Counterfactual Regret Minimization

Best Response

A player’s best response as a strategy that maximizes their expected payoff assuming all other players play according to $\sigma$.

This is really important, we need to look at the paper: Accelerating Best Response Calculation in Large Extensive Games

Given a strategy profile $\sigma$, we define a player $i$’s best response $b_i$ as $b_i({\sigma }_{-i})={\max }_{{\sigma }_i^{\prime }\in {\sum }_i}{u}_i({\sigma }_i^{\prime },{\sigma }_{-i})$ In other words, player $i$’s best response is a strategy ${\sigma }_i^{\prime }$ that maximizes their expected payoff assuming all other players play according to $\sigma$.

Personal Notes

I remember somewhere that the best response strategy is always deterministic.