Related papers: Deterministic Dynamics in the Minority Game

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…

We investigate a stochastic differential game in which a major player has a private information (the knowledge of a random variable), which she discloses through her control to a population of small players playing in a Nash Mean Field Game…

Spatial evolutionary games model individuals who are distributed in a spatial domain and update their strategies upon playing a normal form game with their neighbors. We derive integro-differential equations as deterministic approximations…

The effects of quenched disorder on the overdamped motion of a driven particle on a periodic, asymmetric potential is studied. While for the unperturbed potential the transport is due to a regular drift, the quenched disorder induces a…

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…

We study the dynamics of the `batch' minority game with market-impact correction using generating functional techniques to carry out the quenched disorder average. We find that the assumption of weak long-term memory, which one usually…

Agent-based models of the binary naming game are generalized here to represent a family of models parameterized by the introduction of two continuous parameters. These parameters define varying listener-speaker interactions on the…

We consider a non-atomic congestion game where each decision maker performs selfish optimization over states of a common MDP. The decision makers optimize for their own expected costs, and influence each other through congestion effects on…

We study a stochastic game where one player tries to find a strategy such that the state process reaches a target of controlled-loss-type, no matter which action is chosen by the other player. We provide, in a general setup, a relaxed…

We study the role of imitation within the Minority Game model of market. The players can exchange information locally, which leads to formation of groups which act as if they were single players. Coherent spatial areas of rich and poor…

We study the problem of resilient strategies in the presence of uncertainty. Resilient strategies enable an agent to make decisions that are robust against disturbances. In particular, we are interested in those disturbances that are able…

Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and…

This paper revisits well-studied dynamic decisions of weakly coupled large-population (LP) systems. Specifically, three types of LP decision problems: mean-field game (MG), mean-field team (MT), and mean-field-type control (MC), are…

In this paper we study the minority game in the presence of evolution. In particular, we examine the behavior in games in which the dimension of the strategy space, m, is the same for all agents and fixed for all time. We find that for all…

We demonstrate that minority mechanisms arise in the dynamics of markets because of effects of price impact; accordingly the relative importance of minority and delayed majority mechanisms depends on the frequency of trading. We then use…

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…

We derive a class of macroscopic differential equations that describe collective adaptation, starting from a discrete-time stochastic microscopic model. The behavior of each agent is a dynamic balance between adaptation that locally…

We consider deterministic mean field games where the dynamics of a typical agent is non-linear with respect to the state variable and affine with respect to the control variable. Particular instances of the problem considered here are mean…

It is generally believed that in a situation where individual and collective interests are in conflict, the availability of optional participation is a key mechanism to maintain cooperation. Surprisingly, this effect is sensitive to the use…

In this paper, we present a simple stock market model (the market game) which incorporates, as ab initio dynamics delayed majority dynamics, according to which agents (with heterogeneous strategies and price expectations) are rewarded if…