Company size and spatial localization – game theory and experimental approach Przemysław...
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Transcript of Company size and spatial localization – game theory and experimental approach Przemysław...
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Company size and spatial localization game theory and experimental approachPrzemysaw Kusztelak (spatial economist)Macjej Pogorzelski (mathematician)Tomasz Kopczewski (experimental economist)Research Seminar Warsaw, 24.04.2008
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Presentation PlanScientific hypothesis Spatial economic literature descriptionNew idea of including company size into a researchPresentation of special experimental tool Model verification experimental approach Discussion
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Scientific hypothesisCompany size has a great influence on competition level between them. Exist the inverse relation between company size and their mutual distance in equilibrium:Large companies choose central location (Principal of Minimum Product Differentiation);Small enterprises sprawl to avoid competition (Principal of Maximum Product Differentiation).
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What is Space?
Space factors concerning company location:distancetimeagepolitical reasons.
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Space example (distance)Population density in Poland (2000) rdo: http://www.mos.gov.pl/rio10/agenda21/A21_1.pdf
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Space example (age)Population of Poland (2005)rdo: http://www.stat.gov.pl/cps/rde/xchg/gus
Wykres1
362651
354223
348971
352351
362435
376326
380551
391640
407249
426848
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Arkusz1
Ludno w 2005 roku
POLSKA OGEM
WiekPe
OgemMczyznaKobieta
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100 +2,4545441,910
3815705501910
Arkusz1
Arkusz2
Arkusz3
Ludno w 2005 roku
POLSKA OGEM
Wiek Pe
Ogem Mczyzna Kobieta
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1 rok 354223 182341 171882
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OGEM 38157055 18453855 19703200
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Spatial location theory (1)Hotelling H. Stability in competition. Economic Journal 39, 1929, s. 41 57.NE: A=0 ; B=1
PE (social): A=0.25 ; B=0.75
Wykres4
0
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A
B
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b
miasto_na_prostej
00
01
miasto_na_prostej
0
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A
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rozkad_trjktny
11111
0121000.250.50.751
00.250.50.750.1
rozkad_trjktny
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Odlego od pocztku miasta
Gsto zaludnienia
Funcja_ popytu
0
0
0
0
0
Odlego od pocztku miasta
Gsto zaludnienia
Poczenie rozk z popytem
Cena0.1
Funkcja popytu firmy 20.65990.66960.67910.68840.69750.70640.71510.72360.73190.740.74790.75560.76310.77040.77750.78440.79110.79760.80390.810.81590.82160.82710.83240.83750.84240.84710.85160.85590.860.86390.86760.87110.87440.87750.88040.88310.88560.88790.890.89190.89360.89510.89640.89750.89840.89910.89960.89990.9
Funkcja popytu firmy 10.90.89990.89960.89910.89840.89750.89640.89510.89360.89190.890.88790.88560.88310.88040.87750.87440.87110.86760.86390.860.85590.85160.84710.84240.83750.83240.82710.82160.81590.810.80390.79760.79110.78440.77750.77040.76310.75560.74790.740.73190.72360.71510.70640.69750.68840.67910.66960.65990.650.63990.62960.61910.60840.59750.58640.57510.56360.55190.540.52790.51560.50310.49040.47750.46440.45110.43760.42390.410.39590.38160.36710.35240.33750.32240.30710.29160.27590.260.24390.22760.21110.19440.17750.16040.14310.12560.10790.090.07190.05360.03510.0164000000
Odlego od pocztku miasta00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.210.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.650.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.950.960.970.980.991
0.65990.66960.67910.68840.69750.70640.71510.72360.73190.740.74790.75560.76310.77040.77750.78440.79110.79760.80390.810.81590.82160.82710.83240.83750.84240.84710.85160.85590.860.86390.86760.87110.87440.87750.88040.88310.88560.88790.890.89190.89360.89510.89640.89750.89840.89910.89960.89990.9
0.90.89990.89960.89910.89840.89750.89640.89510.89360.89190.890.88790.88560.88310.88040.87750.87440.87110.86760.86390.860.85590.85160.84710.84240.83750.83240.82710.82160.81590.810.80390.79760.79110.78440.77750.77040.76310.75560.74790.740.73190.72360.71510.70640.69750.68840.67910.66960.6599
Poczenie rozk z popytem
0
0
0
0
0
0
0
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0
0
0
0
0
0
0
0
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0
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0
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0
0
0
0
0
Odlego od pocztku miasta
Warto funcji popytu
Po.rozk. z popytem razem
Cena0.1
Funkcja popytu firmy 10.90.89990.89960.89910.89840.89750.89640.89510.89360.89190.890.88790.88560.88310.88040.87750.87440.87110.86760.86390.860.85590.85160.84710.84240.83750.83240.82710.82160.81590.810.80390.79760.79110.78440.77750.77040.76310.75560.74790.740.73190.72360.71510.70640.69750.68840.67910.66960.65990.650.63990.62960.61910.60840.59750.58640.57510.56360.55190.540.52790.51560.50310.49040.47750.46440.45110.43760.42390.410.39590.38160.36710.35240.33750.32240.30710.29160.27590.260.24390.22760.21110.19440.17750.16040.14310.12560.10790.090.07190.05360.03510.0164000000
Odlego od pocztku miasta00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.210.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.650.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.950.960.970.980.991
Gsto zaludnienia00.040.080.120.160.20.240.280.320.360.40.440.480.520.560.60.640.680.720.760.80.840.880.920.9611.041.081.121.161.21.241.281.321.361.41.441.481.521.561.61.641.681.721.761.81.841.881.921.9621.961.921.881.841.81.761.721.681.641.61.561.521.481.441.41.361.321.281.241.21.161.121.081.0410.960.920.880.840.80.760.720.680.640.60.560.520.480.440.40.360.320.280.240.20.160.120.080.040000000000000
Gsto zaludnienia klientw firmy A00.0359960.0719680.1078920.1437440.17950.2151360.2506280.2859520.3210840.3560.3906760.4250880.4592120.4930240.52650.5596160.5923480.6246720.6565640.6880.7189560.7494080.7793320.8087040.83750.8656960.8932680.9201920.9464440.9720.9968361.0209281.0442521.0667841.08851.1093761.1293881.1485121.1667241.1841.2003161.2156481.2299721.2432641.25551.2666561.2767081.2856321.2934041.31.2542041.2088321.1639081.1194561.07551.0320640.9891720.9468480.9051160.8640.8235240.7837120.7445880.7061760.66850.6315840.5954520.5601280.5256360.4920.4592440.4273920.3964680.3664960.33750.3095040.2825320.2566080.2317560.2080.1853640.1638720.1435480.1244160.10650.0898240.0744120.0602880.0474760.0360.0258840.0171520.0098280.003936000000
Po.rozk. z popytem razem
0
0
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0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Odlego od pocztku miasta
Gsto zaludnienia klientw firmy A
Funkcje popytu_razem
Cena0.1
Funkcja popytu firmy 20.650.65990.66960.67910.68840.69750.70640.71510.72360.73190.740.74790.75560.76310.77040.77750.78440.79110.79760.80390.810.81590.82160.82710.83240.83750.84240.84710.85160.85590.860.86390.86760.87110.87440.87750.88040.88310.88560.88790.890.89190.89360.89510.89640.89750.89840.89910.89960.89990.9
Funkcja popytu firmy 10.90.89990.89960.89910.89840.89750.89640.89510.89360.89190.890.88790.88560.88310.88040.87750.87440.87110.86760.86390.860.85590.85160.84710.84240.83750.83240.82710.82160.81590.810.80390.79760.79110.78440.77750.77040.76310.75560.74790.740.73190.72360.71510.70640.69750.68840.67910.66960.65990.65
Odlego od pocztku miasta00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.210.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.650.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.950.960.970.980.991
Gsto zaludnienia00.040.080.120.160.20.240.280.320.360.40.440.480.520.560.60.640.680.720.760.80.840.880.920.9611.041.081.121.161.21.241.281.321.361.41.441.481.521.561.61.641.681.721.761.81.841.881.921.9621.961.921.881.841.81.761.721.681.641.61.561.521.481.441.41.361.321.281.241.21.161.121.081.0410.960.920.880.840.80.760.720.680.640.60.560.520.480.440.40.360.320.280.240.20.160.120.080.040000000000000
Gsto zaludnienia klientw firmy A00.0359960.0719680.1078920.1437440.17950.2151360.2506280.2859520.3210840.3560.3906760.4250880.4592120.4930240.52650.5596160.5923480.6246720.6565640.6880.7189560.7494080.7793320.8087040.83750.8656960.8932680.9201920.9464440.9720.9968361.0209281.0442521.0667841.08851.1093761.1293881.1485121.1667241.1841.2003161.2156481.2299721.2432641.25551.2666561.2767081.2856321.2934041.300000000000000000000000000000000000000000000000000
Gsto zaludnienia klientw firmy B000000000000000000000000000000000000000000000000001.31.2934041.2856321.2767081.2666561.25551.2432641.2299721.2156481.2003161.1841.1667241.1485121.1293881.1093761.08851.0667841.0442521.0209280.9968360.9720.9464440.9201920.8932680.8656960.83750.8087040.7793320.7494080.7189560.6880.6565640.6246720.5923480.5596160.52650.4930240.4592120.4250880.3906760.3560.3210840.2859520.2506280.2151360.17950.1437440.1078920.0719680.0359960
0.650.65990.66960.67910.68840.69750.70640.71510.72360.73190.740.74790.75560.76310.77040.77750.78440.79110.79760.80390.810.81590.82160.82710.83240.83750.84240.84710.85160.85590.860.86390.86760.87110.87440.87750.88040.88310.88560.88790.890.89190.89360.89510.89640.89750.89840.89910.89960.89990.9
0.90.89990.89960.89910.89840.89750.89640.89510.89360.89190.890.88790.88560.88310.88040.87750.87440.87110.86760.86390.860.85590.85160.84710.84240.83750.83240.82710.82160.81590.810.80390.79760.79110.78440.77750.77040.76310.75560.74790.740.73190.72360.71510.70640.69750.68840.67910.66960.65990.65
Funkcje popytu_razem
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Odlego od pocztku miasta
Gsto zaludnienia klientw firm A i B
Cena0.1
Funkcja popytu firmy 20.650.65990.66960.67910.68840.69750.70640.71510.72360.73190.740.74790.75560.76310.77040.77750.78440.79110.79760.80390.810.81590.82160.82710.83240.83750.84240.84710.85160.85590.860.86390.86760.87110.87440.87750.88040.88310.88560.88790.890.89190.89360.89510.89640.89750.89840.89910.89960.89990.9
Funkcja popytu firmy 10.90.89990.89960.89910.89840.89750.89640.89510.89360.89190.890.88790.88560.88310.88040.87750.87440.87110.86760.86390.860.85590.85160.84710.84240.83750.83240.82710.82160.81590.810.80390.79760.79110.78440.77750.77040.76310.75560.74790.740.73190.72360.71510.70640.69750.68840.67910.66960.65990.65
Odlego od pocztku miasta00.010.020.030.040.050.060.070.080.090.10.110.120.130.140.150.160.170.180.190.20.210.220.230.240.250.260.270.280.290.30.310.320.330.340.350.360.370.380.390.40.410.420.430.440.450.460.470.480.490.50.510.520.530.540.550.560.570.580.590.60.610.620.630.640.650.660.670.680.690.70.710.720.730.740.750.760.770.780.790.80.810.820.830.840.850.860.870.880.890.90.910.920.930.940.950.960.970.980.991
0.65990.66960.67910.68840.69750.70640.71510.72360.73190.740.74790.75560.76310.77040.77750.78440.79110.79760.80390.810.81590.82160.82710.83240.83750.84240.84710.85160.85590.860.86390.86760.87110.87440.87750.88040.88310.88560.88790.890.89190.89360.89510.89640.89750.89840.89910.89960.89990.9
0.90.89990.89960.89910.89840.89750.89640.89510.89360.89190.890.88790.88560.88310.88040.87750.87440.87110.86760.86390.860.85590.85160.84710.84240.83750.83240.82710.82160.81590.810.80390.79760.79110.78440.77750.77040.76310.75560.74790.740.73190.72360.71510.70640.69750.68840.67910.66960.6599
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Odlego od pocztku miasta
Warto funcji popytu
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Spatial location theory (2)Salop S.C. Monopolistic competition with outside goods. Bell Journal of Economics 10, 1979, s. 141156.PE: f1=0 ; f2=1/n; ; fn=(n-1)/nNE: the same
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Spatial location theory (3)Vendrop E., Majeed A. Diferentation in a two-dimensional market. Regional Science and Urban Economics 25, 1995, s. 75-83.
NE:[A=(0;0.5) ; B=(1;0.5)][A=(0.5;0) ; B=(0.5);1]
-
Evolution of spatial location theory:Firm choice: space, price, product characteristics Adding new uncontrolable variables: consumer distribution (uniform, triangular), cost of transportation Results ???
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Different firm size treoretical model (1)The relaxation of the full market saturation assumption (not all consumers will buy good)Small firms:Medium firms:Large firms:
-
Different firm size treoretical model (2)The relaxation of the full market saturation assumption (not all consumers will buy good)Small firms:brak konkurencjiMedium firms: czciowa konkurencjaLarge firms:cakowita konkurencja
-
Different firm size treoretical modelConclusion:
Small firms pick peripheral locations. By dispersing, they divide the market between themselves and do not need to compete;
With the increase in firm size, the competition becomes stronger and the dispersion is lower;
When none of the firms is able to serve the total market demand, the maximum differentiation principle will apply;
For large firms, which are able to satisfy the total demand, competition leads to minimum product differentiation.
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Different firm size empirical verification (1)Experimental approach (LabSEE special platform )
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Different firm size empirical verification (2)Experimental approach (LabSEE special platform )
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Different firm size empirical verification (3)Assumptions:Uniform distribution of consumers;
Market saturation of small / medium-sized / large firms located at point X;
Firms sell only one homogeneous product at the same, exogenous price.
-
Different firm size empirical verification (4)Small firms: NE and Pareto-effective NE
Percentage of small firms in equilibrium in each round
Wykres1
13.6363636364
22.7272727273
50
45.4545454545
59.0909090909
63.6363636364
68.1818181818
72.7272727273
86.3636363636
81.8181818182
rounds
percentage of small firms in equilibrium
wyniki
numer parydane graczyrunda 1runda 2runda 3runda 4runda 5runda 6runda 7runda 8runda 9runda 10runda 11runda 12runda 13runda 14runda 15runda 16runda 17runda 18runda 19runda 20runda 21runda 22runda 23runda 24runda 25runda 26runda 27runda 28runda 29runda 30wynik kocowy
NazwiskoIminr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypatanr wierszanr kolumnywypata
11332.5434445434334224225225225225229.5229.5229.5229.5229.5229.5229.5229.5229.5229.5321142113310.533133313331333133310.53310.53310.5254.5
1332.5324235424444334445445445445449.5449.5449.5449.5449.5449.5449.5449.5449.5449.5431144113310.5341044934104493310.53310.53310.5240.5
20234214324434314344332.5225225225339239.5439348339346449247336.523113313341044933133310.53310.53310.53310.53310.53310.5233.5
1334345224324235334332.5435445445447439.55354384383462310238336.5547449331333134293310.53310.53310.53310.53310.53310.5225.5
30454424444.5224435434.5224434245244227348438449.5449.5449.5449.5449.5449.5449.53310.5228.52293310.54493310.53310.53310.53310.53310.5232.5
0225334424.5334245234.5334543425334339247348229.5229.5229.5229.5229.5229.5229.53310.5228.533133310.533133310.53310.53310.53310.53310.5241.5
41332.5234224.5244234425425425425425348227328339438336.543832104363210321133133212.54312.53313331333133310.532103310.5243.5
1332.5344244.5234344235235235235235438339339328348336.5348449436249431123103412.52312.53210341043103310.533133310.5234.5
50444.5424.5442.5334445445445445445445229.5448.5349.5349.5349.5349.5349.5349.5349.5349.52411.534104411321143103212329.5321332103313250.5
0424.5224.5442.5444225225225225225225449.5428.5329.5329.5329.5329.5329.5329.5329.5329.54211.53313321343113313429329.5441133133210253.5
60354345345345345345345345345345339336.5348339348.5349349.5349.5349.5349.53310.534112493313331333133310.523103310.53310.5248
0225425425425425425425425425425238336.5438348454.5355329.5329.5329.5329.53310.52311341244934104293310.533133310.53310.5234
71332.542422524524524524524524524523122473463310.5336.5328339336.5336.5336.523113313321033132312.52310331323103310.53313241
1332.5434435425425425425425425425516339346356.5336.5339227336.5336.5336.534113210331334104312.53313231033133310.54310229
80445424245245245245245245245245356.5447339328336.5445.5447229.522743844933133310.53310.53310.53310.53310.53310.53310.53310.5229
01133344254254254254254254254253310.5339348339336.5445.5339449.533932833134493310.53310.53310.53310.53310.53310.53310.53310.5237
90424324.5344244414344425434225225329438238427321034833933932844733133310.5341043113310.52211.52411.52493310.53310.5234.5kiepsko
1334344.533434414423411333444544531532833943844933932834833933934103310.5331332113310.54411.54211.533133310.53310.5235.5
100224424.5332.5444235235235235235235339227236336.5339229.5229.5229.5229.5229.51110221422133313341534103310.53310.53310.53310.5247
1334444.5332.5434445445445445445445438339236336.5438449.5449.5449.5449.5449.555104510351044955533133310.53310.53310.53310.5229
111334334334334334334334334334334336.54310439.5438447238438339336.5239.53310.543103310.53310.53310.53310.53310.53310.53310.53310.5226.5
0244224424444444444444444444444336.5229239.5348339348339438336.5439.53310.533133310.53310.53310.53310.53310.53310.53310.53310.5230.5
121332.5335334334334334334334334334339336.5247339339239.5239.5239.5239.5239.523113313341434103310.5357.534103310.53310.53310.5235
1332.5513244224224224224224224224438336.5339328348439.5439.5439.5439.5439.53411431053833133310.53315.533133310.53310.53310.5237
130553324332.5434244.5225225225225225336.5348438227427336.5339336.53393393310.543103310.53310.53310.53310.53310.53310.53310.53310.5224
0345224332.5444444.5345345345345345336.5247328328339336.5328336.53283483310.533133310.53310.53310.53310.53310.53310.53310.53310.5228
140235344245245245245245245245245336.5348247336.5336.5336.5336.5336.5336.5336.53310.53310.53310.53310.53310.53310.53310.53310.53310.53310.5221
0414334325325325325325325325325336.5339339336.5336.5336.5336.5336.5336.5336.53310.53310.53310.53310.53310.53310.53310.53310.53310.53310.5223
150225244.5225225225225225225225225229.5249.5328248.5229.5447229348229.5229.522114311431343103310.5231043103310.53310.53310.5244.5
0445444.5445445445445445445445445449.5429.5427448.5449.54384310438449.5449.543133411221133133310.5331333133310.53310.53310.5254.5
160422.5425425425425425425425425425336.5227329.5329.5329.5329.5329.5329.5329.5329.533133310.53310.53310.53310.53310.53310.53310.53310.53310.5244.5
0422.5245245245245245245245245245336.5238349.5349.5349.5349.5349.5349.5349.5349.532103310.53310.53310.53310.53310.53310.53310.53310.53310.5242.5
170254444224.5244.51344244342442452453410339328346535.5249349.5349.5349.5349.5128.5
0325434244.5444.5345334324143425425429348438346427.5126329.5329.5329.5329.5126.5
180244.5244.5445445445445445445445445438449349.5349.5349.5349.5349.5349.5349.5349.5142
0224.5224.52252252252252252252252253283210329.5329.5329.5329.5329.5329.5329.5329.5143
1901444254254254254254254254254252311427238336.5238246546449.5449.5449.5130
0435345345345345345345345345345538339339336.53393393311229.5229.5229.5140
200445445445445445445445445445445438339556449.5449.5449.5449.5449.5449.5449.5139.5
0225225225225225225225225225225328447116229.5229.5229.5229.5229.5229.5229.5137.5
210234234153444432.5244.5334524324144336.5336.5336.5336.5336.5336.5336.5336.5336.5336.5103
1334334553344432.5444.5244335334335336.5336.5336.5336.5336.5336.5336.5336.5336.5336.5105
220235235235235235235235235235235238229329.5329.5329.5329.5329.5329.5329.5329.5143
04454454454454454454454454454453393410349.5349.5349.5349.5349.5349.5349.5349.5145
230.30351110131415161918336789111313145366979121414
1423504559646873868214142732364150595964311938385644567588881490.3409090909
240
135743554341714812141191013814141619232123273030
253011169711119793932182732252023301839394453645864758383
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wyniki
13.6363636364
22.7272727273
50
45.4545454545
59.0909090909
63.6363636364
68.1818181818
72.7272727273
86.3636363636
81.8181818182
numer rundy
procenty
Liczba firm maych znajdujcych si w rwnowadze w poszczeglnych rndach w procentach
0
0
0
0
0
0
0
0
0
0
numer rundy
procenty
Liczba firm rednich znajdujcych si w rwnowadze w procentach
0
0
0
0
0
0
0
0
0
0
numer rundy
procenty
Liczba firm duych znajdujcych si w rwnowadze w procentach
0
0
0
0
0
0
0
0
0
0
numer rundy
procenty
Liczba maych firm znajdujcych si w centrum w poszczeglnych rundach w procentach
0
0
0
0
0
0
0
0
0
0
numer rundy
procenty
Liczba maych firm znajdujcych si w centrum w poszczeglnych rundach w procentach
0
0
0
0
0
0
0
0
0
0
numer rundy
procenty
Liczba duych firm znajdujcych si w centrum w poszczeglnych rundach w procentach
Arkusz1
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X551.5
2YYYYY2gracz Y551.5
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;11.522.533223332.533333333333333strategie gracza X1;1
1;23233.543334443.544444444444441;2str. dominujca
1;33.53233.543334443.54444444444441;3
1;443.5323443334443.5444444444441;4str. dominujca
1;5332.521.53332233332.533333333331;5
2;133444233.544334443.54444444442;1str. dominujca
2;24445542.544.554445554.5555555552;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;3544454.542.544.554445554.555555552;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;45544454.542.54554445554.55555552;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;544433443.5324443344443.5444442;5str. dominujca
3;13.5444433444233.544334443.544443;1
3;254.55554445542.544.554445554.55553;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;3554.555544454.542.544.554445554.5553;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;45554.555544454.542.54554445554.553;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;544443.544433443.5324443344443.53;5
4;1444443.5444433444233.544334444;1str. dominujca
4;25555554.55554445542.544.55444554;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;355555554.555544454.542.544.5544454;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;4555555554.555544454.542.54554444;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;54444444443.544433443.532444334;5str. dominujca
5;133333333332.53333223331.522.5335;1
5;2444444444443.5444333443233.545;2str. dominujca
5;34444444444443.544433343.53233.55;3
5;444444444444443.544433343.53235;4str. dominujca
5;5333333333333332.533322332.521.55;5
wypaty Ystrategie gracza Ywypaty Ystrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;11.533.543345543.555544555434443strategie gracza X1;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;22233.533445444.555445554344431;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;32.53232.544444454.55445554344431;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;433.5322454434554.5445554344431;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;5343.531.54554345553.545554344431;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;123443244.554345543.55554344432;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;22334332.544.543445444.5554344432;2str. dominujcastr. dominujcastr. dominujca
2;3333333.542.543.544444454.554344432;3str. dominujcastr. dominujca
2;43433244.542.53454434554.54344432;4str. dominujcastr. dominujcastr. dominujca
2;534432454.5424554345553.5344432;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;12.5444334554244.554345542.544433;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;233.54433445432.544.543445433.54433;2str. dominujcastr. dominujca
3;3343.543444443.542.543.544444343.5433;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;43443.534544344.542.53454433443.533;4str. dominujcastr. dominujca
3;534442.545543454.5424554334442.53;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;1344433.5555434554244.554234434;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;23444344.55543445432.544.54233434;2str. dominujcastr. dominujcastr. dominujca
4;334443454.554444443.542.543.5333334;3str. dominujcastr. dominujca
4;4344434554.544544344.542.53343324;4str. dominujcastr. dominujcastr. dominujca
4;53444345553.545543454.542344324;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;134443455543.55554345541.533.5435;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;2344434555444.5554344542233.535;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;33444345554454.554444442.53232.55;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;434443455544554.544544333.53225;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;5344434555445553.545543343.531.55;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
NEPlayer Y strategyNE
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
Player X strategy1;11;1Player X strategy
1;2NE1;2
1;31;3
1;4NE1;4
1;51;5
2;1NE2;1
2;2NENENE2;2
2;3NENE2;3
2;4NENENE2;4
2;5NE2;5
3;13;1
3;2NENE3;2
3;3NENENENENENENENE3;3
3;4NENE3;4
3;53;5
4;1NE4;1
4;2NENENE4;2
4;3NENE4;3
4;4NENENE4;4
4;5NE4;5
5;15;1
5;2NE5;2
5;35;3
5;4NE5;4
5;55;5
NE1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5NE
Player Y strategy
Arkusz2
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X553
2YYYYY2gracz Y553
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;133455.533456444.566556665.56666strategie gracza X1;1
1;264567544.56765.566.587778887.58881;2
1;3764.56775.555.577.576.577.598889998.5991;3
1;476546764.54586.565.56887778887.581;4
1;55.5543365433664.5446665566665.51;5
2;165678445.577.554.5678666.588778882;1
2;2887.591085.578.5107.57791098.599.51110101011112;2str. dominujcastr. dominujca
2;3108.598.5109.58689.5108881010.5109.51010.512111111122;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;41097.588108.575.58109777.5119.598.5911111010102;4str. dominujcastr. dominujca
2;5876567.575.5448764.55886.566888772;5
3;1777.59965.57894.556.588.565.5789777.5993;1
3;2109.51010.5128.58810119689.5118.5881011109.51010.5123;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;311.51110.51111.5119991110.596.5910.5119991111.51110.51111.53;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;41210.5109.5101110888.5119.58691110888.51210.5109.5103;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;5997.5779875.568.586.554.59875.56997.5773;5
4;177888666.58854.5678445.577.5656784;1
4;2101010111198.599.5117.57791085.578.510887.59104;2str. dominujcastr. dominujca
4;3121111111210.5109.51010.510888109.58689.5108.598.5104;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;41111101010119.598.59109777.5108.575.581097.5884;4str. dominujcastr. dominujca
4;588877886.5668764.557.575.544876564;5
5;15.5666655666444.5663345633455.55;1
5;287.58887778865.566.58544.567645675;2
5;3998.599988897.576.577.575.555.57764.5675;3
5;48887.588877786.565.56764.545765465;4
5;566665.566655664.544654335.554335;5
wypaty Ystrategie gracza Ywypaty Ystrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;136775.5681010871011.5129710121185.58986strategie gracza X1;1str. dominujcastr. dominujca
1;234665588.59779.51110.597101111867.59861;2str. dominujcastr. dominujcastr. dominujca
1;3454.55467.597.567.51010.5107.581011108688.5861;3str. dominujca
1;456643798.585910.5119.57811111076897.561;4str. dominujcastr. dominujcastr. dominujca
1;55.57763810108691211.51078111210768985.51;5str. dominujcastr. dominujca
2;135776489.5107.568.5111196910.5118579862;1str. dominujcastr. dominujcastr. dominujca
2;2345.56545.588.575.58910868.5109.58578862;2str. dominujcastr. dominujca
2;344.554.545.57675.5789876.599.596.5678762;3str. dominujca
2;4565.54378.585.54810985.589.5108.56688752;4str. dominujcastr. dominujca
2;5677537.5109.584911118.5681110.596689752;5str. dominujcastr. dominujcastr. dominujca
3;1467.58657.5101084.5910.5118.557.510108467.5863;1str. dominujca
3;245.576.564.578975699.584.5789745.576.563;2str. dominujca
3;34.566.564.5678766.586.586.5678764.566.564.53;3str. dominujcastr. dominujcastr. dominujcastr. dominujca
3;466.575.5479874.589.596579874.566.575.543;4str. dominujca
3;5687.564810107.558.51110.594.5810107.55687.5643;5str. dominujca
4;1579866910.511868.511119489.5107.5357764;1str. dominujcastr. dominujcastr. dominujca
4;25788668.5109.585.58910845.588.57345.5654;2str. dominujcastr. dominujca
4;3678766.599.596.5789875.57675.544.554.544;3str. dominujca
4;46887589.5108.56810985.578.585.54565.5434;4str. dominujcastr. dominujca
4;56897581110.596911118.567.5109.584677534;5str. dominujcastr. dominujcastr. dominujca
5;15.589867101211871011.5129681010836775.55;1str. dominujcastr. dominujca
5;267.59867101111879.51110.59588.597346655;2str. dominujcastr. dominujcastr. dominujca
5;3688.586810111087.51010.5107.567.597.56454.5545;3str. dominujca
5;46897.5681111107910.5119.57798.585566435;4str. dominujcastr. dominujcastr. dominujca
5;568985.58111210791211.510781010865.577635;5str. dominujcastr. dominujca
rwnowagistrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;1
1;2
1;3
1;4
1;5
2;1
2;2
2;3rwnowaga
2;4
2;5
3;1
3;2rwnowaga
3;3
3;4rwnowaga
3;5
4;1
4;2
4;3rwnowaga
4;4
4;5
5;1
5;2
5;3
5;4
5;5
Arkusz3
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X555
2YYYYY2gracz Y555
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;1545.5784456.585.555.578.576.57810888.51010strategie gracza X1;1
1;2106.578.5107.55689.58778109.59910111110.51111.5131;2
1;310.597910.510757109.587.589.5111010101112.51211.51212.51;3
1;4108.576.5109.58657.51087781110999.51311.51110.5111;4
1;5875.54586.55448.575.555.510876.5710108.5881;5
2;1107.589.5116.557910.57679118.5881011.5109.51011132;1
2;21313111213.5138.5911131199111312111111.51413.5131314152;2
2;3151314131514129.512141411101114141312.5131416151515162;3str. dominujcastr. dominujca
2;413.512111313131198.513131199111411.51111121514131313.52;4
2;5119.587.51010.59756.511976711.510888.51311109.5102;5
3;110.5109.51112.59781012757.51011.5978101210.5109.51112.53;1
3;215141414161312111315149.51012.515131211131515141414163;2str. dominujcastr. dominujca
3;316.51615.51616.5161313131615.51310.51315.5161313131616.51615.51616.53;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;4161414141515131112131512.5109.514151311121316141414153;4str. dominujcastr. dominujca
3;512.5119.51010.5121087911.5107.557121087912.5119.51010.53;5
4;1109.51011138.5881011.57679116.557910.5107.589.5114;1
4;213.51313141512111111.51411991113138.5911131313111213.54;2
4;31615151516141312.51314141110111414129.5121415131413154;3str. dominujcastr. dominujca
4;41514131313.51411.511111213119911131198.51313.5121113134;4
4;51311109.51011.510888.511976710.59756.5119.587.5104;5
5;1888.5101076.578105.555.578.54456.58545.5785;1
5;21110.51111.5139.59910118778107.55689.5106.578.5105;2
5;312.51211.51212.511101010119.587.589.5107571010.597910.55;3
5;41311.51110.5111110999.51087789.58657.5108.576.5105;4
5;510108.58810876.578.575.555.586.5544875.5455;5
wypaty Ystrategie gracza Ywypaty Ystrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;151010.510810131513.51110.51516.51612.51013.516151381112.51310strategie gracza X1;1str. dominujca
1;246.598.577.51313129.510141614119.513151411810.51211.5101;2str. dominujca
1;35.57775.5811141189.51415.5149.510131513108.51111.5118.51;3str. dominujca
1;478.596.549.51213137.51114161410111415139.51011.51210.581;4str. dominujca
1;581010.51051113.515131012.51616.51510.513151613.510101312.51181;5str. dominujca
2;147.5109.586.513141310.59131615128.512141411.579.51111102;1str. dominujca
2;245786.558.5121197121313108111311.5106.59101082;2str. dominujcastr. dominujcastr. dominujca
2;356565799.5978111311881112.51187910972;3str. dominujca
2;46.58754911128.551013131271011.5131188101096.52;4str. dominujcastr. dominujcastr. dominujca
2;589.5107.5410.51314136.512151613911.51414128.51011119.572;5str. dominujca
3;15.589.5108.571114131171415.51511.57111413115.589.5108.53;1str. dominujca
3;257887691111959.51312.5106911119578873;2str. dominujca
3;35.577.575.57910977.51010.5107.57910975.577.575.53;3str. dominujca
3;47887591111961012.5139.559111196788753;4str. dominujca
3;58.5109.585.511131411711.51515.51471113141178.5109.585.53;5str. dominujca
4;179.51111108.512141411.59131615126.513141310.547.5109.584;1str. dominujca
4;26.59101088111311.51071213131058.51211945786.54;2str. dominujcastr. dominujcastr. dominujca
4;379109781112.511881113118799.597565654;3str. dominujca
4;48101096.51011.513118101313127911128.556.587544;4str. dominujcastr. dominujcastr. dominujca
4;51011119.5711.51414128.512151613910.51314136.589.5107.544;5str. dominujca
5;181112.513101013.516151310.51516.51612.510131513.51151010.51085;1str. dominujca
5;2810.51211.5109.51315141110141614117.51313129.546.598.575;2str. dominujca
5;38.51111.5118.510131513109.51415.5149.5811141185.57775.55;3str. dominujca
5;41011.51210.58111415139.511141614109.51213137.578.596.545;4str. dominujca
5;5101312.511813151613.51012.51616.51510.51113.515131081010.51055;5str. dominujca
rwnowagistrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;1
1;2
1;3
1;4
1;5
2;1
2;2
2;3
2;4
2;5
3;1
3;2
3;3rwnowaga
3;4
3;5
4;1
4;2
4;3
4;4
4;5
5;1
5;2
5;3
5;4
5;5
-
Different firm size empirical verification (5)Medium-sized firms: NE and Pareto-effective NE
Percentage of small firms in equilibrium in each round
Arkusz1
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X551.5
2YYYYY2gracz Y551.5
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;11.522.533223332.533333333333333strategie gracza X1;1
1;23233.543334443.544444444444441;2str. dominujca
1;33.53233.543334443.54444444444441;3
1;443.5323443334443.5444444444441;4str. dominujca
1;5332.521.53332233332.533333333331;5
2;133444233.544334443.54444444442;1str. dominujca
2;24445542.544.554445554.5555555552;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;3544454.542.544.554445554.555555552;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;45544454.542.54554445554.55555552;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;544433443.5324443344443.5444442;5str. dominujca
3;13.5444433444233.544334443.544443;1
3;254.55554445542.544.554445554.55553;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;3554.555544454.542.544.554445554.5553;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;45554.555544454.542.54554445554.553;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;544443.544433443.5324443344443.53;5
4;1444443.5444433444233.544334444;1str. dominujca
4;25555554.55554445542.544.55444554;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;355555554.555544454.542.544.5544454;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;4555555554.555544454.542.54554444;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;54444444443.544433443.532444334;5str. dominujca
5;133333333332.53333223331.522.5335;1
5;2444444444443.5444333443233.545;2str. dominujca
5;34444444444443.544433343.53233.55;3
5;444444444444443.544433343.53235;4str. dominujca
5;5333333333333332.533322332.521.55;5
wypaty Ystrategie gracza Ywypaty Ystrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;11.533.543345543.555544555434443strategie gracza X1;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;22233.533445444.555445554344431;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;32.53232.544444454.55445554344431;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;433.5322454434554.5445554344431;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;5343.531.54554345553.545554344431;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;123443244.554345543.55554344432;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;22334332.544.543445444.5554344432;2str. dominujcastr. dominujcastr. dominujca
2;3333333.542.543.544444454.554344432;3str. dominujcastr. dominujca
2;43433244.542.53454434554.54344432;4str. dominujcastr. dominujcastr. dominujca
2;534432454.5424554345553.5344432;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;12.5444334554244.554345542.544433;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;233.54433445432.544.543445433.54433;2str. dominujcastr. dominujca
3;3343.543444443.542.543.544444343.5433;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;43443.534544344.542.53454433443.533;4str. dominujcastr. dominujca
3;534442.545543454.5424554334442.53;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;1344433.5555434554244.554234434;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;23444344.55543445432.544.54233434;2str. dominujcastr. dominujcastr. dominujca
4;334443454.554444443.542.543.5333334;3str. dominujcastr. dominujca
4;4344434554.544544344.542.53343324;4str. dominujcastr. dominujcastr. dominujca
4;53444345553.545543454.542344324;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;134443455543.55554345541.533.5435;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;2344434555444.5554344542233.535;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;33444345554454.554444442.53232.55;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;434443455544554.544544333.53225;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;5344434555445553.545543343.531.55;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
NEPlayer Y strategyNE
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
Player X strategy1;11;1Player X strategy
1;2NE1;2
1;31;3
1;4NE1;4
1;51;5
2;1NE2;1
2;2NENENE2;2
2;3NENE2;3
2;4NENENE2;4
2;5NE2;5
3;13;1
3;2NENE3;2
3;3NENENENENENENENE3;3
3;4NENE3;4
3;53;5
4;1NE4;1
4;2NENENE4;2
4;3NENE4;3
4;4NENENE4;4
4;5NE4;5
5;15;1
5;2NE5;2
5;35;3
5;4NE5;4
5;55;5
NE1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5NE
Player Y strategy
Arkusz2
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X553
2YYYYY2gracz Y553
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;133455.533456444.566556665.56666strategie gracza X1;1
1;264567544.56765.566.587778887.58881;2
1;3764.56775.555.577.576.577.598889998.5991;3
1;476546764.54586.565.56887778887.581;4
1;55.5543365433664.5446665566665.51;5
2;165678445.577.554.5678666.588778882;1
2;2887.591085.578.5107.57791098.599.51110101011112;2str. dominujcastr. dominujca
2;3108.598.5109.58689.5108881010.5109.51010.512111111122;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;41097.588108.575.58109777.5119.598.5911111010102;4str. dominujcastr. dominujca
2;5876567.575.5448764.55886.566888772;5
3;1777.59965.57894.556.588.565.5789777.5993;1
3;2109.51010.5128.58810119689.5118.5881011109.51010.5123;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;311.51110.51111.5119991110.596.5910.5119991111.51110.51111.53;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;41210.5109.5101110888.5119.58691110888.51210.5109.5103;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;5997.5779875.568.586.554.59875.56997.5773;5
4;177888666.58854.5678445.577.5656784;1
4;2101010111198.599.5117.57791085.578.510887.59104;2str. dominujcastr. dominujca
4;3121111111210.5109.51010.510888109.58689.5108.598.5104;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;41111101010119.598.59109777.5108.575.581097.5884;4str. dominujcastr. dominujca
4;588877886.5668764.557.575.544876564;5
5;15.5666655666444.5663345633455.55;1
5;287.58887778865.566.58544.567645675;2
5;3998.599988897.576.577.575.555.57764.5675;3
5;48887.588877786.565.56764.545765465;4
5;566665.566655664.544654335.554335;5
wypaty Ystrategie gracza Ywypaty Ystrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;136775.5681010871011.5129710121185.58986strategie gracza X1;1str. dominujcastr. dominujca
1;234665588.59779.51110.597101111867.59861;2str. dominujcastr. dominujcastr. dominujca
1;3454.55467.597.567.51010.5107.581011108688.5861;3str. dominujca
1;456643798.585910.5119.57811111076897.561;4str. dominujcastr. dominujcastr. dominujca
1;55.57763810108691211.51078111210768985.51;5str. dominujcastr. dominujca
2;135776489.5107.568.5111196910.5118579862;1str. dominujcastr. dominujcastr. dominujca
2;2345.56545.588.575.58910868.5109.58578862;2str. dominujcastr. dominujca
2;344.554.545.57675.5789876.599.596.5678762;3str. dominujca
2;4565.54378.585.54810985.589.5108.56688752;4str. dominujcastr. dominujca
2;5677537.5109.584911118.5681110.596689752;5str. dominujcastr. dominujcastr. dominujca
3;1467.58657.5101084.5910.5118.557.510108467.5863;1str. dominujca
3;245.576.564.578975699.584.5789745.576.563;2str. dominujca
3;34.566.564.5678766.586.586.5678764.566.564.53;3str. dominujcastr. dominujcastr. dominujcastr. dominujca
3;466.575.5479874.589.596579874.566.575.543;4str. dominujca
3;5687.564810107.558.51110.594.5810107.55687.5643;5str. dominujca
4;1579866910.511868.511119489.5107.5357764;1str. dominujcastr. dominujcastr. dominujca
4;25788668.5109.585.58910845.588.57345.5654;2str. dominujcastr. dominujca
4;3678766.599.596.5789875.57675.544.554.544;3str. dominujca
4;46887589.5108.56810985.578.585.54565.5434;4str. dominujcastr. dominujca
4;56897581110.596911118.567.5109.584677534;5str. dominujcastr. dominujcastr. dominujca
5;15.589867101211871011.5129681010836775.55;1str. dominujcastr. dominujca
5;267.59867101111879.51110.59588.597346655;2str. dominujcastr. dominujcastr. dominujca
5;3688.586810111087.51010.5107.567.597.56454.5545;3str. dominujca
5;46897.5681111107910.5119.57798.585566435;4str. dominujcastr. dominujcastr. dominujca
5;568985.58111210791211.510781010865.577635;5str. dominujcastr. dominujca
rwnowagistrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;1
1;2
1;3
1;4
1;5
2;1
2;2
2;3rwnowaga
2;4
2;5
3;1
3;2rwnowaga
3;3
3;4rwnowaga
3;5
4;1
4;2
4;3rwnowaga
4;4
4;5
5;1
5;2
5;3
5;4
5;5
Arkusz3
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X555
2YYYYY2gracz Y555
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;1545.5784456.585.555.578.576.57810888.51010strategie gracza X1;1
1;2106.578.5107.55689.58778109.59910111110.51111.5131;2
1;310.597910.510757109.587.589.5111010101112.51211.51212.51;3
1;4108.576.5109.58657.51087781110999.51311.51110.5111;4
1;5875.54586.55448.575.555.510876.5710108.5881;5
2;1107.589.5116.557910.57679118.5881011.5109.51011132;1
2;21313111213.5138.5911131199111312111111.51413.5131314152;2
2;3151314131514129.512141411101114141312.5131416151515162;3str. dominujcastr. dominujca
2;413.512111313131198.513131199111411.51111121514131313.52;4
2;5119.587.51010.59756.511976711.510888.51311109.5102;5
3;110.5109.51112.59781012757.51011.5978101210.5109.51112.53;1
3;215141414161312111315149.51012.515131211131515141414163;2str. dominujcastr. dominujca
3;316.51615.51616.5161313131615.51310.51315.5161313131616.51615.51616.53;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;4161414141515131112131512.5109.514151311121316141414153;4str. dominujcastr. dominujca
3;512.5119.51010.5121087911.5107.557121087912.5119.51010.53;5
4;1109.51011138.5881011.57679116.557910.5107.589.5114;1
4;213.51313141512111111.51411991113138.5911131313111213.54;2
4;31615151516141312.51314141110111414129.5121415131413154;3str. dominujcastr. dominujca
4;41514131313.51411.511111213119911131198.51313.5121113134;4
4;51311109.51011.510888.511976710.59756.5119.587.5104;5
5;1888.5101076.578105.555.578.54456.58545.5785;1
5;21110.51111.5139.59910118778107.55689.5106.578.5105;2
5;312.51211.51212.511101010119.587.589.5107571010.597910.55;3
5;41311.51110.5111110999.51087789.58657.5108.576.5105;4
5;510108.58810876.578.575.555.586.5544875.5455;5
wypaty Ystrategie gracza Ywypaty Ystrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;151010.510810131513.51110.51516.51612.51013.516151381112.51310strategie gracza X1;1str. dominujca
1;246.598.577.51313129.510141614119.513151411810.51211.5101;2str. dominujca
1;35.57775.5811141189.51415.5149.510131513108.51111.5118.51;3str. dominujca
1;478.596.549.51213137.51114161410111415139.51011.51210.581;4str. dominujca
1;581010.51051113.515131012.51616.51510.513151613.510101312.51181;5str. dominujca
2;147.5109.586.513141310.59131615128.512141411.579.51111102;1str. dominujca
2;245786.558.5121197121313108111311.5106.59101082;2str. dominujcastr. dominujcastr. dominujca
2;356565799.5978111311881112.51187910972;3str. dominujca
2;46.58754911128.551013131271011.5131188101096.52;4str. dominujcastr. dominujcastr. dominujca
2;589.5107.5410.51314136.512151613911.51414128.51011119.572;5str. dominujca
3;15.589.5108.571114131171415.51511.57111413115.589.5108.53;1str. dominujca
3;257887691111959.51312.5106911119578873;2str. dominujca
3;35.577.575.57910977.51010.5107.57910975.577.575.53;3str. dominujca
3;47887591111961012.5139.559111196788753;4str. dominujca
3;58.5109.585.511131411711.51515.51471113141178.5109.585.53;5str. dominujca
4;179.51111108.512141411.59131615126.513141310.547.5109.584;1str. dominujca
4;26.59101088111311.51071213131058.51211945786.54;2str. dominujcastr. dominujcastr. dominujca
4;379109781112.511881113118799.597565654;3str. dominujca
4;48101096.51011.513118101313127911128.556.587544;4str. dominujcastr. dominujcastr. dominujca
4;51011119.5711.51414128.512151613910.51314136.589.5107.544;5str. dominujca
5;181112.513101013.516151310.51516.51612.510131513.51151010.51085;1str. dominujca
5;2810.51211.5109.51315141110141614117.51313129.546.598.575;2str. dominujca
5;38.51111.5118.510131513109.51415.5149.5811141185.57775.55;3str. dominujca
5;41011.51210.58111415139.511141614109.51213137.578.596.545;4str. dominujca
5;5101312.511813151613.51012.51616.51510.51113.515131081010.51055;5str. dominujca
rwnowagistrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;1
1;2
1;3
1;4
1;5
2;1
2;2
2;3
2;4
2;5
3;1
3;2
3;3rwnowaga
3;4
3;5
4;1
4;2
4;3
4;4
4;5
5;1
5;2
5;3
5;4
5;5
Arkusz1
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X551.5
2YYYYY2gracz Y551.5
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;11.522.533223332.533333333333333strategie gracza X1;1
1;23233.543334443.544444444444441;2str. dominujca
1;33.53233.543334443.54444444444441;3
1;443.5323443334443.5444444444441;4str. dominujca
1;5332.521.53332233332.533333333331;5
2;133444233.544334443.54444444442;1str. dominujca
2;24445542.544.554445554.5555555552;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;3544454.542.544.554445554.555555552;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;45544454.542.54554445554.55555552;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;544433443.5324443344443.5444442;5str. dominujca
3;13.5444433444233.544334443.544443;1
3;254.55554445542.544.554445554.55553;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;3554.555544454.542.544.554445554.5553;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;45554.555544454.542.54554445554.553;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;544443.544433443.5324443344443.53;5
4;1444443.5444433444233.544334444;1str. dominujca
4;25555554.55554445542.544.55444554;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;355555554.555544454.542.544.5544454;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;4555555554.555544454.542.54554444;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;54444444443.544433443.532444334;5str. dominujca
5;133333333332.53333223331.522.5335;1
5;2444444444443.5444333443233.545;2str. dominujca
5;34444444444443.544433343.53233.55;3
5;444444444444443.544433343.53235;4str. dominujca
5;5333333333333332.533322332.521.55;5
wypaty Ystrategie gracza Ywypaty Ystrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;11.533.543345543.555544555434443strategie gracza X1;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;22233.533445444.555445554344431;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;32.53232.544444454.55445554344431;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;433.5322454434554.5445554344431;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
1;5343.531.54554345553.545554344431;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;123443244.554345543.55554344432;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;22334332.544.543445444.5554344432;2str. dominujcastr. dominujcastr. dominujca
2;3333333.542.543.544444454.554344432;3str. dominujcastr. dominujca
2;43433244.542.53454434554.54344432;4str. dominujcastr. dominujcastr. dominujca
2;534432454.5424554345553.5344432;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;12.5444334554244.554345542.544433;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;233.54433445432.544.543445433.54433;2str. dominujcastr. dominujca
3;3343.543444443.542.543.544444343.5433;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;43443.534544344.542.53454433443.533;4str. dominujcastr. dominujca
3;534442.545543454.5424554334442.53;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;1344433.5555434554244.554234434;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;23444344.55543445432.544.54233434;2str. dominujcastr. dominujcastr. dominujca
4;334443454.554444443.542.543.5333334;3str. dominujcastr. dominujca
4;4344434554.544544344.542.53343324;4str. dominujcastr. dominujcastr. dominujca
4;53444345553.545543454.542344324;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;134443455543.55554345541.533.5435;1str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;2344434555444.5554344542233.535;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;33444345554454.554444442.53232.55;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;434443455544554.544544333.53225;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
5;5344434555445553.545543343.531.55;5str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
NEPlayer Y strategyNE
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
Player X strategy1;11;1Player X strategy
1;2NE1;2
1;31;3
1;4NE1;4
1;51;5
2;1NE2;1
2;2NENENE2;2
2;3NENE2;3
2;4NENENE2;4
2;5NE2;5
3;13;1
3;2NENE3;2
3;3NENENENENENENENE3;3
3;4NENE3;4
3;53;5
4;1NE4;1
4;2NENENE4;2
4;3NENE4;3
4;4NENENE4;4
4;5NE4;5
5;15;1
5;2NE5;2
5;35;3
5;4NE5;4
5;55;5
NE1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5NE
Player Y strategy
Arkusz2
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X553
2YYYYY2gracz Y553
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;133455.533456444.566556665.56666strategie gracza X1;1
1;264567544.56765.566.587778887.58881;2
1;3764.56775.555.577.576.577.598889998.5991;3
1;476546764.54586.565.56887778887.581;4
1;55.5543365433664.5446665566665.51;5
2;165678445.577.554.5678666.588778882;1
2;2887.591085.578.5107.57791098.599.51110101011112;2str. dominujcastr. dominujca
2;3108.598.5109.58689.5108881010.5109.51010.512111111122;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;41097.588108.575.58109777.5119.598.5911111010102;4str. dominujcastr. dominujca
2;5876567.575.5448764.55886.566888772;5
3;1777.59965.57894.556.588.565.5789777.5993;1
3;2109.51010.5128.58810119689.5118.5881011109.51010.5123;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;311.51110.51111.5119991110.596.5910.5119991111.51110.51111.53;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;41210.5109.5101110888.5119.58691110888.51210.5109.5103;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;5997.5779875.568.586.554.59875.56997.5773;5
4;177888666.58854.5678445.577.5656784;1
4;2101010111198.599.5117.57791085.578.510887.59104;2str. dominujcastr. dominujca
4;3121111111210.5109.51010.510888109.58689.5108.598.5104;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
4;41111101010119.598.59109777.5108.575.581097.5884;4str. dominujcastr. dominujca
4;588877886.5668764.557.575.544876564;5
5;15.5666655666444.5663345633455.55;1
5;287.58887778865.566.58544.567645675;2
5;3998.599988897.576.577.575.555.57764.5675;3
5;48887.588877786.565.56764.545765465;4
5;566665.566655664.544654335.554335;5
wypaty Ystrategie gracza Ywypaty Ystrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;136775.5681010871011.5129710121185.58986strategie gracza X1;1str. dominujcastr. dominujca
1;234665588.59779.51110.597101111867.59861;2str. dominujcastr. dominujcastr. dominujca
1;3454.55467.597.567.51010.5107.581011108688.5861;3str. dominujca
1;456643798.585910.5119.57811111076897.561;4str. dominujcastr. dominujcastr. dominujca
1;55.57763810108691211.51078111210768985.51;5str. dominujcastr. dominujca
2;135776489.5107.568.5111196910.5118579862;1str. dominujcastr. dominujcastr. dominujca
2;2345.56545.588.575.58910868.5109.58578862;2str. dominujcastr. dominujca
2;344.554.545.57675.5789876.599.596.5678762;3str. dominujca
2;4565.54378.585.54810985.589.5108.56688752;4str. dominujcastr. dominujca
2;5677537.5109.584911118.5681110.596689752;5str. dominujcastr. dominujcastr. dominujca
3;1467.58657.5101084.5910.5118.557.510108467.5863;1str. dominujca
3;245.576.564.578975699.584.5789745.576.563;2str. dominujca
3;34.566.564.5678766.586.586.5678764.566.564.53;3str. dominujcastr. dominujcastr. dominujcastr. dominujca
3;466.575.5479874.589.596579874.566.575.543;4str. dominujca
3;5687.564810107.558.51110.594.5810107.55687.5643;5str. dominujca
4;1579866910.511868.511119489.5107.5357764;1str. dominujcastr. dominujcastr. dominujca
4;25788668.5109.585.58910845.588.57345.5654;2str. dominujcastr. dominujca
4;3678766.599.596.5789875.57675.544.554.544;3str. dominujca
4;46887589.5108.56810985.578.585.54565.5434;4str. dominujcastr. dominujca
4;56897581110.596911118.567.5109.584677534;5str. dominujcastr. dominujcastr. dominujca
5;15.589867101211871011.5129681010836775.55;1str. dominujcastr. dominujca
5;267.59867101111879.51110.59588.597346655;2str. dominujcastr. dominujcastr. dominujca
5;3688.586810111087.51010.5107.567.597.56454.5545;3str. dominujca
5;46897.5681111107910.5119.57798.585566435;4str. dominujcastr. dominujcastr. dominujca
5;568985.58111210791211.510781010865.577635;5str. dominujcastr. dominujca
rwnowagistrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;1
1;2
1;3
1;4
1;5
2;1
2;2
2;3rwnowaga
2;4
2;5
3;1
3;2rwnowaga
3;3
3;4rwnowaga
3;5
4;1
4;2
4;3rwnowaga
4;4
4;5
5;1
5;2
5;3
5;4
5;5
Arkusz3
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X555
2YYYYY2gracz Y555
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;1545.5784456.585.555.578.576.57810888.51010strategie gracza X1;1
1;2106.578.5107.55689.58778109.59910111110.51111.5131;2
1;310.597910.510757109.587.589.5111010101112.51211.51212.51;3
1;4108.576.5109.58657.51087781110999.51311.51110.5111;4
1;5875.54586.55448.575.555.510876.5710108.5881;5
2;1107.589.5116.557910.57679118.5881011.5109.51011132;1
2;21313111213.5138.5911131199111312111111.51413.5131314152;2
2;3151314131514129.512141411101114141312.5131416151515162;3str. dominujcastr. dominujca
2;413.512111313131198.513131199111411.51111121514131313.52;4
2;5119.587.51010.59756.511976711.510888.51311109.5102;5
3;110.5109.51112.59781012757.51011.5978101210.5109.51112.53;1
3;215141414161312111315149.51012.515131211131515141414163;2str. dominujcastr. dominujca
3;316.51615.51616.5161313131615.51310.51315.5161313131616.51615.51616.53;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;4161414141515131112131512.5109.514151311121316141414153;4str. dominujcastr. dominujca
3;512.5119.51010.5121087911.5107.557121087912.5119.51010.53;5
4;1109.51011138.5881011.57679116.557910.5107.589.5114;1
4;213.51313141512111111.51411991113138.5911131313111213.54;2
4;31615151516141312.51314141110111414129.5121415131413154;3str. dominujcastr. dominujca
4;41514131313.51411.511111213119911131198.51313.5121113134;4
4;51311109.51011.510888.511976710.59756.5119.587.5104;5
5;1888.5101076.578105.555.578.54456.58545.5785;1
5;21110.51111.5139.59910118778107.55689.5106.578.5105;2
5;312.51211.51212.511101010119.587.589.5107571010.597910.55;3
5;41311.51110.5111110999.51087789.58657.5108.576.5105;4
5;510108.58810876.578.575.555.586.5544875.5455;5
wypaty Ystrategie gracza Ywypaty Ystrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;151010.510810131513.51110.51516.51612.51013.516151381112.51310strategie gracza X1;1str. dominujca
1;246.598.577.51313129.510141614119.513151411810.51211.5101;2str. dominujca
1;35.57775.5811141189.51415.5149.510131513108.51111.5118.51;3str. dominujca
1;478.596.549.51213137.51114161410111415139.51011.51210.581;4str. dominujca
1;581010.51051113.515131012.51616.51510.513151613.510101312.51181;5str. dominujca
2;147.5109.586.513141310.59131615128.512141411.579.51111102;1str. dominujca
2;245786.558.5121197121313108111311.5106.59101082;2str. dominujcastr. dominujcastr. dominujca
2;356565799.5978111311881112.51187910972;3str. dominujca
2;46.58754911128.551013131271011.5131188101096.52;4str. dominujcastr. dominujcastr. dominujca
2;589.5107.5410.51314136.512151613911.51414128.51011119.572;5str. dominujca
3;15.589.5108.571114131171415.51511.57111413115.589.5108.53;1str. dominujca
3;257887691111959.51312.5106911119578873;2str. dominujca
3;35.577.575.57910977.51010.5107.57910975.577.575.53;3str. dominujca
3;47887591111961012.5139.559111196788753;4str. dominujca
3;58.5109.585.511131411711.51515.51471113141178.5109.585.53;5str. dominujca
4;179.51111108.512141411.59131615126.513141310.547.5109.584;1str. dominujca
4;26.59101088111311.51071213131058.51211945786.54;2str. dominujcastr. dominujcastr. dominujca
4;379109781112.511881113118799.597565654;3str. dominujca
4;48101096.51011.513118101313127911128.556.587544;4str. dominujcastr. dominujcastr. dominujca
4;51011119.5711.51414128.512151613910.51314136.589.5107.544;5str. dominujca
5;181112.513101013.516151310.51516.51612.510131513.51151010.51085;1str. dominujca
5;2810.51211.5109.51315141110141614117.51313129.546.598.575;2str. dominujca
5;38.51111.5118.510131513109.51415.5149.5811141185.57775.55;3str. dominujca
5;41011.51210.58111415139.511141614109.51213137.578.596.545;4str. dominujca
5;5101312.511813151613.51012.51616.51510.51113.515131081010.51055;5str. dominujca
rwnowagistrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;1
1;2
1;3
1;4
1;5
2;1
2;2
2;3
2;4
2;5
3;1
3;2
3;3rwnowaga
3;4
3;5
4;1
4;2
4;3
4;4
4;5
5;1
5;2
5;3
5;4
5;5
Arkusz1
12345nr. wierszanr. kolumnyzdobyte punkty
1YYYYY1gracz X551.5
2YYYYY2gracz Y551.5
3YYYYY3
4YYYYY4
5YYYYX , Y5
12345
wypaty Xstrategie gracza Ywypaty Xstrategie gracza Y
1;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;51;11;21;31;41;52;12;22;32;42;53;13;23;33;43;54;14;24;34;44;55;15;25;35;45;5
strategie gracza X1;11.522.533223332.533333333333333strategie gracza X1;1
1;23233.543334443.544444444444441;2str. dominujca
1;33.53233.543334443.54444444444441;3
1;443.5323443334443.5444444444441;4str. dominujca
1;5332.521.53332233332.533333333331;5
2;133444233.544334443.54444444442;1str. dominujca
2;24445542.544.554445554.5555555552;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;3544454.542.544.554445554.555555552;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;45544454.542.54554445554.55555552;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
2;544433443.5324443344443.5444442;5str. dominujca
3;13.5444433444233.544334443.544443;1
3;254.55554445542.544.554445554.55553;2str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;3554.555544454.542.544.554445554.5553;3str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujca
3;45554.555544454.542.54554445554.553;4str. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. dominujcastr. domi