Dimension and codimension of simple games

This paper studies the complexity of computing a representation of a simple game as the intersection (union) of weighted majority games, as well as, the dimension or the codimension. We also present some examples with linear dimension and exponential codimension with respect to the number of players.Comment: 5 page

The men who weren't even there: Legislative voting with absentees

Voting power in voting situations is measured by the probability of changing decisions by altering the cast `yes' or `no' votes. Recently this analysis has been extended by strategic abstention. Abstention, just as `yes' or `no' votes can change decisions. This theory is often applied to weighted voting situations, where voters can cast multiple votes. Measuring the power of a party in a national assembly seems to fit this model, but in fact its power comprises of votes of individual representatives each having a single vote. These representatives may vote yes or no, or may abstain, but in some cases they are not even there to vote. We look at absentees not due to a conscious decision, but due to illness, for instance. Formally voters will be absent, say, ill, with a certain probability and only present otherwise. As in general not all voters will be present, a thin majority may quickly melt away making a coalition that is winning in theory a losing one in practice. A simple model allows us to differentiate between winning and more winning and losing and less losing coalitions reflected by a voting game that is not any more simple. We use data from Scotland, Hungary and a number of other countries both to illustrate the relation of theoretical and effective power and show our results working in the practice.a priori voting power; power index; being absent from voting; minority; Shapley-Shubik index; Shapley valuea priori voting power; power index; being absent from voting; minority; Shapley-Shubik index; Shapley value

The men who weren't even there: Legislative voting with absentees

Voting power in voting situations is measured by the probability of changing decisions by altering the cast 'yes' or 'no' votes. Recently this analysis has been extended by strategic abstention. Abstention, just as 'yes' or 'no' votes can change decisions. This theory is often applied to weighted voting situations, where voters can cast multiple votes. Measuring the power of a party in a national assembly seems to fit this model, but in fact its power comprises of votes of individual representatives each having a single vote. These representatives may vote yes or no, or may abstain, but in some cases they are not even there to vote. We look at absentees not due to a conscious decision, but due to illness, for instance. Formally voters will be absent, say, ill, with a certain probability and only present otherwise. As in general not all voters will be present, a thin majority may quickly melt away making a coalition that is winning in theory a losing one in practice. A simple model allows us to differentiate between winning and more winning and losing and less losing coalitions reected by a voting game that is not any more simple. We use data from Scotland, Hungary and a number of other countries both to illustrate the relation of theoretical and effective power and show our results working in the practice.a priori voting power; power index; being absent from voting; minority; Shapley-Shubik index; Shapley value

Cooperation through social influence

We consider a simple and altruistic multiagent system in which the agents are eager to perform a collective task but where their real engagement depends on the willingness to perform the task of other influential agents. We model this scenario by an influence game, a cooperative simple game in which a team (or coalition) of players succeeds if it is able to convince enough agents to participate in the task (to vote in favor of a decision). We take the linear threshold model as the influence model. We show first the expressiveness of influence games showing that they capture the class of simple games. Then we characterize the computational complexity of various problems on influence games, including measures (length and width), values (Shapley-Shubik and Banzhaf) and properties (of teams and players). Finally, we analyze those problems for some particular extremal cases, with respect to the propagation of influence, showing tighter complexity characterizations.Peer ReviewedPostprint (author’s final draft

Multi-Robot Coalition Formation for Distributed Area Coverage

The problem of distributed area coverage using multiple mobile robots is an important problem in distributed multi-robot sytems. Multi-robot coverage is encountered in many real world applications, including unmanned search & rescue, aerial reconnaissance, robotic demining, inspection of engineering structures, and automatic lawn mowing. To achieve optimal coverage, robots should move in an efficient manner and reduce repeated coverage of the same region that optimizes a certain performance metric such as the amount of time or energy expended by the robots. This dissertation especially focuses on using mini-robots with limited capabilities, such as low speed of the CPU and limited storage of the memory, to fulfill the efficient area coverage task. Previous research on distributed area coverage use offline or online path planning algorithms to address this problem. Some of the existing approaches use behavior-based algorithms where each robot implements simple rules and the interaction between robots manifests in the global objective of overall coverage of the environment. Our work extends this line of research using an emergent, swarming based technique where robots use partial coverage histories from themselves as well as other robots in their vicinity to make local decisions that attempt to ensure overall efficient area coverage. We have then extended this technique in two directions. First, we have integreated the individual-robot, swarming-based technique for area coverage to teams of robots that move in formation to perform area coverage more efficiently than robots that move individually. Then we have used a team formation technique from coalition game theory, called Weighted Voting Game (WVG) to handle situations where a team moving in formation while performing area coverage has to dynamically reconfigure into sub-teams or merge with other teams, to continue the area coverage efficiently. We have validated our techniques by testing them on accurate models of e-puck robots in the Webots robot simulation platform, as well as on physical e-puck robots

Forms of representation for simple games: sizes, conversions and equivalences

Simple games are cooperative games in which the benefit that a coalition may have is always binary, i.e., a coalition may either win or loose. This paper surveys different forms of representation of simple games, and those for some of their subfamilies like regular games and weighted games. We analyze the forms of representations that have been proposed in the literature based on different data structures for sets of sets. We provide bounds on the computational resources needed to transform a game from one form of representation to another one. This includes the study of the problem of enumerating the fundamental families of coalitions of a simple game. In particular we prove that several changes of representation that require exponential time can be solved with polynomial-delay and highlight some open problems.Peer ReviewedPostprint (author’s final draft