@present SchMarkovGame(FreeSchema) begin
    State::Ob
    Action::Ob
    Player::Ob
    Transition::Ob
    
    src_state::Hom(Transition, State)
    tgt_state::Hom(Transition, State)
    action::Hom(Transition, Action)
    player::Hom(Transition, Player)
    
    probability::Attr(Transition, Float64)
    reward::Attr(Transition, Float64)
end

# σ(s) ≠ s for all states s
is_derangement(mg::MarkovGame) = all(
    t -> src_state(mg, t) != tgt_state(mg, t),
    transitions(mg)
)

function step!(game::MarkovGame, state::State, actions::Dict{Player,Action})
    valid_transitions = filter(transitions(game)) do t
        src_state(game, t) == state &&
        all(p -> action(game, t) == actions[p], players(game))
    end
    
    probs = [probability(game, t) for t in valid_transitions]
    chosen = sample(valid_transitions, Weights(probs))
    
    rewards = Dict(p => reward(game, chosen) for p in players(game))
    next_state = tgt_state(game, chosen)
    
    (next_state, rewards)
end

MarkovGame ─────► OpenGame
    │                │
    │ ACSet          │ Para/Optic
    │                │
    ▼                ▼
Transition ────► Play/CoPlay