A Fictitious Play Algorithm for Matrix Games with Fuzzy Payoffs

Table 1

The Brown-Robinson method for solving the example.

𝑘	𝑖(𝑘)	𝑗(𝑘)	Min𝜆(𝑈𝑘)/𝑘	Max𝜆(𝑉𝑘)/𝑘
1	1	1	(.450𝑒−1,.1)𝑇	(.1230,.2300)𝑇
2	1	3	(.4500000000𝑒−1,.5000000000𝑒−1)𝑇	(.8400000000𝑒−1,.1150000000)𝑇
3	1	3	(.4500000000𝑒−1,.3333333333𝑒−1)𝑇	(.7099999999𝑒−1,.7666666666𝑒−1)𝑇
4	1	3	(.4500000000𝑒−1,.2500000000𝑒−1)𝑇	(.6450000000𝑒−1,.5750000000𝑒−1)𝑇
5	1	3	(.4500000000𝑒−1,.2000000000𝑒−1)𝑇	(.6060000000𝑒−1,.4600000000𝑒−1)𝑇
6	1	3	(.4500000001𝑒−1,.1666666667𝑒−1)𝑇	(.5800000001𝑒−1,.3833333334𝑒−1)𝑇
7	1	3	(.4500000001𝑒−1,.1428571429𝑒−1)𝑇	(.5614285716𝑒−1,.3285714287𝑒−1)𝑇
8	1	3	(.4500000000𝑒−1,.1250000000𝑒−1)𝑇	(.5475000000𝑒−1,.2875000000𝑒−1)𝑇
9	1	3	(.4500000000𝑒−1,.1111111111𝑒−1)𝑇	(.5366666666𝑒−1,.2555555555𝑒−1)𝑇
10	1	3	(.4500000000𝑒−1,.1000000000𝑒−1)𝑇	(.5280000000𝑒−1,.2300000000𝑒−1)𝑇
⋮			⋮	⋮
10^2	1	3	(.4500000000𝑒−1,.1000000000𝑒−2)𝑇	(.4578000000𝑒−1,.2300000000𝑒−2)𝑇
⋮			⋮	⋮
10^3	1	3	(.4500000000𝑒−1,.1000000000𝑒−3)𝑇	(.4507800000𝑒−1,.2300000000𝑒−3)𝑇
⋮			⋮	⋮
10^4	1	3	(.4500000000𝑒−1,.1000000000𝑒−4)𝑇	(.4500780000𝑒−1,.2300000000𝑒−4)𝑇
⋮			⋮	⋮
10^5	1	3	(.4500000000𝑒−1,.1000000000𝑒−5)𝑇	(.4500078000𝑒−1,.2300000000𝑒−5)𝑇
⋮			⋮	⋮
10^6	1	3	(.4500000000𝑒−1,.1000000000𝑒−6)𝑇	(.4500007800𝑒−1,.2300000000𝑒−6)𝑇