Related papers: Minority games, evolving capitals and replicator d…
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…
The Parallel Minority Game (PMG) refers to a set of Minority Games (MG), played in parallel, where each agent only has two choices to pick from, but each choice can host agents of many kind i.e., their other alternative can be from any…
Both the phenomenology and the theory of minority games (MG) with more than two strategies per agent are different from those of the conventional and extensively studied case S=2. MGs with $S>2$ exhibit nontrivial statistics of the…
By considering diffusion on De Bruijn graphs, we study in details the dynamics of the histories in the Minority Game, a model of competition between adaptative agents. Such graphs describe the structure of temporal evolution of $M$ bits…
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…
The minority model was introduced to study the competition between agents with limited information. It has the remarkable feature that, as the amount of information available increases, the collective gain made by the agents is reduced.…
We study the role of strategy correlations and timing of adaptation for the dynamics of Minority Games, both simulationally and analytically. Using the exact generating functional approach a la De Dominicis we compute the phase diagram and…
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 study effects of strategy-dependent time delays on equilibria of evolving populations. It is well known that time delays may cause oscillations in dynamical systems. Here we report a novel behavior. We show that microscopic models of…
We formulate a theory of agent-based models in which agents compete to be in a winning group. The agents may be part of a network or not, and the winning group may be a minority group or not. The novel feature of the present formalism is…
We study the dynamics of the batch minority game, with random external information, using generating functional techniques a la De Dominicis. The relevant control parameter in this model is the ratio $\alpha=p/N$ of the number $p$ of…
Based on the adiabatic theory for the evolutionary minority game (EMG) that we proposed earlier[1], we perform a detail analysis of the EMG limited to three groups of agents. We derive a formula for the critical point of the transition from…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
Adaptive populations such as those in financial markets and distributed control can be modeled by the Minority Game. We consider how their dynamics depends on the agents' initial preferences of strategies, when the agents use linear or…
Here, we examine a mean-field game (MFG) that models the economic growth of a population of non-cooperative rational agents. In this MFG, agents are described by two state variables - the capital and consumer goods they own. Each agent…
In this paper, we consider a mean field game model inspired by crowd motion in which several interacting populations evolving in $\mathbb R^d$ aim at reaching given target sets in minimal time. The movement of each agent is described by a…
Starting from the Minority Game and building more and more sophisticated models of adaptive agents, we show that minority mechanisms underly any model where agents learn collectively a resource level that can be either obvious and constant…
We introduce and study a mean-field model for a system of spatially distributed players interacting through an evolutionary game driven by a replicator dynamics. Strategies evolve by a replicator dynamics influenced by the position and the…
We present a spherical version of the grand-canonical minority game (GCMG), and solve its dynamics in the stationary state. The model displays several types of transitions between multiple ergodic phases and one non-ergodic phase. We derive…
Evolutionary game theory combines game theory and dynamical systems and is customarily adopted to describe evolutionary dynamics in multi-agent systems. In particular, it has been proven to be a successful tool to describe multi-agent…