Important Definitions
function mapping each action profile to a vector of utilities for each player
a strategy profile which mapping information set and actions' probabilities for player
reach probability of game history with strategy profile
probability of reaching information set through all possible game histories in
After all things above, we can get these:
We can define the at nonterminal history
as:
The of not taking action
at history
is defined as:
The of not taking action
at information set
is then:
Let refer to the regret whe players use
of not taking action
at information set
belonging to player
. The
is defined as:
Then we can use regret matching to get new strategy:
