Related papers: On the strategy frequency problem in batch Minorit…
The majority game, modelling a system of heterogeneous agents trying to behave in a similar way, is introduced and studied using methods of statistical mechanics. The stationary states of the game are given by the (local) minima of a…
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…
Generalization of the minority game to more than one market is considered. At each time step every agent chooses one of its strategies and acts on the market related to this strategy. If the payoff function allows for strong fluctuation of…
We study discrete-time, finite-state mean-field games (MFGs) under model uncertainty, where agents face ambiguity about the state transition probabilities. Each agent maximizes its expected payoff against the worst-case transitions within…
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…
The Minority Game framework was recently generalized to account for the possibility that agents adapt not only through strategy selection but also by diversifying their response according to the kind of dynamical regime, or the risk, they…
In this paper we study the continuum time dynamics of a stock in a market where agents behavior is modeled by a Minority Game and a Grand Canonical Minority Game. The dynamics derived is a generalized geometric Brownian motion; from the…
The Minority Game is a simple yet highly non-trivial agent-based model for a complex adaptive system. Despite its importance, a quantitative explanation of the game's fluctuations which applies over the entire parameter range of interest…
We present a comprehensive study of utility function of the minority game in its efficient regime. We develop an effective description of state of the game. For the payoff function $g(x)=\sgn (x)$ we explicitly represent the game as the…
The Full Strategy Minority Game (FSMG) is an instance of the Minority Game (MG) which includes a single copy of every potential agent. In this work, we explicitly solve the FSMG thanks to certain symmetries of this game. Furthermore, by…
We develop a game theoretical model of $N$ heterogeneous interacting agents called the intelligent minority game. The ``intelligent'' agents play the basic minority game and depending on their performances, generate new strategies using the…
We present a formal treatment of the Crowd-Anticrowd theory of Minority Games played by a population of competing agents. This theory is built around a description of the crowding which arises within the game's strategy space. Earlier works…
In this paper we show that the continuum time version of the Minority Game satisfies the criteria for the application of a theorem on the existence of an invariant measure. We consider the special case of a game with "sufficiently"…
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…
Minority games where groups of agents remember, react or incorporate information with different timescales are investigated. We study how their respective gains depend on their timescales for standard models and games with no public…
A finite memory is introduced in the score dynamics of Minority Games. As expected, this removes the dependence of the stationary state on the initial conditions. However, it also causes an unexpected increase of fluctuations in…
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…
We study a static game played by a finite number of agents, in which agents are assigned independent and identically distributed random types and each agent minimizes its objective function by choosing from a set of admissible actions that…
We show analytically how the fluctuations (i.e. standard deviation) in the Minority Game (MG) can be made to decrease below the random coin-toss limit if the agents use more general behavioral strategies. This suppression of the standard…
A stochastic evolutionary dynamics of two strategies given by 2 x 2 matrix games is studied in finite populations. We focus on stochastic properties of fixation: how a strategy represented by a single individual wins over the entire…