The purpose of this research is to analyze allocation rules that describe how to distribute limited resources among agents. We explain two results obtained in this research. 

    First, we identify desirable allocation rules in the framework of cooperative games. The is a joint work with Professor Andre Casajus at HHL Leipzig Graduate School of Management.  We introduce a new axiom, termed weak differential monotonicity. This axiom requires monotonicity of the difference of final rewards between two specific players. We prove that this axiom characterizes the class of egalitarian Shapley values. I presented this result at East Asian Game Ttheory Conference 2017 held in Singapore. 

    Second, we apply discrete separation theorem to an auction model. Discrete convex analysis is a branch of mathematics that studies convexity in discrete settings. In an auction model, a non-equilibrium situation induces the discrepancy between aggregate demand and supply. Applying the discrete separation theorem to this situation, we obtain a new characterization of competitive price vectors. This result enables a unified understanding of existing auctions. I summarized this result in a working paper, which is accesible through Munich Personal Repec Archive.