Cartels via the modiclus

Rosenmüller J, Sudhölter P. Cartels via the modiclus. Working Papers. Institute of Mathematical Economics. Vol 320. Bielefeld: Center for Mathematical Economics; 2000

A monotonic and merge-proof rule in minimum cost spanning tree situations

We present a new model for cost sharing in minimum cost spanning tree problems, so that the planner can identify the agents that merge. Under this new framework, and as opposed to the traditional model, there exist rules that satisfy merge-proofness. Besides, by strengthening this property and adding some other properties, such as population-monotonicity and solidarity, we characterize a unique rule that coincides with the weighted Shapley value of an associated cost game

On the Replication of the Pre-Kernel and Related Solutions

Based on results discussed by Meinhardt (2013), which presents a dual characterization of the prekernel by a finite union of solution sets of a family of quadratic and convex objective functions, we could derive some results related to the single-valuedness of the pre-kernel. Rather than extending the knowledge of game classes for which the pre-kernel consists of a single point, we apply a different approach. We select a game from an arbitrary game class with a single pre-kernel element satisfying the non-empty interior condition of a payoff equivalence class, and then establish that the set of related and linear independent games which are derived from this pre-kernel point of the default game replicates this point also as its sole pre-kernel element. Hence, a bargaining outcome related to this pre-kernel element is stable. Furthermore, we establish that on the restricted subset on the game space that is constituted by the convex hull of the default and the set of related games, the pre-kernel correspondence is single-valued, and therefore continuous. In addition, we provide sufficient conditions that preserve the pre-nucleolus property for related games even when the default game has not a single pre-kernel point. Finally, we apply the same techniques to related solutions of the pre-kernel, namely the modiclus and anti-pre-kernel, to work out replication results for them

Cartels via the modiclus

Rosenmüller J, Sudhölter P. Cartels via the modiclus. Working Papers. Institute of Mathematical Economics. Vol 320. Bielefeld: Center for Mathematical Economics; 2000

Cartels via the modiclus

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