相关论文: Computing Power Indices in Weighted Majority Games…

We study the algorithm of Gurvich, Khachyian and Karzanov (GKK algorithm) when it is ran over mean-payoff games with no simple cycle of weight zero. We propose a new symmetric analysis, lowering the $O(n^2 N)$ upper-bound of Pisaruk on the…

Data valuation, the task of quantifying the contribution of individual data points to model performance, has emerged as a fundamental challenge in machine learning. Game-theoretic approaches, such as the Banzhaf value, offer principled…

We consider the computation of a Nash equilibrium in attack and defense games on networks (Bloch et al. [1]). We prove that a Nash Equilibrium of the game can be computed in polynomial time with respect to the number of nodes in the…

For $f$ a weighted voting scheme used by $n$ voters to choose between two candidates, the $n$ \emph{Shapley-Shubik Indices} (or {\em Shapley values}) of $f$ provide a measure of how much control each voter can exert over the overall outcome…

Based on Holler (1982) and Armijos-Toro et al. (2021) we propose two power indices to measure the influence of the players in the class of weighted majority games in partition function form. We compare these new power indices with their…

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…

We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual…

Let $f$ be a fixed (holomorphic or Maass) modular cusp form. Let $\cq$ be a Dirichlet character mod $q$. We describe a fast algorithm that computes the value $L(1/2,f\times\chi_q)$ up to any specified precision. In the case when $q$ is…

A number of recent works [Goldberg 2006; O'Donnell and Servedio 2011; De, Diakonikolas, and Servedio 2017; De, Diakonikolas, Feldman, and Servedio 2014] have considered the problem of approximately reconstructing an unknown weighted voting…

We consider some well-known families of two-player, zero-sum, perfect information games that can be viewed as special cases of Shapley's stochastic games. We show that the following tasks are polynomial time equivalent: - Solving simple…

Shapley values, originating in game theory and increasingly prominent in explainable AI, have been proposed to assess the contribution of facts in query answering over databases, along with other similar power indices such as Banzhaf…

The Shapley value---probably the most important normative payoff division scheme in coalitional games---has recently been advocated as a useful measure of centrality in networks. However, although this approach has a variety of real-world…

The Banzhaf power and interaction indexes for a pseudo-Boolean function (or a cooperative game) appear naturally as leading coefficients in the standard least squares approximation of the function by a pseudo-Boolean function of a specified…

We study the Shapley value in weighted voting games. The Shapley value has been used as an index for measuring the power of individual agents in decision-making bodies and political organizations, where decisions are made by a majority vote…

We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to…

In this research, we discuss a problem of calculating the Shapley value in bankruptcy games. We show that the decision problem of computing the Shapley value in bankruptcy games is NP-complete. We also investigate the relationship between…

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…

Parity games play an important role in model checking and synthesis. In their paper, Calude et al. have shown that these games can be solved in quasi-polynomial time. We show that their algorithm can be implemented efficiently: we use their…

In this dissertation, we analyze the computational properties of game-theoretic centrality measures. The key idea behind game-theoretic approach to network analysis is to treat nodes as players in a cooperative game, where the value of each…

In a mean-payoff parity game, one of the two players aims both to achieve a qualitative parity objective and to minimize a quantitative long-term average of payoffs (aka. mean payoff). The game is zero-sum and hence the aim of the other…