Sure it's not an algebraic object; but it's still a well-defined mathematical notion. Nah, it's just an informal concept. A game theoretic "rational agent" in

Sure it's not an algebraic object; but it's still a well-defined mathematical notion. Nah, it's just an informal concept. A game theoretic "rational agent" in general isn't assumed to have any limitations on it's computing ability, for example. [Game theory is] trying to solve a partially-observable Markov decision problem Not according to standard texts on game theory. In fact, this is just can't be true in any usual interpretation. POMDPs are "single agent" problems whereas game theory nearly always deals with two competing players/agents each assume attempting to optimize their returns - it's the difference between a single optimum and a saddle point, maximum and minimax. This actually references the work of Marcus Hutter, who added an extra axiom to these established definitions: that agents and environments are (Turing) computable. This is my point. You can't "add an extra axiom" and be referencing a standard mathematical object at the same time.