A mathematical analysis of the card game of betweenies through Kelly's criterion.
A mathematical framework for learning and adaption: (generalized) random systems with complete connections.
The aim of this paper is to show that the theory of (generalized) random systems with complete connection may serve as a mathematical framework for learning and adaption. Chapter 1 is of an introductory nature and gives a general description of the problems with which one is faced. In Chapter 2 the mathematical model and some results about it are explained. Chapter 3 deals with special learning and adaption models.
A winner's mean earnings in lottery and inverse moments of the binomial distribution.
Approximations of dynamic Nash games with general state and action spaces and ergodic costs for the players
The purpose of this paper is to prove existence of an ε -equilib- rium point in a dynamic Nash game with Borel state space and long-run time average cost criteria for the players. The idea of the proof is first to convert the initial game with ergodic costs to an ``equivalent" game endowed with discounted costs for some appropriately chosen value of the discount factor, and then to approximate the discounted Nash game obtained in the first step with a countable state space game for which existence...
BSDEs with two reflecting barriers driven by a Brownian and a Poisson noise and related Dynkin game.
Convergence of values in optimal stopping and convergence of optimal stopping times.
Cycles in war.
Discrete bidding games.
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point x ∈ Ω, Players I and II play an ε-step tug-of-war game with probability α, and with probability β (α + β = 1), a random point in the ball of radius ε centered at x is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that...
Dynamic Programming Principle for tug-of-war games with noise
We consider a two-player zero-sum-game in a bounded open domain Ω described as follows: at a point x ∈ Ω, Players I and II play an ε-step tug-of-war game with probability α, and with probability β (α + β = 1), a random point in the ball of radius ε centered at x is chosen. Once the game position reaches the boundary, Player II pays Player I the amount given by a fixed payoff function F. We give a detailed proof of the fact that the value functions of this game satisfy the Dynamic Programming Principle...
Exact solution of the Bellman equation for a -discounted reward in a two-armed bandit with switching arms.
Information and entropy. A double game with probabilities. (Information et entropie. Un double jeu avec les probabilités.)
Je lepšie hrať ruletu alebo blackjack?
Lacan and probability.
Limit theorems for Parrondo's paradox.
Loi du “tout ou rien” dans un jeu de pile ou face
Negotiations under uncertainty.
Non-compact random generalized games and random quasi-variational inequalities.
Nonlinear elliptic systems in stochastic game theory.
Observation on the problem of the gambler's ruin. (Poznámka k problemu ruinováni hrácu.)