Related papers: Dynamical Solution of the On-Line Minority Game
The Minority Game is a generic model of competing adaptive agents, which is often believed to be a model of financial markets. We discuss to which extend this is a reasonable statement, and present minimal modifications that make this model…
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 study minority games in efficient regime. By incorporating the utility function and aggregating agents with similar strategies we develop an effective mesoscale notion of state of the game. Using this approach, the game can be…
We consider a Mean Field Games model where the dynamics of the agents is subdiffusive. According to the optimal control interpretation of the problem, we get a system involving fractional time-derivatives for the Hamilton-Jacobi-Bellman and…
In this work we propose a kinetic formulation for evolutionary game theory for zero sum games when the agents use mixed strategies. We start with a simple adaptive rule, where after an encounter each agent increases the probability of play…
The goal of this paper is to study weak solutions of the Fokker-Planck equation. We first discuss existence and uniqueness of weak solutions in an irregular context, providing a unified treatment of the available literature along with some…
Behavior in the context of game theory is described as a natural process that follows the 2nd law of thermodynamics. The rate of entropy increase as the payoff function is derived from statistical physics of open systems. The thermodynamic…
Discrete-time replicator map is a prototype of evolutionary selection game dynamical models that have been very successful across disciplines in rendering insights into the attainment of the equilibrium outcomes, like the Nash equilibrium…
We study large fluctuations in evolutionary games belonging to the coordination and anti-coordination classes. The dynamics of these games, modeling cooperation dilemmas, is characterized by a coexistence fixed point separating two…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
Adaptive dynamics describes a deterministic approximation of the evolution of scalar- and function-valued traits. Applying it to the team game developed by Menden-Deuer and Rowlett [Menden-Deuer & Rowlett 2019], we constructed an…
We consider a constrained hierarchical opinion dynamics in the case of leaders' competition and with complete information among leaders. Each leaders' group tries to drive the followers' opinion towards a desired state accordingly to a…
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…
We analyze grand-canonical minority games with infinite and finite score memory and different updating timescales (from `on-line' games to `batch' games) in detail with various complementary methods, both analytical and numerical. We focus…
It is well-known that in finite strategic games true common belief (or common knowledge) of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies. We…
In strategic scenarios where decision-makers operate at different hierarchical levels, traditional optimization methods are often inadequate for handling uncertainties from incomplete information or unpredictable external factors. To fill…
We study the regularity and well-posedness of the local, first-order forward-backward mean field games system, assuming a polynomially growing cost function and a Hamiltonian of quadratic growth. We consider systems and terminal data that…
Economic ensembles can be modeled as networks of interacting agents whose be-haviors are described in terms of game theory. The evolutionary paradigm has been applied to two-person games to discover strategies in this context.…
We propose an approach to directly estimate the moments or marginals for a high-dimensional equilibrium distribution in statistical mechanics, via solving the high-dimensional Fokker-Planck equation in terms of low-order cluster moments or…
We introduce new kinetic equations modeling opinion dynamics inside a population of individuals, whose propensity to interact with each other is described by their level of social activity. We show that opinion polarization can arise among…