over the game’s outcomes. Coordination between players can exist, thus, this distribution need not factor into independent strategies for each player. Conceptually, a trusted signaling mechanism, such as a traffic light, can be thought to sample an outcome from ${\sigma^{{\Gamma}}}$ and communicate to each player ${a}_{{i}}$, its portion of the joint-action. Even in situations where players are incapable of communication prior to play, correlated play is attainable through repetition. In particular, there are simple learning dynamics that, when employed by each player independently, converge to a correlated solution [@foster96; @hart2000].

If a player can benefit through a unilateral deviation from the proposed joint strategy, the strategy is unstable. As we are considering coordinated strategies, a player may condition its deviations on the recommended action. That is, a [****]{} is a function ${{f_{{i}}}: {A_{{i}}}\rightarrow {A_{{i}}}}$ [@agt4]. To ease the notation, we overload ${{f_{{i}}}: {\mathcal A}\rightarrow {\mathcal A}}$ to be the function that modifies only player ${i}$’s action according to ${f_{{i}}}$.

Two well-studied classes of deviations are the switch deviation, $$\begin{aligned}
{{\operatorname{switch}^{{x}\rightarrow{y}}_{{i}}}({{a}_{{i}}})} &= \left\{\begin{array}{cl} 
y & \mbox{if ${{a}_{{i}}}= {x}$}\\ 
{{a}_{{i}}}& \mbox{otherwise},
\end{array}\right.\end{aligned}$$ which substitutes one action for another, and the fixed deviation, $$\begin{aligned}
{{\operatorname{fixed}^{\rightarrow{y}}_{{i}}}({{a}_{{i}}})} &= y,\end{aligned}$$ which does not condition its change 