An Alternative Characterization for Iterated Kalai-Smorodinsky-Nash Compromise

In this paper, we offer for two-person games an alternative characterization of Iterated Kalai-Smorodinsky-Nash Compromise (IKSNC), which was introduced and first characterized by Saglam (2016) for $n$-person games. We present an axiom called Gamma-Decomposability, satisfied by any solution that is decomposable with respect to a given reference solution Gamma. We then show that the IKSNC solution is uniquely characterized by Gamma-Decomposability whenever Gamma satisfies the standard axioms of Independence of Equivalent Utility Representations and Symmetry, along with three additional axioms, namely Restricted Monotonicity of Individually Best Extensions, Weak Independence of Irrelevant Alternatives, and Weak Pareto Optimality under Symmetry.