  In an iterated game between two players, there is much interest in
characterizing the set of feasible payoffs for both players when one player
uses a fixed strategy and the other player is free to switch. Such
characterizations have led to extortionists, equalizers, partners, and rivals.
Most of those studies use memory-one strategies, which specify the
probabilities to take actions depending on the outcome of the previous round.
Here, we consider "reactive learning strategies," which gradually modify their
propensity to take certain actions based on past actions of the opponent. Every
linear reactive learning strategy, $\mathbf{p}^{\ast}$, corresponds to a memory
one-strategy, $\mathbf{p}$, and vice versa. We prove that for evaluating the
region of feasible payoffs against a memory-one strategy,
$\mathcal{C}\left(\mathbf{p}\right)$, we need to check its performance against
at most $11$ other strategies. Thus, $\mathcal{C}\left(\mathbf{p}\right)$ is
the convex hull in $\mathbb{R}^{2}$ of at most $11$ points. Furthermore, if
$\mathbf{p}$ is a memory-one strategy, with feasible payoff region
$\mathcal{C}\left(\mathbf{p}\right)$, and $\mathbf{p}^{\ast}$ is the
corresponding reactive learning strategy, with feasible payoff region
$\mathcal{C}\left(\mathbf{p}^{\ast}\right)$, then
$\mathcal{C}\left(\mathbf{p}^{\ast}\right)$ is a subset of
$\mathcal{C}\left(\mathbf{p}\right)$. Reactive learning strategies are
therefore powerful tools in restricting the outcomes of iterated games.
