S. Rahman, Z. McConaughey, A. Klev, N. Clerbout: Immanent Reasoning or Equality in Action. A Plaidoyer for the Play level. Springer (2018). https://www.springer.com/gp/book/9783319911489.
For an application of the dialogical approach to intuitionistic type theory to the axiom of choice see S. Rahman and N. Clerbout: Linking Games and Constructive Type Theory: Dialogical Strategies, CTT-Demonstrations and the Axiom of Choice. Springer-Briefs (2015). https://www.springer.com/gp/book/9783319190624.