Related papers: A geometric and combinatorial view of weighted vot…
We propose a class of cooperative games, called d Partitioned Compbinatorial Optimization Games (PCOGs). The input of PCOG consists of a set of agents and a combinatorial structure (typically a graph) with a fixed optimization goal on this…
Federated learning is a setting where agents, each with access to their own data source, combine models from local data to create a global model. If agents are drawing their data from different distributions, though, federated learning…
Weighted timed games are zero-sum games played by two players on a timed automaton equipped with weights, where one player wants to minimise the accumulated weight while reaching a target. Weighted timed games are notoriously difficult and…
We introduce a game where players selfishly choose a resource and endure a cost depending on the number of players choosing nearby resources. We model the influences among resources by a weighted graph, directed or not. These games are…
This thesis presents some geometric insights into three different types of two player prediction games -- namely general learning task, prediction with expert advice, and online convex optimization. These games differ in the nature of the…
This paper concerns the analysis of the Shapley value in matching games. Matching games constitute a fundamental class of cooperative games which help understand and model auctions and assignments. In a matching game, the value of a…
LP-duality theory has played a central role in the study of cores of games, right from the early days of this notion to the present time. The classic paper of Shapley and Shubik \cite{Shapley1971assignment} introduced the "right" way of…
We propose a class of two person perfect information games based on weighted graphs. One of these games can be described in terms of a round pizza which is cut radially into pieces of varying size. The two players alternately take pieces…
Cooperative 2-matching games are a generalization of cooperative matching games, where the value function is given by maximum-weight b-matchings, for a vertex capacity vector $b \leq 2$. We show how to separate over the core of 2-matching…
Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
Letting $P$ be a convex polytope in $\mathbb{R}^d$ with $n>d$ vertices, we study geometric and analytical properties of the set of generalized barycentric coordinates relative to any point $p\in P$. We prove that such sets are polytopes in…
We investigate a new class of congestion games, called Totally Unimodular (TU) Congestion Games, where the players' strategies are binary vectors inside polyhedra defined by totally unimodular constraint matrices. Network congestion games…
Various decomposition of finite games have been proposed. The inner product of vectors plays a key role in the decomposition of finite games. This paper considers the effect of different inner products on the orthogonal decomposition of…
The preference graph is a combinatorial representation of the structure of a normal-form game. Its nodes are the strategy profiles, with an arc between profiles if they differ in the strategy of a single player, where the orientation…
We consider a class of Nash games, termed as aggregative games, being played over a networked system. In an aggregative game, a player's objective is a function of the aggregate of all the players' decisions. Every player maintains an…
We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…
A Graph of Convex Sets (GCS) is a graph in which vertices are associated with convex programs and edges couple pairs of programs through additional convex costs and constraints. Any optimization problem over an ordinary weighted graph…
We study optimal simple second-order cone representations (a particular subclass of second-order cone representations) for weighted geometric means, which turns out to be closely related to minimum mediated sets. Several lower and upper…
We consider restricted games on weighted graphs associated with minimum partitions. We replace in the classical definition of Myerson restricted game the connected components of any subgraph by the subcomponents corresponding to a minimum…