Related papers: The lattice of embedded subsets
Positional games are a mathematical class of two-player games comprising Tic-tac-toe and its generalizations. We propose a novel encoding of these games into Quantified Boolean Formulas (QBFs) such that a game instance admits a winning…
Sharing economy is a transformative socio-economic phenomenon built around the idea of sharing underused resources and services, e.g. transportation and housing, thereby reducing costs and extracting value. Anticipating continued reduction…
Cores of cooperative games are ubiquitous in information theory, and arise most frequently in the characterization of fundamental limits in various scenarios involving multiple users. Examples include classical settings in network…
Haynes et al. (2020) introduced and investigated the concept of coalition in graphs \cite{hhhmm1}. Their study examined this concept from a vertex-based perspective, whereas in this paper, we extend the investigation to an edge-based…
The report suggests the concept of risk, outlining two mathematical structures necessary for risk genesis: the set of outcomes and, in a general case, partial order of preference on it. It is shown that this minimum partial order should…
We analyse a coalition formation game between strategic service providers of a congestible service. The key novelty of our formulation is that it is a constant sum game, i.e., the total payoff across all service providers (or coalitions of…
Game theory-based approaches have recently gained traction in a wide range of applications, importantly in power and energy systems. With the onset of cooperation as a new perspective for solving power system problems, as well as the nature…
An $n$-valued map is a set-valued continuous function $f$ such that $f(x)$ has cardinality $n$ for every $x$. Some $n$-valued maps will "split" into a union of $n$ single-valued maps. Characterizations of splittings has been a major theme…
We demonstrate that statistics for several types of set partitions are described by generating functions which appear in the theory of integrable equations.
Distributed Nash equilibrium (NE) seeking problem for multi-coalition games has attracted increasing attention in recent years, but the research mainly focuses on the case without agreement demand within coalitions. This paper considers a…
Research in cooperative games often assumes that agents know the coalitional values with certainty, and that they can belong to one coalition only. By contrast, this work assumes that the value of a coalition is based on an underlying…
We establish a connection between federated learning, a concept from machine learning, and mean-field games, a concept from game theory and control theory. In this analogy, the local federated learners are considered as the players and the…
The main ambition of this thesis is to contribute to the development of cooperative game theory towards combinatorics, algorithmics and discrete geometry. Therefore, the first chapter of this manuscript is devoted to highlighting the…
During collaborative board games, cohesion represents a key aspect to define a well functionning group. From the success of the task to the developement of interpersonal relationship, this concept covers many aspects of group dynamics. The…
Independent set games are cooperative games defined on graphs, where players are edges and the value of a coalition is the maximum cardinality of independent sets in the subgraph defined by the coalition. In this paper, we investigate the…
The double slit experiment provides a clear demarcation between classical and quantum theory, while multi-slit experiments demarcate quantum and higher-order interference theories. In this work we show that these experiments pertain to a…
This paper studies a significant problem in green networking called switching off base stations in case of cooperating service providers by means of stochastic geometric and coalitional game tools. The coalitional game herein considered is…
We study two forms of a symmetric cooperative game played by three players, one classical and other quantum. In its classical form making a coalition gives advantage to players and they are motivated to do so. However in its quantum form…
As Aumann stated, cooperation and non-cooperation are different ways of viewing the same game, with the main difference being whether players can reach a binding cooperative agreement. In the real world, many games often coexist competition…
Social distance games have been extensively studied as a coalition formation model where the utilities of agents in each coalition were captured using a utility function $u$ that took into account distances in a given social network. In…