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Here we reconsider the solution of the well-known Prisoner's Dilemma from a binary relation point of view. We identify the Nash equilibrium as single maximum element of a relation (we call it coordination relation) between the cells of a multidimensional payoff array. The comparison between reward vectors of cells is according to a preference relation of each player. This approach allows for an easier...
Fairness models can be roughly categorized into two groups: proportional fairness based models balancing the relative values of allocated goods, and maxmin fairness based models with reference to absolute valuations. In a specific problem domain it appears that only one fairness model can be used. Here a situation is studied where the users of a wireless infrastructure have in fact conflicting interests...
Many network control policies can benefit from introducing priorities among users, traffic flows, or service provisions e.g. For QoS improvement or network congestion avoidance. In order to ensure fairness of concomitant resource sharing tasks, generic extensions of maxmin fairness under priority are considered. A critical analysis of existing approaches leads to the definition of two fairness relations...
In the relational approach to fairness, fairness is considered as a social choice that coincides with the maximum set of a fairness relation. Here we consider the application of this approach to achieve general fairness in collaborative systems. The approach is based on posing additional conditions on the fairness relation based on representation of collaboration among agents by a social graph, and...
Proportional fairness has been shown to maximize the aggregate utility of rate control for elastic traffic in a resource sharing communication network, and has been applied to a broad range of resource allocation problems. For a refined analysis, however, the representation of proportional fairness as a relation between vectors with positive components will often not provide the level of detail that...
In this paper, formal representations for user preferences will be provided, which also take fairness in the achievement of probably conflicting goals into account. The analysis of the Bottleneck Flow Control (BFC) algorithm for congestion avoidance in traffic networks will serve as a base to specify extensions of relations among preference sets. In particular, these relations are the lexicographic...
Maxmin fairness can be characterized as a state obtained from the application of the bottleneck flow control algorithm, allowing for a formally efficient definition of a fairness concept. But a number of problems with the related maxmin fairness vector relation, esp. non-uniqueness of the maximum, preference for improving least components, artefacts appearing in the discrete domain, and lack of numerical...
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