Related papers: Generating functional analysis of batch minority g…
We consider two-player games with imperfect information and the synthesis of a randomized strategy for one player that ensures the objective is satisfied almost-surely (i.e., with probability 1), regardless of the strategy of the other…
We consider perfect-information reachability stochastic games for 2 players on infinite graphs. We identify a subclass of such games, and prove two interesting properties of it: first, Player Max always has optimal strategies in games from…
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…
Evolutionary game theory has been an important tool for describing economic and social behaviour for decades. Approximate mean value equations describing the time evolution of strategy concentrations can be derived from the players'…
Mean-field games (MFGs) are models of large populations of rational agents who seek to optimize an objective function that takes into account their location and the distribution of the remaining agents. Here, we consider stationary MFGs…
Strategic-form min-max game theory examines the existence, multiplicity, selection of equilibria, and the worst-case computational complexity under perfect rationality. However, in many applications, games are drawn from an ensemble, and…
We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding…
We consider qualitative strategy synthesis for the formalism called consumption Markov decision processes. This formalism can model dynamics of an agents that operates under resource constraints in a stochastic environment. The presented…
Multi-dimensional mean-payoff and energy games provide the mathematical foundation for the quantitative study of reactive systems, and play a central role in the emerging quantitative theory of verification and synthesis. In this work, we…
Two-player games on graphs provide the mathematical foundation for the study of reactive systems. In the quantitative framework, an objective assigns a value to every play, and the goal of player 1 is to minimize the value of the objective.…
We study the structure of the underlying network of connections in the Minority Game. There is not an explicit interaction among the agents, but they interact via global magnitudes of the model and mainly through their strategies. We define…
In this work the properties of minority games containing agents which try to winning all the time are studied by means of computational simulations. We have considered several ways of introducing above the rules clever players using…
We study the behavior of simple models for financial markets with widely spread frequency either in the trading activity of agents or in the occurrence of basic events. The generic picture of a phase transition between information efficient…
A population of heterogenous agents compeeting through a minority rule is investigated. Agents which frequently loose are selected for evolution by changing their strategies. The stationary composition of the population resulting for this…
This paper concerns the simultaneous effect of homogenization and of the small noise limit for a $2^{\textrm {nd}}$ order mean field games (MFG) system with local coupling and quadratic Hamiltonian. We show under some additional assumptions…
In this paper, we settle the sampling complexity of solving discounted two-player turn-based zero-sum stochastic games up to polylogarithmic factors. Given a stochastic game with discount factor $\gamma\in(0,1)$ we provide an algorithm that…
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…
We model evolution according to an asymmetric game as occurring in multiple finite populations, one for each role in the game, and study the effect of subjecting individuals to stochastic strategy mutations. We show that, when these…
Mean-field games (MFGs) are a modeling framework for systems with a large number of interacting agents. They have applications in economics, finance, and game theory. Normalizing flows (NFs) are a family of deep generative models that…
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…