Techniques based on using principal eigenvectors of matrices representing binary relations of sets of alternatives are commonly used in social sciences, bibliometrics, and web search engines. In most applications the binary relations can be represented by a directed graph and the question of ranking or scoring the alternatives can be turned into the relevant question of how to score the nodes of the graph. This paper characterizes the principal eigenvector as a scoring function with a set of axioms. A zero-sum scoring function based on the difference of principal right and left eigenvectors is introduced and axiomatized. Furthermore, a method of assessing individual and group centralities simultaneously is characterized by a set of axioms. The specific case of this method is the Hyperlink-Induced Topic Search (HITS) used in ranking websites.

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This paper examines the pure-strategy subgame-perfect equilibrium payoffs in discounted supergames with perfect monitoring. It is shown that the equilibrium payoffs can be identified as sub-self-affine sets or graph-directed iterated function systems. We propose a method to estimate the Hausdorff dimension of the equilibrium payoffs and relate it to the equilibrium paths and their graph presentation.

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We describe a web-site containing material and tools for learning mathematical models of negotiation analysis and discuss students' experiences of its use. It is part of e-learning decision making site, www.dm.hut.fi, which is developed at Systems