Population monotonic solutions on convex games

The Dutta–Ray solution and the Shapley value are two well-known examples of population-monotonic solutions on the domain of convex games. We provide a new formula for the Dutta–Ray solution from which population-monotonicity immediately follows. Then we define a new family of population-monotonic solutions, which we refer to as ‘sequential Dutta–Ray solutions’. We also show that it is possible to contruct several symmetric and population-monotonic solutions by using the solutions in this family.