Related papers: The power of the largest player
Electing a committee of size k from m alternatives (k < m) is an interesting problem under the multi-winner voting rules. However, very few committee selection rules found in the literature consider the coalitional possibilities among the…
We present numerical simulations of a model of social influence, where the opinion of each agent is represented by a binary vector. Agents adjust their opinions as a result of random encounters, whenever the difference between opinions is…
In approval-based multiwinner voting, voters express approval preferences over a set of candidates, and the goal is to return a winning committee. This model captures a broad range of subset selection problems under preferences. Prior work…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
For centuries, it has been widely believed that the influence of a small coalition of voters is negligible in a large election. Consequently, there is a large body of literature on characterizing the likelihood for an election to be…
In this paper we extend the framework of evolutionary inspection game put forward recently by the author and coworkers to a large class of conflict interactions dealing with the pressure executed by the major player (or principal) on the…
Herding, where investors imitate others' decisions rather than relying on their own analysis, is a prevalent phenomenon in financial markets. Excessive herding distorts rational decisions, amplifies volatility, and can be exploited by…
Devising an index to measure the quality of research is a challenging task. In this paper, we propose a set of indices to evaluate the quality of research produced by an author. Our indices utilize a policy that assigns the weights to…
It is well known that the Penrose-Banzhaf index of a weighted game can differ starkly from corresponding weights. Limit results are quite the opposite, i.e., under certain conditions the power distribution approaches the weight…
Power law is one of the the simplest forms of the relationship between different variables of a system. It leads naturally to the introduction of compound parameters describing physical properties of the system. Often one of the variables…
We introduce and analyze a novel family of power indices tailored for sharing networks in technological markets, where firms operate competitively within, but not across, distinct industrial sectors. In these settings, inter-firm…
A general model for opinion formation and competition, like in ideological struggles is formulated. The underlying set is a closed one, like a country but in which the population size is variable in time. Several ideologies compete to…
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…
One of the fundamental principles driving diversity or homogeneity in domains such as cultural differentiation, political affiliation, and product adoption is the tension between two forces: influence (the tendency of people to become…
Asymmetric evolutionary games, such as the Ultimatum Game, provide keys to understanding the emergence of fairness in social species. Building on this framework, we explore the evolution of social value systems and the operational role that…
Feature attribution methods have become essential for explaining machine learning models. Many popular approaches, such as SHAP and Banzhaf values, are grounded in power indices from cooperative game theory, which measure the contribution…
The Naming Game is a classic model for studying the emergence and evolution of language within a population. In this paper, we extend the traditional Naming Game model to encompass multiple committed opinions and investigate the system…
Algorithms are often used to produce decision-making rules that classify or evaluate individuals. When these individuals have incentives to be classified a certain way, they may behave strategically to influence their outcomes. We develop a…
We consider the dynamics, existence and stability of the equilibrium states for large populations of individuals who can play various types of non--cooperative games. The players imitate the most attractive strategies, and the choice is…
We introduce the prediction value (PV) as a measure of players' informational importance in probabilistic TU games. The latter combine a standard TU game and a probability distribution over the set of coalitions. Player $i$'s prediction…