In the present work, we study multi-agent environnements where each peer specifies the agents such that it supports their credibility. We tackle the important question of how to derive, from the agents' input, a global ranking showing the relative credibility of each peer. The Internet pages accompanied by the links between them constitute such an environment, provided that a link from P to Q is interpreted as an indication that P supports the credibility of Q. Moreover, the PageRank algorithm (which has been implemented by Google) provides a well known possible solution to the aforementioned problem.
Our first contribution is to propose a new solution based on the notion of mark of support. In a nutshell, if an agent A supports (the credibility of) an agent B, then we put in the "bag'" of B a mark of 1st-degree support. Moreover, if A supports C and C supports B, we put in the bag of B a mark of 2nd-degree support, and so on. Then, we propose methods for comparing the bags of the agents, which provide means to decide their positions in the global ranking.
In the second part of this work, we assume that the environment is relative to a particular agent called the source, that is, the input corresponds to the source's view of the environment (which is partial in general) and the methods for ranking agents must be personalized, that is, they must give a special importance to the input provided by the source. We propose ranking methods in this more complex framework.