  This paper presents a uniform substitution calculus for differential game
logic (dGL). Church's uniform substitutions substitute a term or formula for a
function or predicate symbol everywhere. After generalizing them to
differential game logic and allowing for the substitution of hybrid games for
game symbols, uniform substitutions make it possible to only use axioms instead
of axiom schemata, thereby substantially simplifying implementations. Instead
of subtle schema variables and soundness-critical side conditions on the
occurrence patterns of logical variables to restrict infinitely many axiom
schema instances to sound ones, the resulting axiomatization adopts only a
finite number of ordinary dGL formulas as axioms, which uniform substitutions
instantiate soundly. This paper proves soundness and completeness of uniform
substitutions for the monotone modal logic dGL. The resulting axiomatization
admits a straightforward modular implementation of dGL in theorem provers.
