Related papers: Deterministic Dynamics in the Minority Game
We consider a stochastic game of contribution to the common good in which the players have continuous control over the degree of contribution, and we examine the gradualism arising from the free rider effect. This game belongs to the class…
We study mean-field game (MFG) problems with rough common noise, in which the representative state dynamics are governed by a controlled rough stochastic differential equation driven by an idiosyncratic Brownian motion and a deterministic…
The paper is concerned with the deterministic limit of mean field games with the nonlocal coupling. It is assumed that the dynamics of mean field games are given by nonlinear Markov processes. This type of games includes stochastic mean…
In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We…
We consider deterministic mean field games in which the agents control their acceleration and are constrained to remain in a domain of R n. We study relaxed equilibria in the Lagrangian setting; they are described by a probability measure…
In this work, we study a class of stationary mean-field games of singular stochastic control under model uncertainty. The representative agent adjusts the dynamics of an It\^o diffusion via one-sided singular stochastic control, aiming to…
Convergence of discrete-time Markov chains with two timescales is a powerful tool to study stochastic evolutionary games in subdivided populations. Focusing on linear games within demes, convergence to a diffusion process for the strategy…
To demonstrate the usefulness of physical approaches for the study of realistic economic systems, we investigate the inequality of players' wealth in one of the most extensively studied econophysical models, namely, the minority game (MG).…
The game dynamical equations are derived from Boltzmann-like equations for individual pair interactions by assuming a certain kind of imitation behavior, the so-called proportional imitation rule. They can be extended to a stochastic…
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…
We study the equilibrium distribution of relative strategy scores of agents in the asymmetric phase ($\alpha\equiv P/N\gtrsim 1$) of the basic Minority Game using sign-payoff, with $N$ agents holding two strategies over $P$ histories. We…
In the present work, we study deterministic mean field games (MFGs) with finite time horizon in which the dynamics of a generic agent is controlled by the acceleration. They are described by a system of PDEs coupling a continuity equation…
We study the parallel Minority Game, where a group of agents, each having two choices, try to independently decide on a strategy such that they stay on minority between their own two choices. However, there are multiple such groups of…
In this paper, a non-autonomous stochastic logistic system is considered. An interesting result on the effect of stochastically perturbation for the dynamic behavior are obtained. That is, under certain conditions the stochastic system have…
Evolutionary game theory has impacted many fields of research by providing a mathematical framework for studying the evolution and maintenance of social and moral behaviors. This success is owed in large part to the demonstration that the…
We study 2-player turn-based perfect-information stochastic games with countably infinite state space. The players aim at maximizing/minimizing the probability of a given event (i.e., measurable set of infinite plays), such as reachability,…
We investigate different versions of the minority game, a toy model for agents buying and selling a commodity. The Hamming distance between the strategies used by agents to take decisions is introduced as an analytical tool to determine…
We propose a new evolutionary dynamics for population games with a discrete strategy set, inspired by the theory of optimal transport and Mean field games. The dynamics can be described as a Fokker-Planck equation on a discrete strategy…
In this paper we introduce a new approach for the study of the complex behavior of Minority Game using the tools of algorithmic complexity, physical entropy and information theory. We show that physical complexity and mutual information…
Mirror play (MP) is a well-accepted primal-dual multi-agent learning algorithm where all agents simultaneously implement mirror descent in a distributed fashion. The advantage of MP over vanilla gradient play lies in its usage of mirror…