Games with a permission structure - A survey on generalizations and applications

In the field of cooperative games with restricted cooperation, various restrictions on coalition formation are studied. The most studied restrictions are those that arise from restricted communication and hierarchies. This survey discusses several models of hierarchy restrictions and their relation with communication restrictions. In the literature, there are results on game properties, Harsanyi dividends, core stability, and various solutions that generalize existing solutions for TU-games. In this survey, we mainly focus on axiomatizations of the Shapley value in different models of games with a hierarchically structured player set, and their applications. Not only do these axiomatizations provide insight in the Shapley value for these models, but also by considering the types of axioms that characterize the Shapley value, we learn more about different network structures. A central model of games with hierarchies is that of games with a permission structure where players in a cooperative transferable utility game are part of a permission structure in the sense that there are players that need permission from other players before they are allowed to cooperate. This permission structure is represented by a directed graph. Generalizations of this model are, for example, games on antimatroids, and games with a local permission structure. Besides discussing these generalizations, we briefly discuss some applications, in particular auction games and hierarchically structured firms

Predictors of trend in CD4-positive T-cell count and mortality among HIV-1-infected individuals with virological failure to all three antiretroviral-drug classes

Background Treatment strategies for patients in whom HIV replication is not suppressed after exposure to several drug classes remain unclear. We aimed to assess the inter-relations between viral load, CD4-cell count, and clinical outcome in patients who had experienced three-class virological failure. Methods We undertook collaborative joint analysis of 13 HIV cohorts from Europe, North America, and Australia, involving patients who had had three-class virological failure (viral load >1000 copies per mL for >4 months). Regression analyses were used to quantify the associations between CD4-cell-count slope, HIV-1 RNA concentration, treatment information, and demographic characteristics. Predictors of death were analysed by Cox's proportional-hazards models. Findings 2488 patients were included. 2118 (85%) had started antiretroviral therapy with single or dual therapy. During 5015 person-years of follow-up, 276 patients died (mortality rate 5.5 per 100 person-years; 3-year mortality risk 15.3% (95% Cl 13.5-17.3). Risk of death was strongly influenced by the latest CD4-cell count with a relative hazard of 15.8 (95% CI 9.28-27.0) for counts below 50 cells per muL versus above 200 cells per muL. The latest viral load did not independently predict death. For any given viral load, patients on treatment had more favourable CD4-cell-count slopes than those off treatment. For patients on treatment and with stable viral load, CD4-cell counts tended to be increasing at times when the current viral load was below 10 000 copies per mL or 1.5 log(10) copies per mL below off-treatment values. Interpretation In patients for whom viral-load suppression to below the level of detection is not possible, achievement and maintenance of a CD4-cell count above 200 per muL becomes the primary aim. Treatment regimens that maintain the viral load below 10 000 copies per mL or at least provide 1.5 log(10) copies per mL suppression below the off-treatment value do not seem to be associated with appreciable CD4-cell-count decline