Related papers: The Delta Game
By following the study in [24], we consider an inverse boundary problem for the mean field game system where a probability density constraint is enforced on the game agents. That is, we consider the case that reflective boundary conditions…
We propose a general class of symmetric games called position-optimization games. Given a probability distribution $Q$ over a set of targets $\mathcal{Y}$, the $n$ players each choose a position in a space $\mathcal{X}$. A player's utility…
We show a method of uniform approximation of the value functions of uniformly nondegenerate stochastic differential games in smooth domains up to a constant over $K$ with the ones having second-order derivatives bounded by a constant times…
We present a quantum approach to a signaling game; a special kind of extensive games of incomplete information. Our model is based on quantum schemes for games in strategic form where players perform unitary operators on their own qubits of…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
We describe a communication game, and a conjecture about this game, whose proof would imply the well-known Sensitivity Conjecture asserting a polynomial relation between sensitivity and block sensitivity for Boolean functions. The author…
We introduce a zero-sum game problem of mean-field type as an extension of the classical zero-sum Dynkin game problem to the case where the payoff processes might depend on the value of the game and its probability law. We establish…
We propose the study of quantum games from the point of view of quantum information theory and statistical mechanics. Every game can be described by a density operator, the von Neumann entropy and the quantum replicator dynamics. There…
Congestion games are attractive because they can model many concrete situations where some competing entities interact through the use of some shared resources, and also because they always admit pure Nash equilibria which correspond to the…
Effects of quantum and classical correlations on game theory are studied to clarify the new aspects brought into game theory by the quantum mechanical toolbox. In this study, we compare quantum correlation represented by a maximally…
Stochastic games are an important class of problems that generalize Markov decision processes to game theoretic scenarios. We consider finite state two-player zero-sum stochastic games over an infinite time horizon with discounted rewards.…
We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…
Population games can be regarded as a tool to study the strategic interaction of a population of players. Although several attention has been given to such field, most of the available works have focused only on the unconstrained case. That…
We present a consistent formulation of quantum game theory that accommodates all possible strategies in Hilbert space. The physical content of the quantum strategy is revealed as a family of classical games representing altruistic game play…
The paper is concerned with two-person games with saddle point. We investigate the limits of value functions for long-time-average payoff, discounted average payoff, and the payoff that follows a probability density. Most of our assumptions…
Let $f$ be a continuous real function defined in a subset of the real line. The standard definition of continuity at a point $x$ allow us to correlate any given epsilon with a (possibly depending of $x$) delta value. This pairing is known…
This work considers stochastic differential games with a large number of players, whose costs and dynamics interact through the empirical distribution of both their states and their controls. We develop a new framework to prove convergence…
Quantum games with incomplete information can be studied within a Bayesian framework. We consider a version of prisoner's dilemma (PD) in this framework with three players and characterize the Nash equilibria. A variation of the standard PD…
This paper investigates the powers and limitations of quantum entanglement in the context of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement…
In this paper we study mean field games with possibly multiple mean field equilibria. Instead of focusing on the individual equilibria, we propose to study the set of values over all possible equilibria, which we call the set value of the…