Related papers: Dynamics of multi-frequency minority games
We study the structure of the underlying network of connections in the Minority Game. There is not an explicit interaction among the agents, but they interact via global magnitudes of the model and mainly through their strategies. We define…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
The Parallel Minority Game (PMG) is a synchronous adaptive multi-agent model that exhibits active-absorbing transitions characteristic of non-equilibrium statistical systems. We perform a comprehensive numerical study of the PMG under two…
Logit dynamics are dynamical systems describing transitions and equilibria of actions of interacting players under uncertainty. An uncertainty is embodied in logit dynamic as a softmax type function often called a logit function originating…
We consider a simplified version of the Wealth Game, which is an agent-based financial market model with many interesting features resembling the real stock market. Market makers are not present in the game so that the majority traders are…
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…
In this work the system of agents is applied to establish a model of the nonlinear distributed signal processing. The evolution of the system of the agents - by the prediction time scale diversified trend followers, has been studied for the…
Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…
This work extends the theory presented in Mean Field Games with a Dominating Player by Bensoussan, Chau and Yam on mean field games with a dominating player, to the case in which the utility and cost functions depend not only on the law of…
We use the cavity method from statistical physics for analyzing the transient and stationary dynamics of a minority game that is played by agents performing market arbitrage. On the level of linear response the method allows to include the…
This paper presents recent results from Mean Field Game theory underlying the introduction of common noise that imposes to incorporate the distribution of the agents as a state variable. Starting from the usual mean field games equations…
We provide a theoretical description of the Minority Game in terms of crowd effects. The size of the fluctuations arising in the game is controlled by the interplay between crowds of like-minded agents and their anti-correlated partners…
We show analytically how the fluctuations (i.e. standard deviation) in the Minority Game (MG) can decrease below the random coin-toss limit if the agents use more general, stochastic strategies. This suppression of the standard deviation…
Mean Field Games (MFG) theory describes strategic interactions in differential games with a large number of small and indistinguishable players. Traditionally, the players' control impacts only the drift term in the system's dynamics,…
Mating preferences of many biological species are not constant but season-dependent. Within the framework of evolutionary game theory this can be modeled with two finite opposite-sex populations playing against each other following the…
We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong…
This paper studies a class of stationary mean-field games of singular stochastic control with regime-switching. The representative agent adjusts the dynamics of a Markov-modulated It\^o-diffusion via a two-sided singular stochastic control…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
Our aim is to model a game for power as a dynamical process, where an excess of power possessed by a player allows him to gain even more power. Such a positive feedback is often termed as the Matthew effect. Analytical and numerical methods…
Dynamics of many-body Hamiltonian systems with long range interactions is studied, in the context of the so called $\alpha-$HMF model. Building on the analogy with the related mean field model, we construct stationary states of the…