duaLabOpen problems and questions
Open problems
Games, Problem 5.1 (Lax monoidal structures)
Classify all non-unital monoidal structures on Games for which the forgetful functor $U:\mathbf{Games}\to\mathbf{Set}$ is lax monoidal. See Question 5.6 in the original paper.
Open questions
Games, Question 6.1 (Meaning of the internal hom)
The Conway addition is closed. What is the game-theoretic meaning of its internal hom? Classically, closedness corresponds to switching the two players (Joyal 1977). See Question 5.7 in the original paper.
Games, Question 6.2 (Generalization)
To what extent does this framework extend to other endofunctors, for example an accessible endofunctor $T$ on a locally presentable category $\mathcal{C}$? See Question 5.9 in the original paper.
Rieg, Question 4.1 (Riegs and games)
Objects of the free cartesian closed category on one object $x$ are built from $x$ by products and exponentials, and Dolan and Trimble read each of them as a two-player game (Baez; Trimble). On the other hand, Games carry sums, and game values such as the Grundy number turn them into monoid operations (Bouton monoid; Hora, §4). How are riegs related to game theory?