Soluciones estables en juegos cooperativos bajo incertidumbre

Los juegos cooperativos con múltiples escenarios modelan situaciones de decisión bajo incertidumbre, cuando se tiene que repartir un bien entre un conjunto de individuos, teniendo en cuenta los valores de las coaliciones bajo diferentes escenarios simultáneamente o bajo diferentes estados de la naturaleza. En este trabajo se proponen y analizan diferentes conceptos de solución para este tipo de juegos y se proporcionan procedimientos para calcular los repartos que generan. En particular, se introducen los núcleos de ponderación como solución y se analizan las relaciones entre estos y los conceptos existentes en la literatura: núcleo de preferencia y núcleo de dominancia. A continuación, se considera la posibilidad de incorporar información parcial sobre las probabilidades de ocurrencia de los distintos escenarios con objeto de obtener conjuntos de repartos que sean estables cuando se dispone de información probabilística. Para ello se presentan nuevos conceptos de núcleo con información parcial que extienden las nociones de núcleo de preferencia y núcleo de dominancia. Se investigan las relaciones entre ellos y se proporciona el procedimiento para el cálculo de los resultados que generan.Multiple scenario cooperative games model situations where the worth of the coalitions is valued in several scenarios simultaneously or under diferent states of nature. We focus on the identification of those allocations which are stable in the sense that agents have no incentives to abandon the group. The stability of an allocation depends on how the quantities the coalitions obtain are compared with the vector-valued worth of the coalition, therefore, different extensions of the notion of core emerge, depending on how these comparisons are made. We introduce the new notions of weighting cores and analize the relationships between them and the existing core solutions. We also address the inclusion in the model of partial information about the probabilities of occurrence of the scenarios. In order to identify allocations which are also stable in the presence of probability information, we extend the notions of core to this new setting, and provide results which permit the efective calculation of the corresponding sets of allocations

Rivaroxaban with or without aspirin in stable cardiovascular disease

BACKGROUND: We evaluated whether rivaroxaban alone or in combination with aspirin would be more effective than aspirin alone for secondary cardiovascular prevention. METHODS: In this double-blind trial, we randomly assigned 27,395 participants with stable atherosclerotic vascular disease to receive rivaroxaban (2.5 mg twice daily) plus aspirin (100 mg once daily), rivaroxaban (5 mg twice daily), or aspirin (100 mg once daily). The primary outcome was a composite of cardiovascular death, stroke, or myocardial infarction. The study was stopped for superiority of the rivaroxaban-plus-aspirin group after a mean follow-up of 23 months. RESULTS: The primary outcome occurred in fewer patients in the rivaroxaban-plus-aspirin group than in the aspirin-alone group (379 patients [4.1%] vs. 496 patients [5.4%]; hazard ratio, 0.76; 95% confidence interval [CI], 0.66 to 0.86; P<0.001; z=−4.126), but major bleeding events occurred in more patients in the rivaroxaban-plus-aspirin group (288 patients [3.1%] vs. 170 patients [1.9%]; hazard ratio, 1.70; 95% CI, 1.40 to 2.05; P<0.001). There was no significant difference in intracranial or fatal bleeding between these two groups. There were 313 deaths (3.4%) in the rivaroxaban-plus-aspirin group as compared with 378 (4.1%) in the aspirin-alone group (hazard ratio, 0.82; 95% CI, 0.71 to 0.96; P=0.01; threshold P value for significance, 0.0025). The primary outcome did not occur in significantly fewer patients in the rivaroxaban-alone group than in the aspirin-alone group, but major bleeding events occurred in more patients in the rivaroxaban-alone group. CONCLUSIONS: Among patients with stable atherosclerotic vascular disease, those assigned to rivaroxaban (2.5 mg twice daily) plus aspirin had better cardiovascular outcomes and more major bleeding events than those assigned to aspirin alone. Rivaroxaban (5 mg twice daily) alone did not result in better cardiovascular outcomes than aspirin alone and resulted in more major bleeding events