arXiv subjects

Frank Huettner

Publications and source records attributed to Frank Huettner.

4 recordsLinked to original sources

arXiv2026

Balanced Contributions in Networks and Games with Externalities

For networks with externalities, where each component's worth may depend on the full network structure, balanced contributions and fairness lead to distinct component-efficient allocation rules. We characterize the unique component-efficient allocation rule satisfying balanced contributions -- the BCE rule. Existence is the main challenge: balanced contributions must hold on every edge, but the construction uses only spanning-tree edges. A cycle-sum identity bridges this gap by reducing balanced contributions on non-tree edges to relations in proper subnetworks. The BCE rule coincides with the Myerson value for TU games and with its generalization by Jackson--Wolinsky for network games without externalities, it recovers the externality-free value on the complete network, and -- unlike the fairness-based FCE rule -- it does not reduce to a graph-free formula applied to the graph-restricted game.

econ.TH↗

arXiv2025

Balanced contributions, consistency, and value for games with externalities

We consider fair and consistent extensions of the Shapley value for games with externalities. Based on the restriction identified by Casajus et al. (2024, Games Econ. Behavior 147, 88-146), we define balanced contributions, Sobolev's consistency, and Hart and Mas-Colell's consistency for games with externalities, and we show that these properties lead to characterizations of the generalization of the Shapley value introduced by Macho-Stadler et al. (2007, J. Econ. Theory 135, 339-356), that parallel important characterizations of the Shapley value.

econ.TH↗

arXiv2024

Random partitions, potential, value, and externalities

The Shapley value equals a player's contribution to the potential of a game. The potential is a most natural one-number summary of a game, which can be computed as the expected accumulated worth of a random partition of the players. This computation integrates the coalition formation of all players and readily extends to games with externalities. We investigate those potential functions for games with externalities that can be computed this way. It turns out that the potential that corresponds to the MPW solution introduced by Macho-Stadler et al. (2007, J. Econ. Theory 135, 339--356) is unique in the following sense. It is obtained as the expected accumulated worth of a random partition, it generalizes the potential for games without externalities, and it induces a solution that satisfies the null player property even in the presence of externalities.

econ.TH↗

arXiv2023

Coalitional Manipulations and Immunity of the Shapley Value

We consider manipulations in the context of coalitional games, where a coalition aims to increase the total payoff of its members. An allocation rule is immune to coalitional manipulation if no coalition can benefit from internal reallocation of worth on the level of its subcoalitions (reallocation-proofness), and if no coalition benefits from a lower worth while all else remains the same (weak coalitional monotonicity). Replacing additivity in Shapley's original characterization by these requirements yields a new foundation of the Shapley value, i.e., it is the unique efficient and symmetric allocation rule that awards nothing to a null player and is immune to coalitional manipulations. We further find that for efficient allocation rules, reallocation-proofness is equivalent to constrained marginality, a weaker variant of Young's marginality axiom. Our second characterization improves upon Young's characterization by weakening the independence requirement intrinsic to marginality.

econ.TH↗