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Matthias Greger

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2 papers

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AAMAS Conference 2026 Conference Paper

Efficiently Computing Equilibria in Budget-Aggregation Games

Patrick Becker
Alexander Fries
Matthias Greger
Erel Segal-Halevi

Budgetaggregationdealswiththesocialchoiceproblemofdistributing an exogenously given budget among a set of public projects, given agents’ preferences. Taking a game-theoretic perspective, we study budget-aggregation games where each agent has virtual decision power over some fraction of the budget. We investigate the structure and show efficient computability of Nash equilibria for various common preference models in this setting. In particular, we show that equilibria for Leontief utilities can be found in polynomial time, solving an open problem from Brandt et al. [15], and give an explicit polynomial-time algorithm for computing equilibria for ℓ1 preferences.

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AIJ Journal 2026 Journal Article

Settling the score: Portioning with cardinal preferences

Edith Elkind
Matthias Greger
Patrick Lederer
Warut Suksompong
Nicholas Teh

We study a portioning setting in which a public resource such as time or money is to be divided among a given set of candidates, and each agent proposes a division of the resource. We consider two families of aggregation rules for this setting -- those based on coordinate-wise aggregation and those that optimize some notion of welfare -- as well as the recently proposed independent markets rule. We provide a detailed analysis of these rules from an axiomatic perspective, both for classic axioms, such as strategyproofness and Pareto optimality, and for novel axioms, some of which aim to capture proportionality in this setting. Our results indicate that a simple rule that computes the average of the proposals satisfies many of our axioms and fares better than all other considered rules in terms of fairness properties. We complement these results by presenting two characterizations of the average rule.

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