pygambit.gambit.MixedBehaviorProfile.belief#
- MixedBehaviorProfile.belief(node: Node | str) float | Rational | None#
Returns the conditional probability that a node is reached, given that its information set is reached.
The conditioning event is that the information set is reached at least once, so beliefs are normalized by the upper-frontier probability returned by infoset_prob (following [HalPas21]), rather than by the sum of the members’ realization probabilities. For a non-absent-minded information set the two approaches agree. For an absent-minded information set they need not: the beliefs over its members may sum to more than one.
If the information set is reached with zero probability under the profile, the belief is not well-defined and the function returns None. This is the same reach probability returned by infoset_prob, so a None belief corresponds exactly to infoset_prob being zero there.
- Parameters:
node – The node of the game tree
- Raises:
MismatchError – If node is not in the same game as the profile
See also