Definition Strategic Equivalence [efr-R46X]

Let \mathcal {D} be a monoidal stochastic module fibration over a Markov category \mathcal {C}, and consider a 2-cell \alpha : G_1 \to G_2: \bar {X} \to \bar {Y} \in \widetilde {\mathsf {Game}}(\mathsf {SLens}(\mathcal {D})).

We say this is a strategic equivalence if the underlying map \Sigma _1 \to \Sigma _2 in \mathcal {C} is an isomorphism, and for every context c \in \mathrm {Ctx}(\bar {X},\bar {Y}), the induced costate k on \overline {\Sigma _2} has the same equilibria (under this isomorphism) as the composite costate k\alpha on \overline {\Sigma _1}