On the existence of population-monotonic solutions on the domain of quasi-convex games

On the domain of convex games, the Shapley value and the Dutta-Ray solutions are two well-known solutions that satisfy population-monotonicity. The existence of a population-monotonic solution on the domain of quasi-convex games has been an open question. In this note, we show that in general, no convex combination of the above two solutions can be extended to the domain of quasi-convex games in such a way that preserves population-monotonicity and efficiency.

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