An axiomatization of the kernel for TU games through reduced game monotonicity and reduced dominance

In the framework of transferable utility games, we modify the 2‐person Davis–Maschler reduced game to ensure non‐emptiness (NE) of the imputation set of the adapted 2‐person reduced game. Based on the modification, we propose two new axioms: reduced game monotonicity (RGM) and reduced dominance (RD). Using RGM, RD, NE, Covariance under strategic equivalence, Equal treatment property and Pareto optimality, we are able to characterize the kernel.