Related papers: A geometric and combinatorial view of weighted vot…
Cooperative games with nonempty core are called balanced, and the set of balanced games is a polyhedron. Given a game with empty core, we look for the closest balanced game, in the sense of the (weighted) Euclidean distance, i.e., the…
We fully characterize the core of a broad class of nonlinear games by identifying a suitable relaxation for inherent nonlinearity, directly generalizing the linear frameworks in the literature. This characterization significantly expands…
This paper investigates the concept of an optimal ratio for regular polytopes in $n$-dimensional space within the framework of the Generalized Chaos Game. The optimal ratio, $r_{\text{opt}}$, is defined as the value at which the…
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…
Network congestion games are a well-understood model of multi-agent strategic interactions. Despite their ubiquitous applications, it is not clear whether it is possible to design information structures to ameliorate the overall experience…
We provide two new characterizations of bounded orthogonally additive polynomials from a uniformly complete vector lattice into a convex bornological space using harmonic means and completely partitioned weighted geometric means. Our result…
We consider, for complete bipartite graphs, the convex hulls of characteristic vectors of all matchings, extended by a binary entry indicating whether the matching contains two specific edges. These polytopes are associated to the quadratic…
We derive multiparty games that, if the winning chance exceeds a certain limit, prove the incompatibility of the parties' causal relations with any partial order. This, in turn, means that the parties exert a back-action on the causal…
Congestion games offer a primary model in the study of pure Nash equilibria in non-cooperative games, and a number of generalized models have been proposed in the literature. One line of generalization includes weighted congestion games, in…
One of possible cryptomorphic definitions of a partially ordered set (= a poset) $P$ on a non-empty finite basic set $N$ is in terms of the set ${\cal L}(P)$ of all its linear extensions, that is, in terms of the set of total orders of $N$…
We consider the problem of maximizing the minimum (weighted) value of all components of a vector over a polymatroid. This is a special case of the lexicographically optimal base problem introduced and solved by Fujishige. We give an…
We encode arbitrary finite impartial combinatorial games in terms of lattice points in rational convex polyhedra. Encodings provided by these \emph{lattice games} can be made particularly efficient for octal games, which we generalize to…
A new game-theoretic approach for combining multiple classifiers is proposed. A short introduction in Game Theory and coalitions illustrate the way any collective decision scheme can be viewed as a competitive game of coalitions that are…
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…
Motivated by the analysis of the performance of the simplex method we study the behavior of families of pivot rules of linear programs. We introduce normalized-weight pivot rules which are fundamental for the following reasons: First, they…
We introduce Contested Logistics Games, a variant of logistics problems that account for the presence of an adversary that can disrupt the movement of goods in selected areas. We model this as a large two-player zero-sum one-shot game…
A connected matching in a graph G consists of a set of pairwise disjoint edges whose covered vertices induce a connected subgraph of G. While finding a connected matching of maximum cardinality is a well-solved problem, it is NP-hard to…
A positional game is a game where two players sequentially label vertices of a hypergraph, consisting of a board and a collection of winning sets, with colors assigned to each player until all vertices of the board are claimed. The first…
We study the properties of elections that have a given position matrix (in such elections each candidate is ranked on each position by a number of voters specified in the matrix). We show that counting elections that generate a given…
This paper contributes to the program of numerical characterisation and classification of simple games outlined in the classical monograph of von Neumann and Morgenstern (1944). One of the most fundamental questions of this program is what…