Related papers: Game theory of undirected graphical models
This paper further develops the algebraic--geometric foundations of conditional independence (CI) equilibria, a refinement of dependency equilibria that integrates conditional independence relations from graphical models into strategic…
We study the Spohn conditional independence (CI) variety $C_X$ of an $n$-player game $X$ for undirected graphical models on $n$ binary random variables consisting of one edge. For a generic game, we show that $C_X$ is a smooth irreducible…
An $n$-person game is specified by $n$ tensors of the same format. We view its equilibria as points in that tensor space. Dependency equilibria are defined by linear constraints on conditional probabilities, and thus by determinantal…
Consider the following two-player game on the edges of $K_n$, the complete graph with $n$ vertices: Starting with an empty graph $G$ on the vertex set of $K_n$, in each round the first player chooses $b \in \mathbb{N}$ edges from $K_n$…
We investigate Spohn curves, the algebro-geometric models of totally mixed dependency equilibria for $2 \times 2$ normal-form games. These curves arise as the intersection of two quadrics in $\mathbb{P}^3$ and are generically elliptic…
Coordination games have been of interest to game theorists, economists, and ecologists for many years to study such problems as the emergence of local conventions and the evolution of cooperative behavior. Approaches for understanding the…
Conventional noncooperative game theory hypothesizes that the joint strategy of a set of players in a game must satisfy an "equilibrium concept". All other joint strategies are considered impossible; the only issue is what equilibrium…
This paper is a significant step forward in understanding dependency equilibria within the framework of real algebraic geometry encompassing both pure and mixed equilibria. In alignment with Spohn's original definition of dependency…
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 work, we introduce graphical modelsfor multi-player game theory, and give powerful algorithms for computing their Nash equilibria in certain cases. An n-player game is given by an undirected graph on n nodes and a set of n local…
We study the classical and quantum values of one- and two-party linear games, an important class of unique games that generalizes the well-known XOR games to the case of non-binary outcomes. We introduce a ``constraint graph" associated to…
This paper studies the rationalization and identification of binary games where players have correlated private types. Allowing for correlation is crucial in global games and in models with social interactions as it represents correlated…
We establish the existence and uniqueness of distributed equilibria to possibly nonsymmetric $N$ player differential games with interactions through controls under displacement semimonotonicity assumptions. Surprisingly, the nonseparable…
Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…
Spatial evolution game has traditionally assumed that players interact with neighbors on a single network, which is isolated and not influenced by other systems. We introduce the simple game model into the interdependent networks composed…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
Competitive games involving thousands or even millions of players are prevalent in real-world contexts, such as transportation, communications, and computer networks. However, learning in these large-scale multi-agent environments presents…
We consider zero-sum games in which players move between adjacent states, where in each pair of adjacent states one state dominates the other. The states in our game can represent positional advantages in physical conflict such as high…
We study potential games on unimodular random graphs of bounded degree, where players interact through the underlying network. Using the unimodular measure, we define a well-posed global potential that captures both finite- and…
Covering spaces of graphs have long been useful for studying expanders (as "graph lifts") and unique games (as the "label-extended graph"). In this paper we advocate for the thesis that there is a much deeper relationship between…