# Calculate utilitiesΒΆ

A game can be passed a pair of mixed strategies (distributions over the set of pure strategies) to return the utilities. Let us create a game to illustrate this:

```
>>> import nash
>>> import numpy as np
>>> A = np.array([[3, 0], [5, 1]])
>>> B = np.array([[3, 5], [0, 1]])
>>> prisoners_dilemma = nash.Game(A, B)
```

The utility for both players when they both play their first strategy:

```
>>> sigma_r = np.array([1, 0])
>>> sigma_c = np.array([1, 0])
>>> prisoners_dilemma[sigma_r, sigma_c]
array([3, 3])
```

The utility to both players when they play uniformly randomly across both their strategies:

```
>>> sigma_r = np.array([1 / 2, 1 / 2])
>>> sigma_c = np.array([1 / 2, 1 / 2])
>>> prisoners_dilemma[sigma_r, sigma_c]
array([ 2.25, 2.25])
```