Adriana Navarro-Ramos
@univ-st-etienne.fr
Université Jean Monnet Saint-Étienne
RESEARCH, TEACHING, or OTHER INTERESTS
Economics, Econometrics and Finance, Applied Mathematics, Statistics, Probability and Uncertainty
Scopus Publications
Scholar Citations
Scholar h-index
Scopus Publications
Sylvain Béal, Sylvain Ferrières, Adriana Navarro‐Ramos, and Philippe Solal
Wiley
AbstractWe introduce a new family of values for TU‐games with a priority structure, which both contains the Priority value recently introduced by Béal et al. and the Weighted Shapley values (Kalai & Samet). Each value of this family is called a Weighted priority value and is constructed as follows. A strictly positive weight is associated with each agent and the agents are partially ordered according to a binary relation. An agent is a priority agent with respect to a coalition if it is maximal in this coalition with respect to the partial order. A Weighted priority value distributes the dividend of each coalition among the priority agents of this coalition in proportion to their weights. We provide an axiomatic characterization of the family of the Weighted Shapley values without the additivity axiom. To this end, we borrow the Priority agent out axiom from Béal et al., which is used to axiomatize the Priority value. We also reuse, in our domain, the principle of Superweak differential marginality introduced by Casajus to axiomatize the Positively weighted Shapley values. We add a new axiom of Independence of null agent position which indicates that the position of a null agent in the partial order does not affect the payoff of the other agents. Together with Efficiency, the above axioms characterize the Weighted Shapley values. We show that this axiomatic characterization holds on the subdomain where the partial order is structured by levels. This entails an alternative characterization of the Weighted Shapley values. Two alternative characterizations are obtained by replacing our principle of Superweak differential marginality by Additivity and invoking other axioms.
Gustavo Bergantiños and Adriana Navarro-Ramos
Springer Science and Business Media LLC
AbstractThis paper considers agglomeration economies. A new firm is planning to open a plant in a country divided into several regions. Each firm receives a positive externality if the new plant is located in its region. In a decentralized mechanism, the plant would be opened in the region where the new firm maximizes its individual benefit. Due to the externalities, it could be the case that the aggregate utility of all firms is maximized in a different region. Thus, the firms in the optimal region could transfer something to the new firm in order to incentivize it to open the plant in that region. We propose two rules that provide two different schemes for transfers between firms already located in the country and the newcomer. The first is based on cooperative game theory. This rule coincides with the $$\\tau$$ τ -value, the nucleolus, and the per capita nucleolus of the associated cooperative game. The second is defined directly. We provide axiomatic characterizations for both rules. We characterize the core of the cooperative game. We prove that both rules belong to the core.
Sylvain Béal, Adriana Navarro-Ramos, Eric Rémila, and Philippe Solal
Springer Science and Business Media LLC
A. Navarro-Ramos
Elsevier BV
G. Bergantiños and A. Navarro-Ramos
Elsevier BV
G. Bergantiños and A. Navarro-Ramos
Elsevier BV
Adriana Navarro-Ramos, , William Olvera-Lopez, and
American Institute of Mathematical Sciences (AIMS)
In this paper we show several results regarding to the classical cost sharing problem when each agent requires a set of services but they can share the benefits of one unit of each service, i.e. there is non rival consumption. Specifically, we show a characterized solution for this problem, mainly adapting the well-known axioms that characterize the Shapley value for TU-games into our context. Finally, we present some additional properties that the shown solution satisfy.