The coincidence of the core and the dominance core on multi-choice games

We propose a necessary and sufficient condition for the existence of dominance core and a necessary and sufficient condition for coincidence of the core and the dominance core to the setting of multi-choice games.

A Note on the Monge-Kantorovich Problem in the Plane

The Monge-Kantorovich mass-transportation problem has been shown to be fundamental for various basic problems in analysis and geometry in recent years. Shen and Zheng (2010) proposed a probability method to transform the celebrated Monge-Kantorovich problem in a bounded region of the Euclidean plane into a Dirichlet boundary problem associated to a nonlinear elliptic equation. Their results are original and sound, however, their arguments leading to the main results are skipped and difficult to follow. In the present paper, we adopt a different approach and give a short and easy-followed detailed proof for their main results