Monotone-path Dutta-Ray solutions on convex games

It is well known that on the domain of convex games, the Dutta-Ray solution satisfies many desirable properties such as population-monotonicity, max consistency, converse max consistency, and conditional self-consistency. In this paper, we define a family of possibly non-symmetric and non-homogeneous generalizations of the Dutta-Ray solution, which we refer to as "monotone-path Dutta-Ray solutions." We show that above four properties are preserved by our generalizations.