Related papers: Ising Game on Graphs
A description of static equilibria in the noisy binary choice (Ising) game on complete and random graphs resulting from maximisation of the likelihood of system configurations is presented. An equivalence of such likelihood equilibria to…
Static and dynamic equilibria in noisy binary choice games on graphs are considered. Equations defining static quantal response equilibria (QRE) for binary choice games on graphs with arbitrary topology and noise distribution are written.…
A partially parallel dynamical noisy binary choice (Ising) game in discrete time of $N$ players on complete graphs with $k$ players having a possibility of changing their strategies at each time moment called $k$-flip Ising game is…
We here study the Battle of the Sexes game, a textbook case of asymmetric games, on small networks. Due to the conflicting preferences of the players, analytical approaches are scarce and most often update strategies are employed in…
Effects of dynamical activity spillover in a noisy binary choice game (Ising game) on a complete graph are studied. Binary choice games are very important for both economics and statistical physics playing a role of the bridge between these…
Static reduction of information structures (ISs) is a method that is commonly adopted in stochastic control, team theory, and game theory. One approach entails change of measure arguments, which has been crucial for stochastic analysis and…
Coordination games describe social or economic interactions in which the adoption of a common strategy has a higher payoff. They are classically used to model the spread of conventions, behaviors, and technologies in societies. Here we…
We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise level on the stochastic stability of Nash…
The Ising model on networks plays a fundamental role as a testing ground for understanding cooperative phenomena in complex systems. Here we solve the synchronous dynamics of the Ising model on random graphs with an arbitrary degree…
Transitions between metastable equilibria in the low-temperature phase of dynamical Ising game with activity spillover are studied in the infinite time limit. It is shown that exponential enhancement due to activity spillover, which takes…
We propose a new mean-field game model with two states to study synchronization phenomena, and we provide a comprehensive characterization of stationary and dynamic equilibria along with their stability properties. The game undergoes a…
We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both…
We introduce a simple stochastic dynamics for game theory. It assumes ``local'' rationality in the sense that any player climbs the gradient of his utility function in the presence of a stochastic force which represents deviation from…
The Naming Game is a model of non-equilibrium dynamics for the self-organized emergence of a linguistic convention or a communication system in a population of agents with pairwise local interactions. We present an extensive study of its…
In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium…
The 2-spin Ising model in statistical mechanics and the 2x2 normal form game in game theory are compared. All configurations allowed by the second are recovered by the first when the only concern is about Nash equilibria. But it holds no…
We consider the use of Bayesian information criteria for selection of the graph underlying an Ising model. In an Ising model, the full conditional distributions of each variable form logistic regression models, and variable selection…
We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…
This work contains the mathematical exploration of a few prototypical games in which central concepts from statistics and probability theory naturally emerge. The first two kinds of games are termed Fisher and Bayesian games, which are…
A one-dimensional Ising model with nearest neighbour interactions is applied to study compaction processes in granular media. An equivalent particle-hole picture is introduced, with the holes being associated to the domain walls of the…