Related papers: Average Weights and Power in Weighted Voting Games
Although manipulation and bribery have been extensively studied under weighted voting, there has been almost no work done on election control under weighted voting. This is unfortunate, since weighted voting appears in many important…
Two-player quantitative zero-sum games provide a natural framework to synthesize controllers with performance guarantees for reactive systems within an uncontrollable environment. Classical settings include mean-payoff games, where the…
The prospects of Kahneman and Tversky, Mega Million and Powerball lotteries, St. Petersburg paradox, premature profits and growing losses criticized by Livermore are reviewed under an angle of view comparing mathematical expectations with…
Conventional Monte Carlo simulations are stochastic in the sense that the acceptance of a trial move is decided by comparing a computed acceptance probability with a random number, uniformly distributed between 0 and 1. Here we consider the…
Let $X,X_1,...,X_n$ be independent identically distributed random variables. In this paper we study the behavior of the concentration functions of the weighted sums $\sum\limits_{k=1}^{n}a_k X_k$ with respect to the arithmetic structure of…
We consider a model of power distribution in a social system where a set of agents play a simple game on a graph: the probability of winning each round is proportional to the agent's current power, and the winner gets more power as a…
In many applications of cooperative game theory -- from corporate governance and cartel formation to parliamentary voting -- not all winning coalitions are feasible. Ideological distances, institutional constraints, or pre-electoral…
Given a system where the real-valued states of the agents are aggregated by a function to a real-valued state of the entire system, we are interested in the influence or importance of the different agents for that function. This generalizes…
We design a recursive measure of voting power based on partial as well as full voting efficacy. Classical measures, by contrast, incorporate solely full efficacy. We motivate our design by representing voting games using a division lattice…
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of ``yea''…
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…
We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power-law with an exponent that increases linearly with the game depth, whereas the pooled…
We introduce a new class of games where each player's aim is to randomise her strategic choices in order to affect the other players' expectations aside from her own. The way each player intends to exert this influence is expressed through…
The paper proposes a natural measure space of zero-sum perfect information games with upper semicontinuous payoffs. Each game is specified by the game tree, and by the assignment of the active player and of the capacity to each node of the…
We explain why numbers occurring in the classification of polygon spaces coincide with numbers of self-dual equivalence classes of threshold functions, or of regular Boolean functions, or of decisive weighted majority games.
The Shapley-Shubik index is a specialization of the Shapley value and is widely applied to evaluate the power distribution in committees drawing binary decisions. It was generalized to decisions with more than two levels of approval both in…
The $k$-majority game is played with $n$ numbered balls, each coloured with one of two colours. It is given that there are at least $k$ balls of the majority colour, where $k$ is a fixed integer greater than $n/2$. On each turn the player…
We consider network aggregative games to model and study multi-agent populations in which each rational agent is influenced by the aggregate behavior of its neighbors, as specified by an underlying network. Specifically, we examine systems…
This paper analyzes a variation on the well-known "power of two choices" allocation algorithms. Classically, the smallest of $d$ randomly-chosen options is selected. We investigate what happens when the largest of $d$ randomly-chosen…
Weighted voting games (WVG) are coalitional games in which an agent's contribution to a coalition is given by his it weight, and a coalition wins if its total weight meets or exceeds a given quota. These games model decision-making in…