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We present new game semantics of Martin-L\"of type theory (MLTT) equippedwith One-, Zero-, N-, Pi-, Sigma- and Id-types. Our game semantics interpretsMLTT more accurately than existing ones. Another advantage of our gamesemantics over existing ones is its interpretation of Sigma-types that isdirect and compatible with the game semantics of product types . Besides, itsmathematical structure is novel and useful; e.g., the category of our games hasall finite limits, which is a key step to an extension of the present work tohomotopy type theory, and our games interpret subtyping on dependent types forthe first time as game semantics. Finally, we provide a new, game-semanticproof of the independence of Markov's principle from MLTT, which demonstratesan advantage of our game semantics over extensional models of MLTT such as theeffective topos.

Game Semantics of Martin-L\"of Type Theory