Experimental Analysis of the Effects of Manipulations in Weighted Voting Games

Weighted voting games are classic cooperative games which provide compact representation for coalition formation models in human societies and multiagent systems. As useful as weighted voting games are in modeling cooperation among players, they are, however, not immune from the vulnerability of manipulations (i.e., dishonest behaviors) by strategic players that may be present in the games. With the possibility of manipulations, it becomes difficult to establish or maintain trust, and, more importantly, it becomes difficult to assure fairness in such games. For these reasons, we conduct careful experimental investigations and analyses of the effects of manipulations in weighted voting games, including those of manipulation by splitting, merging, and annexation . These manipulations involve an agent or some agents misrepresenting their identities in anticipation of gaining more power or obtaining a higher portion of a coalition\u27s profits at the expense of other agents in a game. We consider investigation of some criteria for the evaluation of game\u27s robustness to manipulation. These criteria have been defined on the basis of theoretical and experimental analysis. For manipulation by splitting, we provide empirical evidence to show that the three prominent indices for measuring agents\u27 power, Shapley-Shubik, Banzhaf, and Deegan-Packel, are all susceptible to manipulation when an agent splits into several false identities. We extend a previous result on manipulation by splitting in exact unanimity weighted voting games to the Deegan-Packel index, and present new results for excess unanimity weighted voting games. We partially resolve an important open problem concerning the bounds on the extent of power that a manipulator may gain when it splits into several false identities in non-unanimity weighted voting games. Specifically, we provide the first three non-trivial bounds for this problem using the Shapley-Shubik and Banzhaf indices. One of the bounds is also shown to be asymptotically tight. Furthermore, experiments on non-unanimity weighted voting games show that the three indices are highly susceptible to manipulation via annexation while they are less susceptible to manipulation via merging. Given that the problems of calculating the Shapley-Shubik and Banzhaf indices for weighted voting games are NP-complete, we show that, when the manipulators\u27 coalitions sizes are restricted to a small constant, manipulators need to do only a polynomial amount of work to find a much improved power gain for both merging and annexation, and then present two enumeration-based pseudo-polynomial algorithms that manipulators can use. Finally, we argue and provide empirical evidence to show that despite finding the optimal beneficial merge is an NP-hard problem for both the Shapley-Shubik and Banzhaf indices, finding beneficial merge is relatively easy in practice. Also, while it appears that we may be powerless to stop manipulation by merging for a given game, we suggest a measure, termed quota ratio, that the game designer may be able to control. Thus, we deduce that a high quota ratio decreases the number of beneficial merges

Spectrally Arbitrary Tree Sign Pattern Matrices

A sign pattern (matrix) is a matrix whose entries are from the set {+,–, 0}. A sign pattern matrix A is a spectrally arbitrary pattern if for every monic real polynomial p(x) of degree n there exists a real matrix B whose entries agree in sign with A such that the characteristic polynomial of B is p(x). All 3 × 3 SAP\u27s, as well as tree sign patterns with star graphs that are SAP\u27s, have already been characterized. We investigate tridiagonal sign patterns of order 4. All irreducible tridiagonal SAP\u27s are identified. Necessary and sufficient conditions for an irreducible tridiagonal pattern to be an SAP are found. Some new techniques, such as innovative applications of Gröbner bases for demonstrating that a sign pattern is not potentially nilpotent, are introduced. Some properties of sign patterns that allow every possible inertia are established. Keywords: Sign pattern matrix, Spectrally arbitrary pattern (SAP), Inertially arbitrary pattern (IAP), Tree sign pattern (tsp), Potentially nilpotent pattern, Gröbner basis, Potentially stable pattern, Sign nonsingular, Sign singula

A Smooth-Turn Mobility Model for Airborne Networks

In this article, I introduce a novel airborne network mobility model, called the Smooth Turn Mobility Model, that captures the correlation of acceleration for airborne vehicles across time and spatial coordinates. Effective routing in airborne networks (ANs) relies on suitable mobility models that capture the random movement pattern of airborne vehicles. As airborne vehicles cannot make sharp turns as easily as ground vehicles do, the widely used mobility models for Mobile Ad Hoc Networks such as Random Waypoint and Random Direction models fail. Our model is realistic in capturing the tendency of airborne vehicles toward making straight trajectory and smooth turns with large radius, and whereas is simple enough for tractable connectivity analysis and routing design