arXiv subjects

Silvia Lorenzini

Publications and source records attributed to Silvia Lorenzini.

3 recordsLinked to original sources

arXiv2026

Pairwise comparisons meet optimal transport theory

In this paper, we reinterpret pairwise comparison theory through the lens of optimal transport. The main contribution is the connection established between pairwise comparison matrices, doubly stochastic scaling, and entropy-regularized transport problems. Using Sinkhorn scaling, we show how consistency, priority derivation, and inconsistency assessment can be studied within a common optimal-transport framework. As methodological consequences of this connection, we obtain a new characterization of consistency, a Sinkhorn-based prioritization method, and an entropy-based inconsistency index. We study these proposals both analytically and numerically and compare them with established methods from the literature

math.OC↗

arXiv2026

Cooperative games with uncertainty: a survey

The main stream of the literature in cooperative game theory considers games as being deterministic. In this survey, we review the main models incorporating uncertainty in cooperative games, starting from the seminal paper of Charnes and Granot (1976) and finishing with our own contribution, called Bel coalitional games. The different models are explained and compared, making a focus on the notion of allocation and core, since all the described models propose a notion of core.

cs.GT↗

arXiv2026

Properties of the core and other solution concepts of Bel coalitional games in the ex-ante scenario

We study the properties of the core and other solution concepts of Bel coalitional games, that generalize classical coalitional games by introducing uncertainty in the framework. In this uncertain environment, we work with contracts, that specify how agents divide the values of the coalitions in the different states of the world. Every agent can have different a priori knowledge on the true state of the world, which is modeled through the Dempster-Shafer theory, while agents' preferences between contracts are modeled by the Choquet integral. We focus on the "ex-ante" scenario, when the contract is evaluated before uncertainty is resolved. We investigate the geometrical structure of the ex-ante core when agents have the same a priori knowledge which is a probability distribution. Finally, we define the (pre)nucleolus, the kernel and the bargaining set (a la Mas-Colell) in the ex-ante situation and we study their properties. It is found that the inclusion relations among these solution concepts are the same as in the classical case. Coincidence of the ex-ante core and the ex-ante bargaining set holds for convex Bel coalitional games, at the price of strengthening the definition of bargaining sets.

cs.GT↗