相关论文: Statistical mechanics of the majority game

We propose statistical systems based on $p$-adic numbers. In the systems, the Hamiltonian is a standard real number which is given by a map from the $p$-adic numbers. Therefore we can introduce the temperature as a real number and calculate…

We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…

We consider stationary viscous Mean-Field Games systems in the case of local, decreasing and unbounded coupling. These systems arise in ergodic mean-field game theory, and describe Nash equilibria of games with a large number of agents…

In this paper we investigate a stochastic model for an economic game. To describe this model we have used a Wiener process, as the noise has a stabilization effect. The dynamics are studied in terms of stochastic stability in the stationary…

In the game-theoretic model war of attrition, players are subject to an explicit cost proportional to the duration of contests. We construct a model where the time cost is not explicitly given, but instead depends implicitly on the…

Control of multi-agent systems via game theory is investigated. Assume a system level object is given, the utility functions for individual agents are designed to convert a multi-agent system into a potential game. First, for fixed…

We investigate the large population dynamics of a family of stochastic particle systems with three-state cyclic individual behaviour and parameter-dependent transition rates. On short time scales, the dynamics turns out to be approximated…

It is known that the memory is relevant in the symmetric phase of the minority game. In our previous work we have successfully explained the quasi-periodic behavior of the game in the symmetric phase with the help of the probability theory.…

Using generating functional and replica techniques, respectively, we study the dynamics and statics of a spherical Minority Game (MG), which in contrast with a spherical MG previously presented in J.Phys A: Math. Gen. 36 11159 (2003)…

Here, we develop numerical methods for finite-state mean-field games (MFGs) that satisfy a monotonicity condition. MFGs are determined by a system of differential equations with initial and terminal boundary conditions. These non-standard…

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean…

Stochastic games are a convenient formalism for modelling systems that comprise rational agents competing or collaborating within uncertain environments. Probabilistic model checking techniques for this class of models allow us to formally…

The isolated one-dimensional Heisenberg model with static random magnetic fields has become paradigmatic for the analysis of many-body localization. Here, we study the dynamics of this system initially prepared in a highly-excited…

A brief review is given of the minority game, an idealized model of a market of speculative agents, and its complex many-body behaviour. Particular consideration is given to the consequences and implications of correlations between…

We consider a class of games that are generalizations of the minority game, in that the demand and supply of the resource are specified independently. This allows us to study systems in which agents compete for a resource under different…

There exists a wide variety of works on the dynamics of large populations ranging from simple heuristic modeling to those based on advanced computer supported methods. Their interconnections, however, remain mostly vague, which…

Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…

We investigate the increasingly important and common game-solving setting where we do not have an explicit description of the game but only oracle access to it through gameplay, such as in financial or military simulations and computer…

Games on graphs provide a natural model for reactive non-terminating systems. In such games, the interaction of two players on an arena results in an infinite path that describes a run of the system. Different settings are used to model…

Many-body long-range interacting systems can remain approximately in a quasi-stationary state far-from-thermodynamic equilibrium. These states are typically characterized by a pair of counter-propagating density clusters, or by a single…