# Use fictitious playΒΆ

One of the learning algorithms implemented in `Nashpy`

is called
Fictitious play, this is implemented as a method on the `Game`

class:

```
>>> import nashpy as nash
>>> import numpy as np
>>> A = np.array([[3, 1], [0, 2]])
>>> B = np.array([[2, 0], [1, 3]])
>>> game = nash.Game(A, B)
```

The `fictitious_play`

method returns a generator of a given collection of
learning steps:

```
>>> np.random.seed(0)
>>> iterations = 500
>>> play_counts = game.fictitious_play(iterations=iterations)
>>> for row_play_counts, column_play_counts in play_counts:
... print(row_play_counts, column_play_counts)
[0 0] [0 0]
[1. 0.] [0. 1.]
...
[498. 1.] [497. 2.]
[499. 1.] [498. 2.]
```

Note that this process is stochastic:

```
>>> np.random.seed(1)
>>> play_counts = game.fictitious_play(iterations=iterations)
>>> for row_play_counts, column_play_counts in play_counts:
... print(row_play_counts, column_play_counts)
[0 0] [0 0]
[0. 1.] [0. 1.]
...
[ 0. 499.] [ 0. 499.]
[ 0. 500.] [ 0. 500.]
```

It is also possible to pass a `play_counts`

variable to give a starting
point for the algorithm:

```
>>> np.random.seed(1)
>>> play_counts = (np.array([0., 500.]), np.array([0., 500.]))
>>> play_counts = game.fictitious_play(iterations=iterations, play_counts=play_counts)
>>> for row_play_counts, column_play_counts in play_counts:
... print(row_play_counts, column_play_counts)
[ 0. 500.] [ 0. 500.]
[ 0. 501.] [ 0. 501.]
...
[ 0. 999.] [ 0. 999.]
[ 0. 1000.] [ 0. 1000.]
```