew','s1','s2','s3']
data_a.head()



    


















    
Out[10]:











  
    

      
      Game
      Step
      U1>U
      U2>U
      U3>U
      Unew>U
      U
      U1
      U2
      U3
      Unew
      s1
      s2
      s3
    

  
  
    

      0
      40.0
      2.0
      0.0
      1.0
      1.0
      0.0
      -0.166445
      -0.182068
      -0.166445
      -0.166445
      -0.182068
      1.1
      99.0
      115.0
    

    

      1
      40.0
      3.0
      1.0
      0.0
      0.0
      1.0
      -0.182068
      -0.166445
      -0.182068
      -0.182068
      -0.166445
      1.0
      99.0
      115.0
    

    

      2
      40.0
      4.0
      0.0
      1.0
      1.0
      1.0
      -0.166445
      -0.182068
      0.663205
      0.141136
      4.637448
      1.1
      40.0
      61.5
    

    

      3
      40.0
      5.0
      0.0
      0.0
      1.0
      0.0
      4.637448
      -2.334728
      4.523720
      4.758127
      -2.365943
      115.0
      41.0
      60.5
    

    

      4
      40.0
      6.0
      1.0
      0.0
      1.0
      1.0
      -2.365943
      4.312664
      -42.795611
      -2.119715
      0.061842
      1.0
      91.0
      80.0
    

  




















In [12]:



    


pda = data_a[['U1>U','U2>U','U3>U','Unew>U']]
pdaPar = data_a[data_a['U']>0][['U1>U','U2>U','U3>U','Unew>U']]



    











In [41]:



    


pda.head()



    


















    
Out[41]:











  
    

      
      U1>U
      U2>U
      U3>U
      Unew>U
    

  
  
    

      0
      0.0
      1.0
      1.0
      0.0
    

    

      1
      1.0
      0.0
      0.0
      1.0
    

    

      2
      0.0
      1.0
      1.0
      1.0
    

    

      3
      0.0
      0.0
      1.0
      0.0
    

    

      4
      1.0
      0.0
      1.0
      1.0

YH

Игры с механизмом YH и механизмом остановки "по договорённости" - никто не поменял заявок. Всего шагов 345, если брать для каждого игрока в отдельности, то 1035 = 345 * 3

Функция Нэша: $ U(f,f^0)=\prod_{i} (f_i -f_i^0)') $

Базовые выигрыши: $ f^0 = u(0,0,0) $

Определения для текущего шага $t>1$: $$ U_{prev} = U(f(s^{t-1}),f^0)') $$ $$ U_i =U(f(s_i^t,s_{-i}^{t-1}),f^0) $$ $$ U_{new}=U(f(s^t),f^0) $$





In [13]:



    


def Nash_stat(data):
    a = (data[data>0].count()).values
    return [a[0],a[1],a[2],data[(data['U1>U']*data['U2>U']*data['U3>U']==1)].shape[0],
                data[data['U1>U']*data['U2>U']*data['U3>U']*data['Unew>U']==1].shape[0],
                data[data['Unew>U']==1].shape[0],
                data[(data['Unew>U']==1) & (data['U1>U']*data['U2>U']*data['U3>U']==0)].shape[0],
                data[(data['Unew>U']==1) & (data['U1>U']+data['U2>U']+data['U3>U']==0)].shape[0]
            ]



    











In [14]:



    


pd.DataFrame({'Критерии':['U1 > Uprev','U2 > Uprev','U3 > Uprev','U1>Uprev & U2>Uprev & U3>Uprev',
                          'U1>Uprev & U2>Uprev & U3>Uprev & Unew > Uprev','Unew > Uprev',
                          'Unew > Uprev & Exist Ui < Uprev','Unew > Uprev & All Ui < Uprev'],
              'Число подходящих ходов':Nash_stat(pda),
              'Число подх. ходов Uprev>0':Nash_stat(pdaPar)
             })



    


















    
Out[14]:











  
    

      
      Критерии
      Число подходящих ходов
      Число подх. ходов Uprev>0
    

  
  
    

      0
      U1 > Uprev
      172
      148
    

    

      1
      U2 > Uprev
      181
      155
    

    

      2
      U3 > Uprev
      189
      162
    

    

      3
      U1>Uprev & U2>Uprev & U3>Uprev
      64
      58
    

    

      4
      U1>Uprev & U2>Uprev & U3>Uprev & Unew > Uprev
      64
      58
    

    

      5
      Unew > Uprev
      167
      127
    

    

      6
      Unew > Uprev & Exist Ui < Uprev
      103
      69
    

    

      7
      Unew > Uprev & All Ui < Uprev
      1
      0
    

  




















In [11]:



    


datafile = ospath.join('..','Serious games','data.csv')

brdata = pd.read_csv(datafile,header=None)

brdata.columns=['game','time','g1','g2','g3','br1','br2','br3']

jdata=pd.concat([data_a, brdata], axis=1, join='inner')



    











In [16]:



    


def BR_stat(data):
    return [data[(data['g1']>0)&(data['g1']<=1)].shape[0],
            data[(data['g2']>0)&(data['g2']<=1)].shape[0],
            data[(data['g3']>0)&(data['g3']<=1)].shape[0],
            data[(data['g1']>0)&(data['g1']<=1)&(data['g3']>0)&(data['g3']<=1)|
                 (data['g1']>0)&(data['g1']<=1)&(data['g2']>0)&(data['g2']<=1)|
                 (data['g2']>0)&(data['g2']<=1)&(data['g3']>0)&(data['g3']<=1)].shape[0],
            data[(data['g1']>0)&(data['g1']<=1)& (data['g2']>0)&(data['g2']<=1)& (data['g3']>0)&(data['g3']<=1)].shape[0],
            data[(data['g1']>0)].shape[0],
            data[(data['g2']>0)].shape[0],
            data[(data['g3']>0)].shape[0],
            data[(data['g1']>0)&(data['g2']>0)|
                 (data['g1']>0)&(data['g3']>0)|
                 (data['g2']>0)&(data['g3']>0)].shape[0],
            data[(data['g1']>0)& (data['g2']>0)& (data['g3']>0)].shape[0],

            data[data['g1']==1].shape[0],
            data[data['g2']==1].shape[0],
            data[data['g3']==1].shape[0],
            data[(data['g1']>=0.9)&(data['g1']<=1.1)].shape[0],
            data[(data['g2']>=0.9)&(data['g2']<=1.1)].shape[0],
            data[(data['g3']>=0.9)&(data['g3']<=1.1)].shape[0],
            data[(data['g1']>=0.8)&(data['g1']<=1.2)].shape[0],
            data[(data['g2']>=0.8)&(data['g2']<=1.2)].shape[0],
            data[(data['g3']>=0.8)&(data['g3']<=1.2)].shape[0],
                                       ]



    











In [24]:



    


pd.DataFrame({'Критерии':['IB1','IB2','IB3','IB1&IB2|IB1&IB3|IB2&IB3','IB1&IB2&IB3','IB1+','IB2+','IB3+',
                          'IB1+&IB2+|IB1+&IB3+|IB2+&IB3+','IB1+&IB2+&IB3+',
                          'BR1(0)','BR2(0)','BR3(0)',
                          'BR1(0.1)','BR2(0.1)','BR3(0.1)','BR1(0.2)','BR2(0.2)','BR3(0.2)'],
              'Число подходящих ходов':BR_stat(jdata),
             })



    


















    
Out[24]:











  
    

      
      Критерии
      Число подходящих ходов
    

  
  
    

      0
      IB1
      117
    

    

      1
      IB2
      103
    

    

      2
      IB3
      76
    

    

      3
      IB1&IB2|IB1&IB3|IB2&IB3
      71
    

    

      4
      IB1&IB2&IB3
      9
    

    

      5
      IB1+
      176
    

    

      6
      IB2+
      150
    

    

      7
      IB3+
      116
    

    

      8
      IB1+&IB2+|IB1+&IB3+|IB2+&IB3+
      133
    

    

      9
      IB1+&IB2+&IB3+
      29
    

    

      10
      BR1(0)
      0
    

    

      11
      BR2(0)
      0
    

    

      12
      BR3(0)
      0
    

    

      13
      BR1(0.1)
      11
    

    

      14
      BR2(0.1)
      16
    

    

      15
      BR3(0.1)
      9
    

    

      16
      BR1(0.2)
      16
    

    

      17
      BR2(0.2)
      31
    

    

      18
      BR3(0.2)
      12
    

  




















In [65]:



    


pd.DataFrame([['Шагов одного игрока',len(YHg.groups)],['Всего шагов',YHData.shape[0]]])



    


















    
Out[65]:











  
    

      
      0
      1
    

  
  
    

      0
      Шагов одного игрока
      345
    

    

      1
      Всего шагов
      1035
    

  




















In [17]:



    


jdata.head()



    


















    
Out[17]:











  
    

      
      Game
      Step
      U1>U
      U2>U
      U3>U
      Unew>U
      U
      U1
      U2
      U3
      ...
      s2
      s3
      game
      time
      g1
      g2
      g3
      br1
      br2
      br3
    

  
  
    

      0
      40.0
      2.0
      0.0
      1.0
      1.0
      0.0
      -0.166445
      -0.182068
      -0.166445
      -0.166445
      ...
      99.0
      115.0
      40.0
      2.0
      0.013325
      0.000000
      0.000000
      8.504692
      27.598804
      27.605742
    

    

      1
      40.0
      3.0
      1.0
      0.0
      0.0
      1.0
      -0.182068
      -0.166445
      -0.182068
      -0.182068
      ...
      99.0
      115.0
      40.0
      3.0
      -0.013505
      0.000000
      0.000000
      8.504692
      27.551742
      27.545459
    

    

      2
      40.0
      4.0
      0.0
      1.0
      1.0
      1.0
      -0.166445
      -0.182068
      0.663205
      0.141136
      ...
      40.0
      61.5
      40.0
      4.0
      0.013325
      0.826317
      0.612168
      8.504692
      27.598804
      27.605742
    

    

      3
      40.0
      5.0
      0.0
      0.0
      1.0
      0.0
      4.637448
      -2.334728
      4.523720
      4.758127
      ...
      41.0
      60.5
      40.0
      5.0
      2.953944
      0.057762
      -0.177184
      39.658624
      57.312411
      67.143850
    

    

      4
      40.0
      6.0
      1.0
      0.0
      1.0
      1.0
      -2.365943
      4.312664
      -42.795611
      -2.119715
      ...
      91.0
      80.0
      40.0
      6.0
      1.513113
      -1.400802
      -0.322314
      39.658624
      5.306160
      0.000000
    

  



5 rows × 22 columns



















In [12]:



    


def BRNash_stat(data):
    return pd.DataFrame.from_dict(dict([
        ("BR1(0.1) & U1<=Uprev", data[(data['U']>0) & (data['g1']>=0.9)&(data['g1']<=1.1) & (data['U1>U']==0)].shape[0]),
        ("BR2(0.1) & U2<=Uprev", data[(data['U']>0) & (data['g2']>=0.9)&(data['g2']<=1.1) & (data['U2>U']==0)].shape[0]),
        ("BR3(0.1) & U3<=Uprev", data[(data['U']>0) & (data['g3']>=0.9)&(data['g3']<=1.1) & (data['U3>U']==0)].shape[0]),
        ("BR1(0.2) & U1<=Uprev", data[(data['U']>0) & (data['g1']>=0.8)&(data['g1']<=1.2) & (data['U1>U']==0)].shape[0]),
        ("BR2(0.2) & U2<=Uprev", data[(data['U']>0) & (data['g2']>=0.8)&(data['g2']<=1.2) & (data['U2>U']==0)].shape[0]),
        ("BR3(0.2) & U3<=Uprev", data[(data['U']>0) & (data['g3']>=0.8)&(data['g3']<=1.2) & (data['U3>U']==0)].shape[0]),
        ("IB1 & U1<=Uprev", data[(data['U']>0) & (data['g1']>0)&(data['g1']<=1) & (data['U1>U']==0)].shape[0]),
        ("IB2 & U2<=Uprev", data[(data['U']>0) & (data['g2']>0)&(data['g2']<=1) & (data['U2>U']==0)].shape[0]),
        ("IB3 & U3<=Uprev", data[(data['U']>0) & (data['g3']>0)&(data['g3']<=1) & (data['U3>U']==0)].shape[0]),
        ("IB1+ & U1<=Uprev", data[(data['U']>0) & (data['g1']>0) & (data['U1>U']==0)].shape[0]),
        ("IB2+ & U2<=Uprev", data[(data['U']>0) & (data['g2']>0) & (data['U2>U']==0)].shape[0]),
        ("IB3+ & U3<=Uprev", data[(data['U']>0) & (data['g3']>0) & (data['U3>U']==0)].shape[0]),
        ("not BR1(0.1) & U1>Uprev", data[(data['U']>0) & ((data['g1']<0.9)|(data['g1']>1.1)) & (data['U1>U']==1)].shape[0]),
        ("not BR2(0.1) & U2>Uprev", data[(data['U']>0) & ((data['g2']<0.9)|(data['g2']>1.1)) & (data['U2>U']==1)].shape[0]),
        ("not BR3(0.1) & U3>Uprev", data[(data['U']>0) & ((data['g3']<0.9)|(data['g3']>1.1)) & (data['U3>U']==1)].shape[0]),
        ("not IB1 & U1>Uprev", data[(data['U']>0) & ((data['g1']<=0)|(data['g1']>1)) & (data['U1>U']==1)].shape[0]),
        ("not IB2 & U2>Uprev", data[(data['U']>0) & ((data['g2']<=0)|(data['g2']>1)) & (data['U2>U']==1)].shape[0]),
        ("not IB3 & U3>Uprev", data[(data['U']>0) & ((data['g3']<=0)|(data['g3']>1)) & (data['U3>U']==1)].shape[0]),
        ("not IB1+ & U1>Uprev", data[(data['U']>0) & (data['g1']<=0) & (data['U1>U']==1)].shape[0]),
        ("not IB2+ & U2>Uprev", data[(data['U']>0) & (data['g2']<=0) & (data['U2>U']==1)].shape[0]),
        ("not IB3+ & U3>Uprev", data[(data['U']>0) & (data['g3']<=0) & (data['U3>U']==1)].shape[0]),
    ]),orient='index',columns=['Число подходящих'])



    











In [13]:



    


BRNash_stat(jdata)



    


















    
Out[13]:











  
    

      
      Число подходящих
    

  
  
    

      BR1(0.1) & U1<=Uprev
      3
    

    

      BR2(0.1) & U2<=Uprev
      10
    

    

      BR3(0.1) & U3<=Uprev
      1
    

    

      BR1(0.2) & U1<=Uprev
      4
    

    

      BR2(0.2) & U2<=Uprev
      13
    

    

      BR3(0.2) & U3<=Uprev
      2
    

    

      IB1 & U1<=Uprev
      59
    

    

      IB2 & U2<=Uprev
      48
    

    

      IB3 & U3<=Uprev
      37
    

    

      IB1+ & U1<=Uprev
      83
    

    

      IB2+ & U2<=Uprev
      70
    

    

      IB3+ & U3<=Uprev
      56
    

    

      not BR1(0.1) & U1>Uprev
      143
    

    

      not BR2(0.1) & U2>Uprev
      154
    

    

      not BR3(0.1) & U3>Uprev
      156
    

    

      not IB1 & U1>Uprev
      107
    

    

      not IB2 & U2>Uprev
      123
    

    

      not IB3 & U3>Uprev
      138
    

    

      not IB1+ & U1>Uprev
      89
    

    

      not IB2+ & U2>Uprev
      108
    

    

      not IB3+ & U3>Uprev
      121
    

  




















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Content source: moskvo/allocation-games

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