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We introduce the game INFLUENCE, a scoring combinatorial game, played on a directed graph where each vertex is either colored black or white. The two players, Black and White play alternately by taking a vertex of their color and all its…

The game INFLUENCE is a scoring combinatorial game that has been introduced in 2020 by Duchene et al. It is a good representative of Milnor's universe of scoring games, i.e. games where it is never interesting for a player to miss his turn.…

Given an impartial combinatorial game G, we create a class of related games (CIS-G) by specifying a finite set of positions in G and forbidding players from moving to those positions (leaving all other game rules unchanged). Such…

In this paper, we propose a Quantum variation of combinatorial games, generalizing the Quantum Tic-Tac-Toe proposed by Allan Goff. A combinatorial game is a two-player game with no chance and no hidden information, such as Go or Chess. In…

Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…

This work is concerned with the study of the Game of Graph Nim -- a class of two-player combinatorial games -- on graphs with $4$ edges. To each edge of such a graph is assigned a positive-integer-valued edge-weight, and during each round…

Intransitivity is a critical issue in pairwise preference modeling. It refers to the intransitive pairwise preferences between a group of players or objects that potentially form a cyclic preference chain and has been long discussed in…

By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a "pass" move into a game affects its behavior. We consider two well…

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…

We introduce a class of cooperative games induced by weighted directed graphs. Specifically, the coalitional value combines an internal interaction term given by the induced subgraph game with an external component based on minimal incoming…

We present the Social Influence Game (SIG), a framework for modeling adversarial persuasion in social networks with an arbitrary number of competing players. Our goal is to provide a tractable and interpretable model of contested influence…

Crowdscience games may hold unique potentials as learning opportunities compared to games made for fun or education. They are part of an actual science problem solving process: By playing, players help scientists, and thereby interact with…

We study discrete preference games in heterogeneous social networks. These games model the interplay between a player's private belief and his/her publicly stated opinion (which could be different from the player's belief) as a strategic…

This paper studies two important signal processing aspects of equilibrium behavior in non-cooperative games arising in social networks, namely, reinforcement learning and detection of equilibrium play. The first part of the paper presents a…

There is a growing need for discrete choice models that account for the complex nature of human choices, escaping traditional behavioral assumptions such as the transitivity of pairwise preferences. Recently, several parametric models of…

Intransitivity is a property of connected, oriented graphs representing species interactions that may drive their coexistence even in the presence of competition, the standard example being the three species Rock-Paper-Scissors game. We…

To address the dynamic nature of real-world networks, we generalize competitive diffusion games and Voronoi games from static to temporal graphs, where edges may appear or disappear over time. This establishes a new direction of studies in…

This paper considers the noncooperative maximization of mutual information in the Gaussian interference channel in a fully distributed fashion via game theory. This problem has been studied in a number of papers during the past decade for…

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…

The transitivity of preferences is one of the basic assumptions used in the theory of games and decisions. It is often equated with rationality of choice and is considered useful in building rankings. Intransitive preferences are considered…