Traffic routing oligopoly

The purpose of this paper is to introduce a novel family of games related to congested networks. Traffic routing has been extensively analyzed from the non-cooperative aspect. A common assumption is that each individual optimizes his route in the network selfishly. However looking at the same network from a different scope in some cases we can find some actors that are responsible for the majority part of the traffic. From the point of view of these actors cooperation is indeed an inherent possibility of the game. Sharing information and cooperation with other agents may result in cost savings, and more efficient utilization of network capacities. Depending on the goal and employed strategy of the agents many possible cooperative games can arise. Our aim is to introduce and analyze these wide variety of transferable utility (TU) games. Since the formation of a coalition may affect other players costs via the implied flow and the resulting edge load changes in the network, externalities may arise, thus the underlying games are given in partition function form

Electing the Pope

Few elections attract so much attention as the Papal Conclave that elects the religious leader of over a billion Catholics worldwide. The Conclave is an interesting case of qualified majority voting with many participants and no formal voting blocks. Each cardinal is a well-known public gure with publicly available personal data and well-known positions on public matters. This provides excellent grounds for a study of spatial voting: In this brief note we study voting in the Papal Conclave after the resignation of Benedict XVI. We describe the method of the election and based on a simple estimation of certain factors that seem to influence the electors' preferences we calculate the power of each cardinal in the conclave as the Shapley-Shubik index of the corresponding voting game over a convex geometry

Monotonicity and Competitive Equilibrium in Cake-cutting

We study the monotonicity properties of solutions in the classic problem of fair cake-cutting --- dividing a heterogeneous resource among agents with different preferences. Resource- and population-monotonicity relate to scenarios where the cake, or the number of participants who divide the cake, changes. It is required that the utility of all participants change in the same direction: either all of them are better-off (if there is more to share or fewer to share among) or all are worse-off (if there is less to share or more to share among). We formally introduce these concepts to the cake-cutting problem and examine whether they are satisfied by various common division rules. We prove that the Nash-optimal rule, which maximizes the product of utilities, is resource-monotonic and population-monotonic, in addition to being Pareto-optimal, envy-free and satisfying a strong competitive-equilibrium condition. Moreover, we prove that it is the only rule among a natural family of welfare-maximizing rules that is both proportional and resource-monotonic.Comment: Revised versio

On how to identify experts in a community

The group identification literature mostly revolves around the problem of identifying individuals in the community who belong to groups with ethnic or religious identity. Here we use the same model framework to identify individuals who play key role in some sense. In particular we will focus on expert selection in social networks. Ethnic groups and experts groups need completely different approaches and different type of selection rules are successful for one and for the other. We drop monotonicity and independence, two common requirements, in order to achieve stability, a property which is indispensable in case of expert selection. The idea is that experts are more effective in identifying each other, thus the selected individuals should support each others membership. We propose an algorithm based on the so called top candidate relation. We establish an axiomatization to show that it is theoretically well-founded. Furthermore we present a case study using citation data to demonstrate its effectiveness. We compare its performance with classical centrality measures

The nucleolus of directed acyclic graph games

In this paper we consider a natural generalization of standard tree games where the underlying structure is a directed acyclic graph. We analyze the properties of the game and illustrate its relation with other graph based cost games. We show that although the game is not convex its core is always non-empty. Furthermore we provide a painting algorithm for large families of directed acyclic graph games that finds the nucleolus in polynomial time

Universal characterization sets for the nucleolus in balanced games

We provide a new mo dus op erandi for the computation of the nucleolus in co op- erative games with transferable utility. Using the concept of dual game we extend the theory of characterization sets. Dually essential and dually saturated coalitions determine b oth the core and the nucleolus in monotonic games whenever the core is non-empty. We show how these two sets are related with the existing charac- terization sets. In particular we prove that if the grand coalition is vital then the intersection of essential and dually essential coalitions forms a characterization set itself. We conclude with a sample computation of the nucleolus of bankruptcy games - the shortest of its kind