Related papers: Ising Game on Graphs
Ising models describe the joint probability distribution of a vector of binary feature variables. Typically, not all the variables interact with each other and one is interested in learning the presumably sparse network structure of the…
The theory of learning in games has extensively studied situations where agents respond dynamically to each other by optimizing a fixed utility function. However, in real situations, the strategic environment varies as a result of past…
We study the stochastic parallel dynamics of Ising spin systems defined on finitely connected directed random graphs with arbitrary degree distributions, using generating functional analysis. For fully asymmetric graphs the dynamics of the…
We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her own state and the empirical…
We study a class of games which model the competition among agents to access some service provided by distributed service units and which exhibit congestion and frustration phenomena when service units have limited capacity. We propose a…
One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. "noise") is introduced in players' behavior. In this context, the…
We use the cavity method to study parallel dynamics of disordered Ising models on a graph. In particular, we derive a set of recursive equations in single site probabilities of paths propagating along the edges of the graph. These equations…
Learning problems commonly exhibit an interesting feedback mechanism wherein the population data reacts to competing decision makers' actions. This paper formulates a new game theoretic framework for this phenomenon, called "multi-player…
Learning processes in games explain how players grapple with one another in seeking an equilibrium. We study a natural model of learning based on individual gradients in two-player continuous games. In such games, the arguably natural…
Go gaming is a struggle between adversaries, black and white simple stones, and aim to control the most Go board territory for success. Rules are simple but Go game fighting is highly intricate. Stones placement and interaction on board is…
The Ising model of statistical physics has served as a keystone example of phase transitions, thermodynamic limits, scaling laws, and many other phenomena and mathematical methods. We introduce and explore an Ising game, a variant of the…
Notwithstanding great strides that statistical mechanics has made in recent decades, an analytic solution of arguably the simplest model of relaxation dynamics, the Ising model in an applied external field remains elusive even in $1d$.…
We develop a minimal, timeless game-theoretic representation of the mass-geometry relation. An "Object" (mass) and "Space" (geometry) choose strategies in a static normal-form game; utilities encode stability as mutual consistency rather…
The dynamical properties of finite dynamical systems (FDSs) have been investigated in the context of coding theoretic problems, such as network coding, and in the context of hat games, such as the guessing game and Winkler's hat game. The…
A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an $\epsilon$-Nash equilibrium if no player can gain more than $\epsilon$ by…
This paper proposes a co-evolutionary model of directed graphs and three opinions, i.e., conservative$(+)$, neutral$(\odot)$ and liberal$(-)$. Agents update both opinions and social relationships with bias. We find that an emergent game…
We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become…
We investigate a kinetic Ising model with several single-spin flip dynamics (including Metropolis and heat-bath) on quenched and annealed random regular graphs. As expected, on the quenched structures all proposed algorithms reproduce the…
How complex is an Ising model? Usually, this is measured by the computational complexity of its ground state energy problem. Yet, this complexity measure only distinguishes between planar and non-planar interaction graphs, and thus fails to…
While the Ising model belongs to the realm of equilibrium statistical mechanics, the voter model is an example of a nonequilibrium system. We examine an opinion formation model, which is a mixture of Ising and voter agents with…