相关论文: Parrondo's paradox via redistribution of wealth
Mafia can be described as an experiment in human psychology and mass hysteria, or as a game between informed minority and uninformed majority. Focus on a very restricted setting, Mossel et al. [to appear in Ann. Appl. Probab. Volume 18,…
A binary game is introduced and analysed. N players have to choose one of the two sides independently and those on the minority side win. Players uses a finite set of ad hoc strategies to make their decision, based on the past record. The…
Consider a coin tossing experiment which consists of tossing one of two coins at a time, according to a renewal process. The first coin is fair and the second has probability $1/2 + \theta$, $\theta \in [-1/2,1/2]$, $\theta$ unknown but…
Chances of a gambler are always lower than chances of a casino in the case of an ideal, mathematically perfect roulette, if the capital of the gambler is limited and the minimum and maximum allowed bets are limited by the casino. However, 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…
We discuss some aspects of Astumian suggestions that combination of biased games (Parrondo's paradox) can explain performance of molecular motors. Unfortunately the model is flawed by explicit asymmetry overlooked by the author. In…
The General Lotto game is a popular variant of the famous Colonel Blotto game, in which two opposing players allocate limited resources over many battlefields. In this paper, we consider incomplete and asymmetric information formulations…
In the context of multiplayer games, the parallel repetition problem can be phrased as follows: given a game $G$ with optimal winning probability $1-\alpha$ and its repeated version $G^n$ (in which $n$ games are played together, in…
Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…
We prove a couple of related theorems including Legendre's and Andrica's conjecture. Key to the proofs is an algorithm that delivers the exact upper bound on the greatest gap that can occur in a combinatorial game with the set of P primes…
In the compulsive gambler process there is a finite set of agents who meet pairwise at random times ($i$ and $j$ meet at times of a rate-$\nu_{ij}$ Poisson process) and, upon meeting, play an instantaneous fair game in which one wins the…
This paper analyzes a simple game with $n$ players. We fix a mean, $\mu$, in the interval $[0, 1]$ and let each player choose any random variable distributed on that interval with the given mean. The winner of the zero-sum game is the…
We study the behavior of the capital process of a continuous Bayesian mixture of fixed proportion betting strategies in the one-sided unbounded forecasting game in game-theoretic probability. We establish the relation between the rate of…
In this paper we review some of the main results obtained in the field of truels. A "truel" is a generalization of a duel involving three players. Depending on the rules used for chosing the players, we may distinguish between the random,…
We propose and study a new model for competitions, specifically sports multi-player leagues where the initial strengths of the teams are independent i.i.d. random variables that evolve during different days of the league according to…
Two losing gambling games, when alternated in a periodic or random fashion, can produce a winning game. This paradox has been inspired by certain physical systems capable of rectifying fluctuations: the so-called Brownian ratchets. In this…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner or payoff of the game. Such games are central in formal verification since they model the interaction between a…
Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose…
In the last few decades, numerous experiments have shown that humans do not always behave so as to maximize their material payoff. Cooperative behavior when non-cooperation is a dominant strategy (with respect to the material payoffs) is…
We consider a collective version of Parrondo's games with probabilities parametrized by rho in (0,1) in which a fraction phi in (0,1] of an infinite number of players collectively choose and individually play at each turn the game that…