Related papers: Astumian's Paradox revisited
In a series of papers, G. Harmer and D. Abbott study the behavior of random walks associated with games introduced in 1997 by J. M. R. Parrondo. These games illustrate an apparent paradox that random and deterministic mixtures of losing…
Inspired by asynchronous cooperative Parrondo's games we introduce two new types of games in which all players simultaneously play game A or game B or a combination of these two games. These two types of games differ in the way a…
This paper studies sequential quantum games under the assumption that the moves of the players are drawn from groups and not just plain sets. The extra group structure makes possible to easily derive some very general results characterizing…
We are interested in the convergence of the value of n-stage games as n goes to infinity and the existence of the uniform value in stochastic games with a general set of states and finite sets of actions where the transition is commutative.…
In a zero-sum stochastic game with signals, at each stage, two adversary players take decisions and receive a stage payoff determined by these decisions and a variable called state. The state follows a Markov chain, that is controlled by…
The original Parrondo game, denoted as AB3, contains two independent games: A and B. The winning or losing of A and B game is defined by the change of one unit of capital. Game A is a losing game if played continuously, with winning…
Consider a system of \(n\) players in which each initially starts on a different team. At each time step, we select an individual winner and an individual loser randomly and the loser joins the winner's team. The resulting Markov chain and…
Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…
A stochastic modification of Conway's cellular automaton "Life" is introduced here. Any cell could be perturbed spontaneously to the opposite (dead or alive) state at any iteration with a very low probability. This probability is assumed to…
The "War of Attrition" is a classical game theoretic model that was first introduced to mathematically describe certain non-violent animal behavior. The original setup considers two participating players in a one-shot game competing for a…
We study a combinatorial game derived from a problem in the German National Mathematics Competition. In this game, two players take turns removing numbers from a finite set of natural numbers, aiming to satisfy a certain divisibility…
We study a general formulation of the classical two-player Dynkin game in a discrete time Markovian setting. We identify an appropriate class of mixed strategies -- \textit{Markovian randomized stopping times} -- in which players stop at…
We present some new analytical expressions for the so-called Parrondo effect, where simple coin-flipping games with negative expected value are combined into a winning game. Parrondo games are state-dependent. By identifying the game state…
In this article we will propose a completely new point of view for solving one of the most important paradoxes concerning game theory. The solution develop shifts the focus from the result to the strategy s ability to operate in a cognitive…
Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck…
In repeated interactions between individuals, we do not expect that exactly the same situation will occur from one time to another. Contrary to what is common in models of repeated games in the literature, most real situations may differ a…
Using methods from the statistical mechanics of disordered systems we analyze the properties of bimatrix games with random payoffs in the limit where the number of pure strategies of each player tends to infinity. We analytically calculate…
Splitting probabilities quantify the likelihood of a given outcome out of competitive events. This key observable of random walk theory, historically introduced as the gambler's ruin problem, is well understood for memoryless (Markovian)…
Parrondo's paradox occurs in sequences of games in which a winning expectation may be obtained by playing the games in a random order, even though each game in the sequence may be lost when played individually. Several variations of…
In this paper, we consider two-state mean-field games and its dual formulation. We then discuss numerical methods for these problems. Finally, we present various numerical experiments, exhibiting different behaviours, including shock…